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We address the comments on our paper (Todorinov et al., 2019) presented in Chargui (2020). We show that the points raised in Chargui (2020) do not contain any new results or valid criticisms.

We point out some misleading results reported in the recent study made by Todorinov et al. (2019), concerning a relativistic extension of the generalized uncertainty principle (GUP). We derive, in this frame, the correct deformed Klein–Gordon (KG) and Dirac equations, valid up to the first order in the deformation parameter, and discuss their minimal coupling to external fields.

In this paper, we study the deflection of light by a class of phantom black hole and wormhole solutions in the weak limit approximation. More specifically, in the first part of this work, we study the deflection of light by Garfinkle-Horowitz-Str\"{o}minger black hole and Einstein-Maxwell anti-dilaton black hole using the optical geometry and the Gauss-Bonnet theorem. Our calculations show that gravitational lensing is affected by the phantom scalar field (phantom dilaton). In the second part of this work, we explore the deflection of light by a class of asymptotically flat phantom wormholes. In particular, we have used three types of wormholes: wormhole with a bounded/unbounded mass function, and a wormhole with a vanishing redshift function. We show that the particular choice of the shape function and mass function plays a crucial role in the final expression for the deflection angle of light. In the third part of the paper, we verify our findings with the help of standard geodesics equations. Finally, in the fourth part of this paper, we consider the problem for the observational relevance of our results studying the creation of the weak field Einstein rings., Comment: 15 pages, 5 figure

In this paper, within the framework of a unified mathematical model, the new formulation of quantum mechanics – quantum mechanics of higher order kinematic values – is proposed. In contrast to the well-known formulations of quantum mechanics in the new formulation, the wave function has not only a coordinate or momentum representation, but also representations through acceleration and accelerations of higher orders. The representations of the wave function in terms of higher order kinematic values make it possible to consider the dissipative systems problem and the variable entropy systems one within a single mathematical apparatus. The new formulation is not built phenomenologically, but from first principles and in a particular case contains the formulation of the de Broglie–Bohm 〈 wave-pilot 〉 quantum mechanics. The new formulation is based on the Vlasov equations chain. This approach allows us to obtain a natural connection between classical and quantum systems. Examples of such systems are considered in this paper.

This paper presents a concise and up-to-date tour to the realm of inequality indices. Originally devised for socioeconomic applications, inequality indices gauge the divergence of wealth distributions in human societies from the socioeconomic ‘ground state’ of perfect equality, i.e. pure communism. Inequality indices are quantitative scores that take values in the unit interval, with the zero score characterizing perfect equality. In effect, inequality indices are applicable in the context of general distributions of sizes — non-negative quantities such as count, length, area, volume, mass, energy, and duration. For general size distributions, which are omnipresent in science and engineering, inequality indices provide multi-dimensional and infinite-dimensional quantifications of the inherent inequality — i.e., the statistical heterogeneity, the non-determinism, the randomness. This paper compactly describes the insights and the practical implementation of inequality indices.

First and second order non-equilibrium thermodynamics are studied in the context of particle creation mechanism for homogeneous and isotropic FLRW model and a general formulation of the emergent scenario is investigated. Finally, the stability of the non-equilibrium thermodynamics is examined., Comment: The paper is accepted in Annals of Physics (2017). The authors have given the answers to the criticism in arXiv:1609.09779[gr-qc]. Also, the paper disproves their incorrect comments

This paper is a rebuttal to Eur. Phys. Jour. Plus 130, 191 (2015), which claims that the results in arXiv:1502.04911 (Ann. Phys. 355, 360 (2015)) are incorrect. For this reason, some of the results in arXiv:1502.04911 have been reviewed and clarified. The results in this paper are dedicated to the 100th anniversary of Albert Einstein's presentation of the complete General Theory of Relativity to the Prussian Academy., Comment: 13 pages, 1 figure. Accepted for publication in Annals of Physics. The results in arXiv:1502.04911 have been reviewed and clarified

