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Philip Smith,
Published: 12 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4abf

Abstract:
Biopolymers, like chromatin, are often confined in small volumes. Confinement has a great effect on polymer conformations, including polymer entanglement. Polymer chains and other filamentous structures can be represented by polygonal curves in 3-space. In this manuscript, we examine the topological complexity of polygonal chains in 3-space and in confinement as a function of their length. We model polygonal chains by equilateral random walks in 3-space and by uniform random walks in confinement. For the topological characterization, we use the second Vassiliev measure. This is an integer topological invariant for polygons and a continuous functions over the real numbers, as a function of the chain coordinates for open polygonal chains. For uniform random walks in confined space, we prove that the average value of the Vassiliev measure in the space of configurations increases as $O(n^2)$ with the length of the walks or polygons. We verify this result numerically and our numerical results also show that the mean value of the second Vassiliev measure of equilateral random walks in 3-space increases as $O(n)$. These results reveal the rate at which knotting of open curves and not simply entanglement are affected by confinement.
, Juan Miguel Nieto Garcia
Published: 12 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4abd

Abstract:
We find classical closed string solutions to the non-relativistic AdS$_5\times$S$^5$ string theory which are the analogue of the BMN and GKP solutions for the relativistic theory. We show that non-relativistic AdS$_5\times$S$^5$ string theory admits a $\mathbb{Z}_2$ orbifold symmetry which allows us to impose twisted boundary conditions. Among the solutions in the twisted sector, we find the one around which the semiclassical expansion in \href{https://arxiv.org/abs/2102.00008}{arXiv:2102.00008} takes place.
Published: 12 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4abe

Abstract:
The presence and signiﬁcance of active topological defects is increasingly realised in diverse biological and biomimetic systems. We introduce a continuum model of polar active matter, based on conservation laws and symmetry arguments, that recapitulates both polar and apolar (nematic) features of topological defects in active turbulence. Using numerical simulations of the continuum model, we demonstrate the emergence of both half- and full-integer topological defects in polar active matter. Interestingly, we ﬁnd that crossover from active turbulence with half- to full-integer defects can emerge with the coexistence region characterized by both defect types. These results put forward a minimal, generic framework for studying topological defect patterns in active matter which is capable of explaining the emergence of half-integer defects in polar systems such as bacteria and cell monolayers, as well as predicting the emergence of coexisting defect states in active matter.
Published: 12 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4ac0

Abstract:
We investigate the problem of minimizing the entropy production for a physical process that can be described in terms of a Markov jump dynamics. We show that, without any further constraints, a given time-evolution may be realized at arbitrarily small entropy production, yet at the expense of diverging activity. For a fixed activity, we find that the dynamics that minimizes the entropy production is given in terms of conservative forces. The value of the minimum entropy production is expressed in terms of the graph-distance based Wasserstein distance between the initial and final configuration. This yields a new kind of speed limit relating dissipation, the average number of transitions and the Wasserstein distance. It also allows us to formulate the optimal transport problem on a graph in term of a continuous-time interpolating dynamics, in complete analogy to the continuous space setting. We demonstrate our findings for simple state networks, a time-dependent pump and for spin flips in the Ising model.
Published: 11 January 2022
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac4394

Abstract:
We review recent progress relating to the extreme value statistics of the characteristic polynomials of random matrices associated with the classical compact groups, and of the Riemann zeta-function and other L-functions, in the context of the general theory of logarithmically-correlated Gaussian fields. In particular, we focus on developments related to the conjectures of Fyodorov and Keating concerning the extreme value statistics, moments of moments, connections to Gaussian multiplicative chaos, and explicit formulae derived from the theory of symmetric functions.
, Daniel J VandenHeuvel, Joshua M Wilson,
Published: 11 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4a1d

Abstract:
Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass transfer. While many exact results for MET are known for diffusion in simple geometries involving homogeneous materials, calculating MET for diffusion in realistic geometries involving heterogeneous materials is typically limited to repeated stochastic simulations or numerical solutions of the associated boundary value problem (BVP). In this work we derive exact solutions for the MET in irregular annular domains, including some applications where diffusion occurs in heterogenous media. These solutions are obtained by taking the exact results for MET in an annulus, and then constructing various perturbation solutions to account for the irregular geometries involved. These solutions, with a range of boundary conditions, are implemented symbolically and compare very well with averaged data from repeated stochastic simulations and with numerical solutions of the associated BVP. Software to implement the exact solutions is available on \href{https://github.com/ProfMJSimpson/Exit_time}{GitHub}.
Published: 11 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4a1e

