In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain values of the α parameter, two second-class constraints, which means that this system does not possess gauge invariance. However, we know that it is possible to disclose gauge symmetries in such a system by converting the original second-class system into a first-class one. This procedure can be done through the gauge unfixing (GU) formalism by acting with a projection operator directly on the original second-class Hamiltonian, without adding any extra degrees of freedom in the phase space. One of the constraints becomes the gauge symmetry generator of the theory and the other one is disregarded. At the end, we have a first-class Hamiltonian satisfying a first-class algebra. Here, our goal is to apply a new scheme of embedding second-class constrained systems based on the GU formalism, named improved GU formalism, in the BCSM. The original second-class variables are directly converted into gauge invariant variables, called GU variables. We have verified that the Poisson brackets involving the GU variables are equal to the Dirac brackets between the original second-class variables. Finally, we have found that our improved GU variables coincide with those obtained from an improved BFT method after a particular choice for the Wess-Zumino terms.

In this letter, considering the metric of a rotating polytropic black hole in the Boyer-Lindquist coordinates, at first, we derive the thermodynamic parameters (S, F, U and G) and study its dependence on the outer horizon by depicting suitable graphs. Then after reconstruction of the metric of the same in the Eddington-Finkelstein coordinates, we establish the interior volume of the black hole. We further analyze the variations of the interior volume with the small change of the advanced time with respect to the radius. Here we show the existence of a certain value of the radius for which this variation becomes maximum. Moreover, we show the dependence of this maximum value of the radius on the mass of the black hole. We derive the differential form of the interior volume for this limit of the radius and hence the maximal interior volume of the said black hole. Finally, we analyze the same thermodynamic parameters inside the black hole and present a comparative study between the parameters in the outer and interior regions of the black hole.

We present two novel solutions of real Hilbert state quaternionic quantum mechanics ($\mathbbm H$QM). Firstly, we observe that the angular momentum operator admits two different classes of physically non-equivalent free particles. As a second result, we study the Larmor precession to observe that it has a quaternionic solution where a novel phenomenological interpretation is possible, as well as a different of spin is possible, and these results may encourage experimental and theoretical investigations of the quaternionic theory.

Recent studies have discovered local potentials can induce nontrivial eigenmodes responding to the bulk topology for the system. While previous studies focused on conventional first-order topological states emerging from vacancy superlattice, here we study higher-order topological properties of the vacancy superlattice on a two-dimensional Chern insulator with particle-hole symmetry. The vacancy superlattice with alternate lattice spacings exhibits an emergent second-order topological phase characterized by the nontrivial edge polarization. This topological phase is robust against particle-hole symmetry-preserved perturbations as long as the energy gap remains open for the mid-gap sates. Our work generalizes the nontrivial higher-order topological properties to a Chern insulator with local defect vacancies and provides a controllable platform for engineering higher-order topological corner states.

Our ability to observe the network topology and nodes' behaviors of complex systems has significantly advanced in the past decade, giving rise to a new and fast-developing frontier - inferring the underlying dynamical mechanisms of complex systems from the observation data. Here we explain the rationale of data-driven dynamics inference and review the recent progress in this emerging field. Specifically, we classify the existing methods of dynamics inference into three categories, and describe their key ideas, representative applications and limitations. We also discuss the remaining challenges that are worth the future effort.

Measuring the quantumness of a system can be done with a variety of methods. In this article we compare different criteria, namely quantum discord, Bell inequality violation and non-separability, for systems placed in a Gaussian state. When the state is pure, these criteria are equivalent, while we find that they do not necessarily coincide when decoherence takes place. Finally, we prove that these criteria are essentially controlled by the semi-minor axis of the ellipse representing the state's Wigner function in phase space.

We discuss quantum mechanical systems with Dunkl derivatives by constructing the Dunkl-Heisenberg relation in the momentum representation by means of the reflection operator for momentum and we obtain the corresponding position quantum eigenfunction. We examine the one-dimensional Dunkl oscillator in the momentum space in terms of ν-deformed Hermite polynomials. We obtain the energy levels as well as the ground-state and excited wave functions in terms of the ν-deformed Hermite polynomials. We also describe some properties of the ν-deformed Hermite polynomials and we propose an appropriate form for the Dunkl-Fourier transform. We apply the method to the construction of coherent states.

Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous topological phases and the new phenomenology that they can open. We revisit key experiments suggesting that amorphous topological phases exist in both solid-state and synthetic amorphous systems. We finish by discussing the open questions in the field, that promises to significantly enlarge the set of materials and synthetic systems benefiting from the robustness of topological matter.

We obtain the correct expressions for the energy and normalized eigenfunctions for a spin-zero relativistic quantum oscillator model under the violation of Lorentz symmetry defined by an arbitrary constant vector field $v^{\mu}$.

We consider the geometric phase induced by the two-level atom with inertial and uniformly accelerated motion, which is coupled to massless scalar field in cosmic string spacetime. Our result shows that when the atom is very close to the string, the geometric phase of cosmic string spacetime is $\nu$ times that of Minkowski spacetime. By comparing phase difference induced by the inertial and accelerated motion, we find the sensitive dependence of the phase difference on deficit angle parameter, transition frequencies of the atom, atomic acceleration and the initial state parameter. We also obtain phase difference increases with deficit angle parameter and the atomic acceleration. Although reaching the measurable magnitude of geometric phase requires extremely high acceleration, the detection experiment may be implemented in the future. Our work may suggest a possible way to detect cosmic string scalar field by using geometric phase.