In present paper the Quantum Electrodynamics theory at finite temperatures for the bound states is presented. To describe the thermal effects arising in a heat bath the Hadamard form of thermal photon propagator is employed. This form permits the simple introduction of thermal gauges in a way similar to the 'ordinary' Feynman propagator and, therefore, the gauge invariance can be proved for all the considered effects. Moreover, contrary to the 'standard' form of thermal photon propagator, the Hadamard expression has a well defined analytical properties. However, this thermal photon propagator contains the divergent contribution which requires the introduction of regularization procedure within the framework of constructed theory. The method of regularization in conjunction with the physical interpretation is given in the paper. Correctness of regularization procedure is confirmed also by the gauge invariance of final results and coincidence of the results (on the example of self-energy correction) for two different forms of photon propagator. On the basis of constructed theory the thermal Coulomb potential and its asymptotics at the large distances are found. Finally, we discuss in details the thermal effects of lowest order in the fine structure constant and temperature. Such effects are presented by the thermal one-photon exchange between bound electron and nucleus, thermal one-loop self-energy, thermal vacuum polarization, recoil corrections and correction on the finite size of the nucleus. Introduction of the regularization allows us do not apply the renormalization procedure. To confirm this we describe also the thermal vertex (with one, two and three vertices) corrections within the adiabatic $S$-matrix formalism. Finally, the influence of thermal effects on the determination of proton radius and Rydberg constant is discussed in the paper., 32 pages, 10 figures, 6 Tables

In this paper, a general description for the Hubbard model with nearest-neighbor transfer integral t and on-site repulsion U on a square lattice with N a 2 ≫ 1 sites is introduced. It refers to three types of elementary objects whose occupancy configurations generate the state representations of the model extended global S O ( 3 ) × S O ( 3 ) × U ( 1 ) symmetry recently found in Ref. [11] (Carmelo and Ostlund, 2010). Such objects emerge from a suitable electron–rotated-electron unitary transformation. It is such that rotated-electron single and double occupancy are good quantum numbers for U ≠ 0 . The advantage of the description is that it accounts for the new found hidden U ( 1 ) symmetry in S O ( 3 ) × S O ( 3 ) × U ( 1 ) = [ S U ( 2 ) × S U ( 2 ) × U ( 1 ) ] / Z 2 2 beyond the well-known S O ( 4 ) = [ S U ( 2 ) × S U ( 2 ) ] / Z 2 model (partial) global symmetry. Specifically, the hidden U ( 1 ) symmetry state representations store full information on the positions of the spins of the rotated-electron singly occupied sites relative to the remaining sites. Profiting from that complementary information, for the whole U / 4 t > 0 interaction range independent spin state representations are naturally generated in terms of spin- 1 / 2 spinon occupancy configurations in a spin effective lattice. For all states, such an effective lattice has as many sites as spinons. This allows the extension to intermediate U / 4 t values of the usual large- U / 4 t descriptions of the spin degrees of freedom of the electrons that singly occupy sites, now in terms of the spins of the singly-occupied sites rotated electrons. The operator description introduced in this paper brings about a more suitable scenario for handling the effects of hole doping. Within this, such effects are accounted for in terms of the residual interactions of the elementary objects whose occupancy configurations generate the state representations of the charge hidden U ( 1 ) symmetry and spin S U ( 2 ) symmetry, respectively. This problem is investigated elsewhere. The most interesting physical information revealed by the description refers to the model on the subspace generated by the application of one- and two-electron operators onto zero-magnetization ground states. (This is the square-lattice quantum liquid further studied in Ref. [5] (Carmelo, 2010).) However, to access such an information, one must start from the general description introduced in this paper, which refers to the model in the full Hilbert space.