Abstract:
In this pedagogical review we introduce systematic approaches to deforming integrable 2-dimensional sigma models. We use the integrable principal chiral model and the conformal Wess-Zumino-Witten model as our starting points and explore their Yang-Baxter and current-current deformations. There is an intricate web of relations between these models based on underlying algebraic structures and worldsheet dualities, which is highlighted throughout. We finish with a discussion of the generalisation to other symmetric integrable models, including some original results related to ZT cosets and their deformations, and the application to string theory. This review is based on notes written for lectures delivered at the school "Integrability, Dualities and Deformations," which ran from 23 to 27 August 2021 in Santiago de Compostela and virtually.
Published: 11 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4a1c

Abstract:
Stochastic resetting with home returns is widely found in various manifestations in life and nature. Using the solution to the home return problem in terms of the solution to the corresponding problem without home returns [Pal et al. Phys. Rev. Research 2, 043174 (2020)], we develop a theoretical framework for search with home returns in the case of subdiffusion. This makes a realistic description of restart by accounting for random walks with random stops. The model considers stochastic processes, arising from Brownian motion subordinated by an inverse infinitely divisible process (subordinator).
A V Zolotaryuk,
Published: 11 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4a1f

Abstract:
A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.
Published: 7 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac491a

Abstract:
We study the Stochastic Thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to an identical copy of itself, and resetting, by which some properties of the daughter cells (such as their size or age) are reset to new values following division. We derive the ﬁrst and second laws of Stochastic Thermodynamics for this process, and identify separate contributions due to branching and resetting. We apply our framework to well-known models of cell size control, such as the sizer, the timer, and the adder. We show that the entropy production of resetting is negative and that of branching is positive for these models in the regime of exponential growth of the colony. This property suggests an analogy between our model for cell growth and division and heat engines, and the introduction of a thermodynamic eﬃciency, which quantiﬁes the conversion of one form of entropy production to another.
Hans Havlicek,
Published: 7 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4919

Abstract:
Criteria for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given. This, in particular, has consequences for the task of completing'' one or more bases or contexts of a (hyper)graph: find a complete faithful orthogonal representation (aka coordinatization) of a hypergraph when only a coordinatization of the intertwining observables is known. In general indecomposability and thus physical entanglement and the encoding of relational properties by quantum states prevails'' and occurs more often than separability associated with well defined individual, separable states.
Andrew Liashyk, Stanislav Pakuliak
Published: 7 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac491b

Abstract:
The zero modes method is applied in order to get action of the monodromy matrix entries onto off-shell Bethe vectors in quantum integrable models associated with $U_q(\mathfrak{gl}_N)$-invariant $\RR$-matrices. The action formulas allowto get recurrence relations for off-shell Bethe vectors and for highest coefficients of the Bethe vectors scalar product.
, Viktor Domazetoski, Ljupco Kocarev, , Alexei Chechkin
Published: 7 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac491c

Abstract:
We study a heterogeneous diffusion process with position-dependent diffusion coefficient and Poissonian stochastic resetting. We ﬁnd exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. We also analyze the transition to the non-equilibrium steady state by ﬁnding the large deviation function. We found that similarly to the case of the normal diffusion process where the diffusion length grows like $t^{1⁄2}$ while the length scale ξ(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the heterogeneous diffusion process with diffusion length increasing like $t^{p⁄2}$ the length scale ξ(t) grows like $t^{p}$. The obtained results are verified by numerical solutions of the corresponding Langevin equation.
Mehrdokht Sasanpour, Chenor Ajilian,
Published: 6 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac48ef

Abstract:
We compute the Casimir thermodynamic quantities for a massive fermion field between two parallel plates with the MIT boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method represented by the zeta function method, and the zero temperature subtraction method. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We then do a comparative study of the three different general approaches and their results, and show that they are in principle not equivalent to each other and they yield in general different results. In particular, we show that the Casimir thermodynamic quantities calculated only by the first approach have all three properties of going to zero as the temperature, the mass of the field, or the distance between the plates increases.
François David, Thordur Jonsson
Published: 6 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4897