The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through an interacting quantum dot maintained at finite bias using a concept introduced by Hershfield [Phys. Rev. Lett. 70, 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian. In this paper we provide a pedagogical analysis of the core concepts of the effective equilibrium theory. First, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach, and relate the Green's functions in the two theoretical frameworks. Second, we expound some applications of this method in the context of interacting quantum impurity models. We introduce a novel framework to treat effects of interactions perturbatively while capturing the entire dependence on the bias voltage. For the sake of concreteness, we employ the Anderson model as a prototype for this scheme. Working at the particle-hole symmetric point, we investigate the fate of the Abrikosov-Suhl resonance as a function of bias voltage and magnetic field., Comment: 53 pages, 6 figures, Final Version to be published in Annals of Physics

The Calogero model bears, in the continuum limit, collective excitations in the form of density waves and solitary modulations of the density of particles. This sector of the spectrum of the model was investigated, mostly within the framework of collective-field theory, by several authors, over the past 15 years or so. In this work we shall concentrate on periodic solutions of the collective BPS-equation (also known as “finite amplitude density waves”), as well as on periodic solutions of the full static variational equations which vanish periodically (also known as “large amplitude density waves”). While these solutions are not new, we feel that our analysis and presentation add to the existing literature, as we explain in the text. In addition, we show that these solutions also occur in a certain two-family generalization of the Calogero model, at special points in parameter space. A compendium of useful identities associated with Hilbert transforms, including our own proofs of these identities, appears in Appendix A. In Appendix B we also elucidate in the present paper some fine points having to do with manipulating Hilbert-transforms, which appear ubiquitously in the collective field formalism. Finally, in order to make this paper self-contained, we briefly summarize in Appendix C basic facts about the collective field formulation of the Calogero model.

In our previous paper (Ohkuwa et al., 2016) corrigendum was found in Eqs. (3.4) and (3.6) . However, conclusions of our previous paper are not changed.

Certain zero-bias anomalies (ZBAs) in the voltage, temperature and magnetic field dependence of the conductance $G(V,T,H)$ of quenched Cu point contacts have previously been interpreted to be due to non-magnetic 2-channel Kondo (2CK) scattering from near-degenerate atomic two-level tunneling systems (Ralph and Buhrman, 1992; Ralph et al. 1994), and hence to represent an experimental realization of the non-Fermi-liquid physics of the T=0 fixed point of the 2-channel Kondo model. In this, the first in a series of three papers (I,II,III) devoted to 2-channel Kondo physics, we present a comprehensive review of the quenched Cu ZBA experiments and their 2CK interpretation, including new results on ZBAs in constrictions made from Ti or from metallic glasses. We first review the evidence that the ZBAs are due to electron scattering from stuctural defects that are not static, but possess internal dynamics. In order to distinguish between several mechanisms proposed to explain the experiments, we then analyze the scaling properties of the conductance at low temperature and voltage and extract from the data a universal scaling function $\Gamma(v)$. The theoretical calculation of the corresponding scaling function within the 2CK model is the subject of papers II and III. The main conclusion of our work is that the properties of the ZBAs, and most notably their scaling behavior, are in good agreement with the 2CK model and clearly different from several other proposed mechanisms.

We study in the present paper the multiple stable states of two different atoms in a single-mode quantum cavity by means of variational method. Eigenenergies and eigenstates are obtained analytically in the optical coherent state of cavity field. The ground state displays the known Dicke phase transition from the normal to superradiant phases at the critical value of atom–field coupling. The rich phase diagrams including the stable excited states are presented respectively for two atoms with different level spaces and atom–field couplings. By adjusting the ratios of two-atom couplings or level spaces, one atom can be in the normally populated state, while the other is in the inversely populated state. We also observe the stimulated radiation from the inversely populated state. Particularly, the normal and stimulated radiations are interchangeable respectively for two atoms. Moreover, the maximally entangled state can be generated with two identical atoms.

In this paper we present new nonclassical states of a single mode of the electromagnetic field constructed by superpositions of coherent states distributed over a semi-straight line starting from the origin of the phase space. These states have highly concentrated phase distributions and can be useful as approximations of phase states. We propose feasible schemes to prepare such states in microwave high-Q cavities and as traveling modes. We investigate nonclassical properties and determine the Wigner functions of such pure states. Then we consider the system in contact with a reservoir, taking into account dissipation and gain processes in the Markovian approximation, and study the time-evolution of these states by solving the master equation in the Wigner representation. From explicit expressions of the time-dependent Wigner functions, we study the time-dependence of nonclassical properties and use the negativity of the Wigner function to analyze the disappearance of sub-Planck structures as time evolves.