Abstract:
We study continuous time quantum random walk on a comb with inﬁnite teeth and show that the return probability to the starting point decays with time t as t−1. We analyse the diﬀusion along the spine and into the teeth and show that the walk can escape into the teeth with a ﬁnite probability and goes to inﬁnity along the spine with a ﬁnite probability. The walk along the spine and into the teeth behaves qualitatively as a quantum random walk on a line. This behaviour is quite diﬀerent from that of classical random walk on the comb.
Published: 6 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac48ee

Abstract:
Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each particle only responds to the ﬁelds of the other charged particles. The corresponding stress-energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes. Hence there is no need for any radiation reaction.
, Federico Carollo
Published: 6 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac48ec

Abstract:
We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse ﬁeld Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities —such as the von Neumann entropy, the Rényi entropies, and the associated mutual information— admit a simple description within the so-called quasiparticle picture. Speciﬁcally, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.
Published: 6 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac48ed

Abstract:
These lecture notes concern the semi-holomorphic 4d Chern-Simons theory and its applications to classical integrable field theories in 2d and in particular integrable sigma-models. After introducing the main properties of the Chern-Simons theory in 3d, we will define its 4d analogue and explain how it is naturally related to the Lax formalism of integrable 2d theories. Moreover, we will explain how varying the boundary conditions imposed on this 4d theory allows to recover various occurences of integrable sigma-models through this construction, in particular illustrating this on two simple examples: the Principal Chiral Model and its Yang-Baxter deformation. These notes were written for the lectures delivered at the school “Integrability, Dualities and Deformations”, that ran from 23 to 27 August 2021 in Santiago de Compostela and virtually.
Published: 6 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4898

Abstract:
We study the double scaling limit of the O(N)3-invariant tensor model, initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This model has an interacting part containing two types of quartic invariants, the tetrahedric and the pillow one. For the 2-point function, we rewrite the sum over Feynman graphs at each order in the 1/N expansion as a finite sum, where the summand is a function of the generating series of melons and chains (a.k.a. ladders). The graphs which are the most singular in the continuum limit are characterized at each order in the 1/N expansion. This leads to a double scaling limit which picks up contributions from all orders in the 1/N expansion. In contrast with matrix models, but similarly to previous double scaling limits in tensor models, this double scaling limit is summable. The tools used in order to prove our results are combinatorial, namely a thorough diagrammatic analysis of the Feynman graphs, as well as an analytic analysis of the singularities of the relevant generating series.
Published: 4 January 2022
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac47b2

Abstract:
We construct a conformal field theory dual to string theory on AdS3 with pure NS-NS ﬂux. It is given by a symmetric orbifold of a linear dilaton theory deformed by a marginal operator from the twist-2 sector. We compute two- and three-point functions on the CFT side to 4th order in conformal perturbation theory at large N. They agree with the string computation at genus 0, thus providing ample evidence for a duality. We also show that the full spectra of both short and long strings on the CFT and the string side match. The duality should be understood as perturbative in 1/N.
Zhexu Li, Julian Gonzalez-Ayala, Han-Xin Yang, , A Calvo Hernandez
Published: 4 January 2022
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac47b0

Abstract:
In the present paper, a general non-combined model of three-terminal refrigerator is established based on the low-dissipation assumption. The relation between the optimized cooling power and the corresponding coefficient of performance (COP) is analytically derived, according to which the COP at maximum cooling power (CMP) can be further determined. At two dissipation asymmetry limits, upper and lower bounds of CMP are obtained and found to be in good agreement with experimental and simulated results. Additionally, comparison of the obtained bounds with previous combined model is presented. In particular it is found that the upper bounds are the same, whereas the lower bounds are quite different. This feature indicates that the claimed universal equivalence for the combined and non-combined models under endoreversible assumption is invalid within the frame of low-dissipation assumption. Then, the equivalence between various finite-time thermodynamic models needs to be reevaluated regarding multi-terminal systems. Moreover, the correlation between the combined and non-combined models is further revealed by the derivation of the equivalent condition according to which the identical upper bounds and distinct lower bounds are theoretically shown. Finally, the proposed non-combined model is proved to be the appropriate model for describing various types of thermally driven refrigerator. This work may provide some instructive information for the further establishments and performance analyses of multi-terminal low-dissipation models.
Hsiu-Chung Yeh, Dimitri M Gangardt, A Kamenev
Published: 4 January 2022
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac47b1

Abstract:
We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ργ, where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain inﬁnite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ≥ 1. Our ﬁndings agree with (and signiﬁcantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.
, Richard J Szabo
Published: 28 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac411c

Abstract:
We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by a P-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by an L-algebra which is not a P-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define a P-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based on A-algebras.
, , A Larkin
Published: 23 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac40e3

Abstract:
To account for the interference effects of the Coulomb and exchange interactions of electrons the new path integral representation of the density matrix has been developed in the canonical ensemble at finite temperatures. The developed representation allows to reduce the notorious ‘fermionic sign problem’ in the path integral Monte Carlo simulations of fermionic systems. The obtained results for pair distribution functions in plasma and uniform electron gas demonstrate the short-range quantum ordering of electrons associated in literature with exchange-correlation excitons. The charge estimations show the excitonic electric neutrality. Comparison of the internal energy with available ones in the literature demonstrates that the short range ordering does not give noticeable contributions to integral thermodynamic characteristics. This fine physical effect was not observed earlier in the standard path integral Monte Carlo simulations.
Da Ke, Wei Zhong, ,
Published: 23 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac463d

Abstract:
We develop an effective numerical scheme to capture hydrodynamic modes in general classical anharmonic chains. This scheme is based on the hydrodynamic theory suggested by Ernst-Hauge-van Leeuwen, which takes full role of pressure fluctuations into account. With this scheme we show that the traditional pictures given by the current nonlinear fluctuating hydrodynamic theory are valid only when the system's pressure is zero and the pressure fluctuations are weak. For nonvanishing pressure, the hydrodynamic modes can, however, respond to small and large pressure fluctuations and relax in some distinct manners. Our results shed new light on understanding thermal transport from the perspective of hydrodynamic theory.
Eric Lescano
Published: 23 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac463f

Abstract:
The present notes are based on three lectures, each ninety minutes long, prepared for the school “Integrability, Dualities and Deformations”, that ran from 23 to 27 August 2021 in Santiago de Compostela and virtually. These lectures, aimed at graduate students, require only a basic knowledge of string theory. The main goal is to introduce α′-corrections to the gravitational sector of diﬀerent formulations of closed string theory and to reformulate them using novel techniques based on double ﬁeld theory.
Ekaterina Titova,
Published: 23 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac463e

Abstract:
The boundary integral method is developed for unsteady solid/liquid interfaces propagating into undercooled binary liquids with convection. A single integrodifferential equation for the interface function is derived using the Green function technique. In the limiting cases, the obtained unsteady convective boundary integral equation (CBIE) transforms into a previously developed theory. This integral is simplified for the steady-state growth in arbitrary curvilinear coordinates when the solid/liquid interface is isothermal (isoconcentration). Finally, we evaluate the boundary integral for a binary melt with a forced flow and analyze how the melt undercooling depends on P\'eclet and Reynolds numbers.
Published: 23 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac4640

Abstract:
The open spin-1/2 XXZ spin chain with diagonal boundary magnetic ﬁelds is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of (LM) 2M M! terms, the algorithm requires L + M2+ 2M qubits.
Ian Braga,
Published: 22 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac40e4

Abstract:
Ecological interactions are central to understanding evolution. For example, Darwin noticed that the beautiful colours of the male peacock increase the chance of successful mating. However, the colours can be a threat because of the increased probability of being caught by predators. Eco-evolutionary dynamics takes into account environmental interactions to model the process of evolution. The selection of prey types in the presence of predators may be subjected to pressure on both reproduction and survival. Here, we analyze the evolutionary game dynamics of two types of prey in the presence of predators. We call this model the predator-dependent replicator dynamics. If the evolutionary time scales are different, the number of predators can be assumed constant, and the traditional replicator dynamics is recovered. However, if the time scales are the same, we end up with sixteen possible dynamics: the combinations of four reproduction’s games with four predation’s games. We analyze the dynamics and calculate conditions for the coexistence of prey and predator. The main result is that predators can change the equilibrium of the traditional replicator dynamics. For example, the presence of predators can induce polymorphism in prey if one type of prey is more attractive than the other, with the prey ending with a lower capture rate in this new equilibrium. Lastly, we provide two illustrations of the dynamics, which can be seen as rapid feedback responses in a predator–prey evolutionary arm’s race.
Published: 22 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac3a32