Luttinger semimetals include materials like gray tin ($\alpha$-Sn) and mercury telluride, which are three-dimensional gapless semiconductors having a quadratic band crossing point (QBCP). Due to a growing interest in QBCPs and new experimental efforts, it is essential to study the finite-temperature properties of such systems. In this paper, we investigate the emergence of plasmons in the presence of Coulomb interactions in isotropic Luttinger semimetals, for zero as well as generic nonzero temperatures. When the Fermi level lies right at the QBCP, which is the point where twofold degenerate conduction and valence bands touch each other quadratically, we find that plasmons cannot appear at zero temperature. However, for nonzero temperatures, thermal plasmons are generated. Whether they are long-lived or not depends on the values of temperature, effective electron mass and effective fine-structure constant, and the number of fermion flavors. We also numerically estimate the behavior of the inelastic scattering rate at nonzero temperatures, as a function of energy, where the signatures of the QBCP thermal plasmons show up as a sharp peak. Our results will thus serve as a guide to experimental probes on these systems., Comment: 15 pages, 6 figures; journal version accepted in Annals of Physics

When accelerated by a constant force in the lab frame, a classical charge experiences no self force. In this case, the particle radiates without dissipating its kinetic and potential energy. But what happens when the particle enters another region with equal and opposite acceleration? Does the oscillating charge lose its mechanical energy similar to a radiating dipole, even though it seems to lose no mechanical energy within each region of constant acceleration? In this paper, I will show how mechanical energy is transferred to radiation energy via the Schott energy when the particle crosses the boundary between the two regions. In particular, I will show how preacceleration, which is usually regarded as an unphysical effect of the Lorentz-Abraham-Dirac self force, is essential for the energy transfer. Moreover, I will show that the commonly adopted Landau-Lifshitz approximation, which removes preacceleration, introduces second-order secular energy error. On a more fundamental level, the validity of classical electrodynamics is in fact questionable because quantum effects are likely important. The classical prediction can be tested experimentally by observing frequency chirping of radiation, whereby micro physics leaves signatures on macroscopic scales. The required experimental accuracy is estimated. Trap experiment of this type is complementary to collider experiments that endeavor to observe radiation reaction for elementary particles., 42 pages, 8 figures. LLNL-JRNL-764637

The aim of this paper is to obtain analytic anisotropic spherical solutions in f ( R ) scenario through gravitationally decoupled minimal geometric deformation technique. In this regard, we first consider the known isotropic Krori–Barua solution for f ( R ) Starobinsky model in the interior of the stellar system and then include the effects of two types of anisotropic solutions. The field equations are constructed by applying Krori–Barua solution and the values of unknown constants are evaluated with the help of junction conditions. We analyze the physical acceptability and stability of our resulting solutions via graphical observations of effective energy density, effective radial as well as tangential pressure, energy conditions, stability through speed of sound and adiabatic index. It is found that both solutions satisfy the stability as well as other physical requirements for specific values of anisotropic constant. We conclude that the modified theory yields more stable behavior of a self-gravitating system.

The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies.In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schr\"odinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator., Comment: 6 pages, Revtex

In this paper we develop the charged version of the spacetime proposed by Johannsen and Psaltis. Rotation is introduced in the deformed Reissner-Nordstr\"om spacetime by complex coordinate transformation. The event horizon and Killing horizon are studied. Killing horizons are represented graphically also. The analysis of the determinant of the metric shows that the spacetime does not have Lorentz violating regions. Similarly, from the study of the closed time-like curves, we see that no such curves exist outside the central body. Expressions for the energy and angular momentum for a particle on the equatorial plane are determined. Location of the circular photon orbits and innermost stable circular orbits is also computed., Comment: Matches the published version

The goal of this paper is to obtain a precise expression for the production tensor in a dissipative hyperbolic relativistic theory of gas with internal structure. For this aim, we use a variant of relativistic BGK model for the Boltzmann–Chernikov kinetic equation. Moreover, we deduce some inequalities for the coefficients requiring the entropy principle and the convexity of entropy density. As a limiting case, the expression of the production tensor in the case of monatomic gas is also evaluated.

In this paper, a generalized action integral of both gravity and matter is defined on the sphere bundle over Finsler space–time manifold M with a Lorentz–Finsler metric. The Euler–Lagrange equation of this functional, a generalization of the Riemann–Einstein gravity equation is obtained by using some divergence theorems. Fibres of the sphere bundle are unbounded according to the pseudo-Finsler metric. Moreover, solutions of vacuum Finsler gravity equation under the weakly Landsberg condition are discussed and some concrete examples are provided. At last, we raise some questions for further study.

In this paper, we aim to describe nonlocal extractable work in terms of geometrical correlations, in an attempt to characterize the latter as a resource for the first. Principally, we are going to show an analytical expression that relates these two quantities for two-qubit Bell-diagonal states. This expression is displayed when the correlations are geometrically defined by using the Schatten 1-norm to measure distances among quantum states in the Hilbert space. Additionally, we are also going to show – outside the family of Bell-diagonal states – the existence of correlated bipartite passive states, implying that nonzero correlations are not a sufficient condition for nonlocal work extraction.

In the present paper, we study the effect of the minimal length on two well-known potentials: Coulomb and Hulthen in transitional nuclei near the critical point symmetry X(3). Albeit these two potentials have mathematically similar behaviors at small deformations and give the same results for energy spectra and electromagnetic transition rates of nuclei, they behave differently in the presence of a minimal length. It appears that this latter acts on the intrinsic structure of the potential allowing both potentials’ actions to be differentiated.

Although the spinor field in (1+1) dimensions has the right structure to model a dispersive bimodal system with gain and loss, the plain addition of gain to one component of the field and loss to the other one results in an unstable dispersion relation. In this paper, we advocate a different recipe for the PT -symmetric extension of spinor models — the recipe that does not produce instability of the linear Dirac equation. Having exemplified the physical origins of the P - and T -breaking terms, we consider the extensions of three U(1)-invariant spinor models with cubic nonlinearity. Of these, the PT -symmetric extension of the Thirring model is shown to be completely integrable and possess infinitely many conserved quantities. The PT -symmetric Gross–Neveu equation conserves energy and momentum but does not conserve charge. The third model is introduced for the purpose of comparison with the previous two; its PT -symmetric extension has no conservation laws at all. Despite this dramatic difference in the integrability and conservation properties, all three PT -symmetric models are shown to have exact soliton solutions. Similar to the solitons of the extended Thirring and Gross–Neveu equations, the solitons of the new model are found to be stable — except for a narrow band of frequencies adjacent to the soliton existence boundary. The persistence under the P - and T -breaking perturbations as well as the prevalence of stability highlights a remarkable sturdiness of spinor solitons in (1+1) dimensions.

In modern physics there exist several formulations of relativistic thermodynamics of a moving body. The Planck and Ott formalisms are the main ones. However, it is not clear which one is correct. In the present paper, we have solved this problem. We have required the equivalence of the dynamical Hamiltonian of a system to the fundamental thermodynamic potential in addition to the principle of entropy invariance and derived the first law of thermodynamics from this fundamental potential. We have found that in the case of momentum being an independent variable in the Hamiltonian, the Lorentz transformations of the thermodynamic quantities belong to the Planck formalism. However, if we suppose that the velocity is an independent variable in the Hamiltonian (though it is not correct from the point of view of the relativistic dynamics), the Lorentz transformations of the thermodynamic quantities belong to the Ott formalism. It demonstrates that the Ott formalism cannot be appropriate. Moreover, we have proved that in the Planck description the first law of thermodynamics is covariant and the Legendre transform of the Lagrangian is preserved. However, in the Ott description the first law of thermodynamics is not covariant and the Legendre transform is violated. Thus we have demonstrated that only the Planck formulation of relativistic thermodynamics of a moving body is properly defined and the Ott formalism should be discarded.