Abstract:
We address entanglement, coherence, and information protection in a system of four non-interacting qubits coupled with different classical environments, namely: common, bipartite, tripartite, and independent environments described by Ornstein–Uhlenbeck (ORU) noise. We show that quantum information preserved by the four qubit state is more dependent on the coherence than the entanglement using time-dependent entanglement witness, purity, and Shannon entropy. We find these two quantum phenomena directly interrelated and highly vulnerable in environments with ORU noise, resulting in the pure exponential decay of a considerable amount. The current Markovian dynamical map, as well as suppression of the fluctuating character of the environments, are observed to be entirely attributable to the Gaussian nature of the noise. The increasing number of environments are witnessed to speed up the amount of decay. Unlike other noises, the current noise parameter’s flexible range is readily exploitable, ensuring long enough preserved memory properties. The four-qubit GHZ state, besides having a large information storage potential, stands partially entangled and coherent in common environments for an indefinite duration. In addition, we derive computational values for each system-environment interaction, which will help quantum practitioners to optimize the related classical environments.
Danting Tang, Ping Li, Mingfei Ye, Yongming Li
Published: 21 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac3f87

Abstract:
Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. From the perspective of operational meaning, geometric coherence can be equal to the minimum error probability to discriminate a set of pure states (2018 J. Phys. A: Math. Theor.51 414005). By regarding coherence as a physical resource, Baumgratz et al (2014 Phys. Rev. Lett. 113 140401) presented a comprehensive framework for coherence. Recently, geometric block-coherence as an effective block-coherence measure has been proposed. In this paper, we reveal an equivalence relationship between mixed quantum state discrimination (QSD) task and geometric block-coherence, which provides an operational interpretation for geometric block-coherence and generalizes the main result in coherence resource theory. Meanwhile, we show that partial coherence is a special case of block-coherence. By linking the relationship between geometric partial coherence and QSD tasks, we show that the value range of the two measures is the same. Finally, we reveal the relationship between geometric positive operator-valued measure-based coherence and QSD task.
, Joris Van der Jeugt
Published: 21 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac451d

Abstract:
The parastatistics Fock spaces of order p corresponding to an inﬁnite number of parafermions and parabosons with relative paraboson relations are constructed. The Fock spaces are lowest weight representations of the ℤ2 × ℤ2-graded Lie superalgebra pso(∞|∞), with a basis consisting of row-stable Gelfand-Zetlin patterns.
Jiaozi Wang,
Published: 21 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac451c

Abstract:
Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments under the consideration of Schrödinger evolution of composite systems, from the perspective of the zeroth law of thermodynamics. Namely, we consider a small quantum system that is brought into contact with a large environmental system; after they have relaxed, they are separated and their temperatures are studied. Our question is under what conditions the small system may have a detectable temperature that is identical with the environmental temperature. This should be a necessary condition for the small quantum system to be thermalized and to have a well-defined temperature. By using a two-level probe quantum system that plays the role of a thermometer, we find that the zeroth law is applicable to quantum chaotic systems, but not to integrable systems.
, Pasquale Calabrese, Benjamin Doyon, Jérôme Dubail
Published: 20 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac3d68

Abstract:
We apply the theory of quantum generalized hydrodynamics (QGHD) introduced in (2020 Phys. Rev. Lett.124 140603) to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks–Girardeau (TG) or hard-core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher–Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.
A A Trofimova,
Published: 20 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac3ebb

Abstract:
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two scaled cumulants of the particle current are obtained in the large time limit t → ∞ via the Bethe ansatz and a perturbative solution of the TQ-equation. The results are presented in an integral form suitable for the asymptotic analysis in the large system size limit N → ∞. In this limit the first cumulant, the average current per site or the average velocity of the associated interface, is asymptotically finite below the critical density and grows linearly and exponentially times power law prefactor at the critical density and above, respectively. The scaled second cumulant per site, i.e. the diffusion coefficient or the scaled variance of the associated interface height, shows the O(N−1/2) decay expected for models in the Kardar–Parisi–Zhang universality class below the critical density, while it is growing as O(N3/2) and exponentially times power law prefactor at the critical point and above. Also, we identify the crossover regime and obtain the scaling functions for the uniform asymptotics unifying the three regimes. These functions are compared to the scaling functions describing crossover of the cumulants of the avalanche size, obtained as statistics of the first return area under the time space trajectory of the Vasicek random process.
Michael J W Hall,
Published: 20 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac44ee