This paper investigates wormhole solutions of spherically symmetric spacetime via Noether symmetry approach in f ( R , T ) gravity. For this purpose, we choose f ( R , T ) models appreciating indirect curvature–matter coupling and examine symmetry generators with associated conserved quantities. We determine possible existence of realistic traversable wormhole solutions for both dust as well as non-dust distributions and also study stable behavior of these solutions. For both models, we use constant as well as variable forms of red-shift function. To analyze physical existence of wormhole solutions, we study the behavior of null/weak energy conditions with respect to ordinary as well as effective energy–momentum tensors. It is concluded that there exist physically viable traversable as well as stable wormhole solutions in most of the cases.

In this paper we show that, via an extension of time, some metric structures naturally appear in both classical and quantum mechanics when both are formulated via path integrals. We calculate the various Ricci scalar and curvatures associated to these metrics and prove that they can be choosen to be zero in classical mechanics while this is not possible in quantum mechanics., To appear in ann.of phys

In this paper, the baryonic wave function has been obtained with the Cornell potential, a combination of linear and Coulomb terms, using the hyper-radial Schrodinger equation and an improved variational method while on the other hand, hyperfine interactions are considered, including smeared standard hyperfine term, isospin dependent and spin–isospin dependent terms in order to improve the results. Then, the baryonic Isgur–Wise function in hyperspherical coordinates has been investigated employing both mentioned wave functions. Finally, in particular, the charged radius and the decay width of transition have been reported for both methods and compared with those obtained in experiments or theories.

In this paper, we consider the rotating charged G\"{o}del black hole and study the effect of the higher order corrections of the entropy on the thermodynamics and statistics quantities of the Kerr-Newman-G\"{o}del black hole. The leading order correction is logarithmic while higher-order terms are proportional to the inverse of the area of the black hole. We obtain modified thermodynamics and statistics and find that correction terms are important in the stability of the black hole., Comment: 16 pages, 8 Figures

In this paper we investigate the interrelationship between the unified first law of thermodynamics and the Friedmann equations for three anisotropic and inhomogeneous spacetime metrics namely Lemaitre–Tolman–Bondi and Friedmann–Lemaitre–Robertson–Walker type inhomogeneous spacetime model and Kantowski–Sachs type model. In all these models we find that Einstein field equations are obtained by projecting the unified first law along and perpendicular to the Kodama vector and also along two linearly independent directions.

In this paper we study a unified formalism for Thermal Quantum Field Theories, i.e., for the Matsubara approach, Thermo Field Dynamics and the Path Ordered Method. To do so, we employ a mechanism akin to the Hawking effect which explores a relationship between the concept of temperature and spacetimes endowed with event-horizons. In particular, we consider an eight dimensional static spacetime, the so-called eta-xi spacetime, which we show to form an appropriate geometric background for generic Thermal Quantum Field Theories. Within this framework, the different formalisms of Thermal Field Theory are unified in a very natural way via various analytical continuations and the set of time-paths used in the Path Ordered Method is interpreted in geometric terms. We also explain reported inconsistencies inherent in the Thermo Field Dynamics through the appearance of horizons (and ensuing loss of information) in the eta-xi spacetime., Comment: 19 pages, 3 figures. arXiv admin note: text overlap with arXiv:gr-qc/9908024

In this paper, we study properties of diffraction of a weak probe field interacting with a symmetric semiconductor quantum well that is coherently manipulated by a standing wave. Based on the theory of quantum coherent and of light diffraction, we can obtain distribution of the diffraction spectra of the probe field. We consider the influences of Kerr nonlinear effect on the diffraction pattern, and studies show the distribution of diffraction pattern can be controlled through choosing appropriate physical parameters of system. Kerr nonlinear effect can enhance the brightness of central pattern and improve the transmission efficiency of the incident beam. A controllable diffraction pattern has potential applications in some areas, such as design of quantum diffractive optical elements, grating imaging system, precision measurement and so on.

This paper systematically develops the Schr\"odinger formalism that is valid also for gyrotropic media where the material weights $W = \left ( \begin{smallmatrix} \varepsilon & \chi \chi^* & \mu \end{smallmatrix} \right ) \neq \overline{W}$ are complex. This is a non-trivial extension of the Schr\"odinger formalism for non-gyrotropic media (where $W = \overline{W}$) that has been known since at least the 1960s. Here, Maxwell's equations are rewritten in the form $\mathrm{i} \partial_t \Psi = M \Psi$ where the selfadjoint (hermitian) Maxwell operator $M = W^{-1} \, \mathrm{Rot} \, \big |_{\omega \geq 0} = M^*$ takes the place of the Hamiltonian and $\Psi$ is a complex wave representing the physical field $(\mathbf{E},\mathbf{H}) = 2 \mathrm{Re} \, \Psi$. Writing Maxwell's equations in Schr\"odinger form gives us access to the rich toolbox of techniques initially developed for quantum mechanics and allows us to apply them to classical waves. To show its utility, we explain how to identify conserved quantities in this formalism. Moreover, we sketch how to extend our ideas to other classical waves., Comment: 58 pages, updated version incorporates suggestions from the community

In this paper, the quantum spacetime with a running gravitational coupling is explored. Analyzing the gravity-induced quantum interference pattern and the Gedanken for weighting a photon, we find that the running Newton constant can be inspired by the generalized uncertainty principles. A characteristic momentum associated with the tidal effect is suggested, which incorporates the quantum effect with the geometric nature of gravity. When the simplest generalized uncertainty principle is considered, the minimal model of the regular black holes is reproduced by the effective Newton constant. The black hole’s tunneling probability, accurate to the second order correction, is carefully analyzed. We find that the tunneling probability is regularized by the size of the black hole remnant. Moreover, for a given initial black hole, the remnant is the final state of a transition process that the probability is minimal. We also suggest a theory of modified gravity, by substituting the effective Newton constant into the Hilbert–Einstein action.

This paper shows a new approach to obtain analytical topological defects of a 2 D Myers–Pospelov Lagrangian for two scalar fields. Such a Lagrangian presents higher-order kinetic terms, which lead us to equations of motion which are non-trivial to be integrated. Here we describe three possible scenarios for the equations of motion, named by timelike, spacelike and lightlike respectively. We started our investigation with a kink-like traveling wave Ansatz for the free theory, which led us to constraints for the dispersion relations of each scenario. We also introduced a procedure to obtain analytical solutions for the general theory in the three mentioned scenarios. We exemplified the procedure and discussed the behavior of the defect solutions carefully. It is remarkable that the methodology presented in this study led to analytical models, despite the complexity of the equations of motion derived from the 2D Myers–Pospelov Lagrangian. The methodology here tailored can be applied to several Lagrangians with higher-order derivative terms.

In this paper we have studied the propagation of a massless scalar field minimally coupled to a black hole with the source of cloud of strings in 2 + 1 f ( R ) gravity theory. In particular we have found analytical results for the decay rate, reflection coefficient, greybody factors, as well as the black hole temperature. On the other hand, our quasinormal modes analyses reveal stability in the propagation of a massless scalar field in the cloud of strings black hole spacetime. However, under a suitable choose of parameters an instability is found. Furthermore based on the Bekenstein conjecture on the quantization of the surface area of the black hole we find the minimal surface area associated to the black hole horizon which is in agreement with Bekenstein’s proposal.