Abstract:
The Horodecki criterion provides a necessary and sufficient condition for a two-qubit state to be able to manifest Bell nonlocality via violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It requires, however, the assumption that suitable projective measurements can be made on each qubit, and is not sufficient for scenarios in which noisy or weak measurements are either desirable or unavoidable. By characterising two-valued qubit observables in terms of strength, bias, and directional parameters, we address such scenarios by providing necessary and sufficient conditions for arbitrary qubit measurements having fixed strengths and relative angles for each observer. In particular, we find the achievable maximal values of the CHSH parameter for unbiased measurements on arbitrary states, and, alternatively, for arbitrary measurements on states with maximally-mixed marginals, and determine the optimal angles in some cases. We also show that for certain ranges of measurement strengths it is only possible to violate the CHSH inequality via biased measurements. Finally, we use the CHSH inequality to obtain a simple necessary condition for the compatibility of two qubit observables.
Published: 20 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac44ef

Abstract:
The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with uncorrelated disorder is generalized to the case with correlated disorder. For a class of correlations in disorder that suppress frustration, we show that the average energy in a subspace of the phase diagram is expressed as the expectation value of a local gauge variable of the Z2 gauge Higgs model, from which we prove that the average energy has no singularity although the subspace is likely to have a phase transition on it. Though it is diﬃcult to obtain an explicit expression of the energy in contrast to the case of uncorrelated disorder, an exact closed-form expression of a physical quantity related to the energy is derived in three dimensions using a duality relation. Identities and inequalities are proved for the speciﬁc heat and correlation functions.
, Maximiliano Sandoval
Published: 16 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac3da4

Abstract:
In this work we study the differential aspects of the noncommutative geometry for the magnetic C*-algebra which is a 2-cocycle deformation of the group C*-algebra of R 2 . This algebra is intimately related to the study of the quantum Hall effect in the continuous, and our results aim to provide a new geometric interpretation of the related Kubo’s formula. Taking inspiration from the ideas developed by Bellissard during the 80s, we build an appropriate Fredholm module for the magnetic C*-algebra based on the magnetic Dirac operator which is the square root (à la Dirac) of the quantum harmonic oscillator. Our main result consist of establishing an important piece of Bellissard’s theory, the so-called second Connes’ formula. In order to do so, we establish the equality of three cyclic 2-cocycles defined on a dense subalgebra of the magnetic C*-algebra. Two of these 2-cocycles are new in the literature and are defined by Connes’ quantized differential calculus, with the use of the Dixmier trace and the magnetic Dirac operator.
Veronique Hussin, ,
Published: 16 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac43cc

Abstract:
We extend and generalize the construction of Sturm-Liouville problems for a family of Hamiltonians constrained to fulfill a third-order shape-invariance condition and focusing on the "-2x/3" hierarchy of solutions to the fourth Painlev\'e transcendent. Such a construction has been previously addressed in the literature for some particular cases but we realize it here in the most general case. The corresponding potential in the Hamiltonian operator is a rationally extended oscillator defined in terms of the conventional Okamoto polynomials, from which we identify three different zero-modes constructed in terms of the generalized Okamoto polynomials. The third-order ladder operators of the system reveal that the complete set of eigenfunctions is decomposed as a union of three disjoint sequences of solutions, generated from a set of three-term recurrence relations. We also identify a link between the eigenfunctions of the Hamiltonian operator and a special family of exceptional Hermite polynomial.
, Emmanuel Paspalakis
Published: 16 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac43cb

Abstract:
We use optimal control theory to show that for a closed Λ-system where the excited intermediate level decays to the lower levels with a common large rate, the optimal scheme for population transfer between the lower levels is actually optical pumping. In order to obtain this result we exploit the large decay rate to eliminate adiabatically the weakly coupled excited state, then perform a transformation to the basis comprised of the dark and bright states, and finally apply optimal control to this transformed system. Subsequently, we confirm the optimality of the optical pumping scheme for the original closed Λ-system using numerical optimal control. We also demonstrate numerically that optical pumping remains optimal when the decay rate to the target state is larger than that to the initial state or the two rates are not very different from each other. The present work is expected to find application in various tasks of quantum information processing, where such systems are encountered
P Kalugin, André Katz
Published: 15 December 2021
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4395

Abstract:
We consider the pure point part of the diffraction on families of aperiodic point sets obeying common local rules. It is shown that imposing such rules results in linear constraints on the partial diffraction amplitudes. These relations can be explicitly derived from the geometry of the prototile space representing the local rules.
, Xiaoqin Gao, Borivoje Dakic
Published: 15 December 2021
Journal of Physics A: Mathematical and Theoretical; https://doi.org/10.1088/1751-8121/ac4393

Abstract:
A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results in universal quantum computing. Motivated by the latter, we pose the following question: can one perform universal quantum computation by supplementing a set of classical gates with a quantum control, and a set of quantum gates operating solely on the latter? In this work we provide an affirmative answer to this question by considering a computational model that consists of 2n target bits together with a set of classical gates controlled by log(2n + 1) ancillary qubits. We show that this model is equivalent to a quantum computer operating on n qubits. Furthermore, we show that even a primitive computer that is capable of implementing only SWAP gates, can be lifted to universal quantum computing, if aided with an appropriate quantum control of logarithmic size. Our results thus exemplify the information processing power brought forth by the quantum control system.
Published: 15 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac4396

Abstract:
In this paper, we deﬁne Jacobi ﬁelds for nonholonomic mechanics using a similar characterization than in Riemannian geometry. We give explicit conditions to ﬁnd Jacobi ﬁelds and ﬁnally we ﬁnd the nonholonomic Jacobi fields in two equivalent ways: the ﬁrst one, using an appropriate complete lift of the nonholonomic system and, in the second one, using the curvature and torsion of the associated nonholonomic connection.
Published: 15 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac3aac

Abstract:
At the dawn of thermodynamics, Carnot’s constraint on efficiency of heat engines stimulated the formulation of one of the most universal physical principles, the second law of thermodynamics. In recent years, the field of heat engines acquired a new twist due to enormous efforts to develop and describe microscopic machines based on systems as small as single atoms. At microscales, fluctuations are an inherent part of dynamics and thermodynamic variables such as work and heat fluctuate. Novel probabilistic formulations of the second law imply general symmetries and limitations for the fluctuating output power and efficiency of the small heat engines. Will their complete understanding ignite a similar revolution as the discovery of the second law? Here, we review the known general results concerning fluctuations in the performance of small heat engines. To make the discussion more transparent, we illustrate the main abstract findings on exactly solvable models and provide a thorough theoretical introduction for newcomers to the field.
Published: 14 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac39cf

Published: 13 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac42ac

Abstract:
In these lectures, we give a pedagogical introduction to the superconformal index. This is the writeup of the lectures given at the Winter School “YRISW 2020” and is to appear in a special issue of JPhysA. The lectures are at a basic level and are geared towards a beginning graduate student interested in working with the superconformal index.
Rahul Ghosh
Published: 13 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac3ce0

Abstract:
We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.
Tolson H. Bell, Jerrell M. Cockerham, Clayton M. Mizgerd, Melita F. Wiles,
Published: 13 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac42ab

Abstract:
We present a method for computing transition points of the random cluster model using a generalization of the Newman-Ziff algorithm, a celebrated technique in numerical percolation, to the random cluster model. The new method is straightforward to implement and works for real cluster weight $q>0$. Furthermore, results for an arbitrary number of values of $q$ can be found at once within a single simulation. Because the algorithm used to sweep through bond configurations is identical to that of Newman and Ziff, which was conceived for percolation, the method loses accuracy for large lattices when $q>1$. However, by sampling the critical polynomial, accurate estimates of critical points in two dimensions can be found using relatively small lattice sizes, which we demonstrate here by computing critical points for non-integer values of $q$ on the square lattice, to compare with the exact solution, and on the unsolved non-planar square matching lattice. The latter results would be much more difficult to obtain using other techniques.
Boris G. Konopelchenko,
Published: 13 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac42aa

Abstract:
The paper is devoted to the analysis of the blow-ups of derivatives, gradient catastrophes and dynamics of mappings of ℝn → ℝn associated with the n-dimensional homogeneous Euler equation. Several characteristic features of the multi-dimensional case (n > 1) are described. Existence or nonexistence of blow-ups in diﬀerent dimensions, boundness of certain linear combinations of blow-up derivatives and the ﬁrst occurrence of the gradient catastrophe are among of them. It is shown that the potential solutions of the Euler equations exhibit blow-up derivatives in any dimenson n. Several concrete examples in two- and three-dimensional cases are analysed. Properties of ℝnu → ℝ nx mappings deﬁned by the hodograph equations are studied, including appearance and disappearance of their singularities.
Published: 10 December 2021
Journal of Physics A: Mathematical and Theoretical, Volume 55; https://doi.org/10.1088/1751-8121/ac41e9

Abstract:
Remarks at Conference in Memory of Fritz Haake, Bad Honnef , September 2021
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