The so-called $q$-z-\textit{R\'enyi Relative Entropies} provide a huge two-parameter family of relative entropies which includes almost all well-known examples of quantum relative entropies for suitable values of the parameters. In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant $(0,2)$ symmetric tensors on the space of invertible quantum states in finite dimensions. The geometric formalism developed here allows us to obtain the explicit expressions of such tensor fields in terms of a basis of globally defined differential forms on a suitable unfolding space without the need to introduce a specific set of coordinates. To make the reader acquainted with the intrinsic formalism introduced, we first perform the computation for the qubit case, and then, we extend the computation of the metric-like tensors to a generic $n$-level system. By suitably varying the parameters $q$ and $z$, we are able to recover well-known examples of quantum metric tensors that, in our treatment, appear written in terms of globally defined geometrical objects that do not depend on the coordinates system used. In particular, we obtain a coordinate-free expression for the von Neumann-Umegaki metric, for the Bures metric and for the Wigner-Yanase metric in the arbitrary $n$-level case., Comment: 50 pages, 1 figure

The paper deals with a non--minimally coupled scalar field in the background of homogeneous but anisotropic Kantowski--Sachs space--time model. The form of the coupling function of the scalar field with gravity and the potential function of the scalar field are not assumed phenomenologically, rather they are evaluated by imposing Noether symmetry to the Lagrangian of the present physical system. The physical system gets considerable mathematical simplification by a suitable transformation of the augmented variables $(a, b, \phi)\rightarrow (u, v, w)$ and by the use of the conserved quantities due to the geometrical symmetry. Finally, cosmological solutions are evaluated and analyzed from the point of view of the present evolution of the Universe., Comment: Accepted in "Annals of Physics"

The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantum system. In this paper, a generalized time fractional Schrodinger equation is proposed. To study the fractional dynamics of quantum systems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrodinger equation we proposed is a confirmable system.

In this paper, we investigate the Unruh radiation in the Bohmian field theory on a shape dynamics background setting. Since metric and metric momentum are real quantities, the integral kernel to invert the Lichnerowicz-York equation for first order deviations due to existence of matter terms turns out to be real. This fact makes the interaction Hamiltonian real. On the other hand, the only contribution to guarantee the existence of Unruh radiation has to come from the imaginary part of the temporal part of the wave functional. We have proved the existence of Unruh radiation in this setting. It is also important that we have found the Unruh radiation via an Unruh-DeWitt detector in a theory where there is no Lorentz symmetry and no conventional space-time structure., Comment: 14 pages, 2 figures

The Quantum Cheshire Cat (QCC) is an effect introduced recently within the Weak Measurements framework. The main feature of the QCC effect is that a property of a quantum particle appears to be spatially separated from its position. The status of this effect has however remained unclear, as claims of experimental observation of the QCC have been disputed by strong criticism of the experimental as well as the theoretical aspects of the effect. In this paper we clarify in what precise sense the QCC can be regarded as an unambiguous consequence of the standard quantum mechanical formalism applied to describe quantum pointers weakly coupled to a system. In light of this clarification, the raised criticisms of the QCC effect are rebutted. We further point out that the limitations of the experiments performed to date imply that a loophole-free experimental demonstration of the QCC has not yet been achieved., Comment: Context was clarified. Additional minor edits. Similar to published version

In dealing with quantum mechanics at very high energies, it is essential to adapt to a quasiposition representation using the maximally-localized states because of the generalized uncertainty principle. In this paper, we look at maximally-localized states as eigenstates of the operator ξ = X + i β P that we refer to as the maximally-localized position. We calculate the overlap between maximally-localized states and show that the identity operator can be expressed in terms of the maximally-localized states. Furthermore, we show that the maximally-localized position is diagonal in momentum-space and that the maximally-localized position and its adjoint satisfy commutation and anti-commutation relations reminiscent of the harmonic oscillator commutation and anti-commutation relations. As application, we use the maximally-localized position in developing the Euclidean path-integral and introduce the compact form of the propagator for maximal localization. The free particle momentum-space propagator and the propagator for maximal localization are analytically evaluated up to quadratic-order in β . Finally, we obtain a path-integral expression for the partition function of a thermodynamic system using the maximally-localized states. The partition function of a gas of noninteracting particles is evaluated. At temperatures exceeding the Planck energy, we obtain the gas’ maximum internal energy N ∕ 2 β and recover the zero heat capacity of an ideal gas.

In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are related to quantum state tomography (Caves et al., 2004), quantum cryptography (Fuchs and Sasaki, 2003) [ 1 ], and foundational studies (Fuchs, 2002) [ 2 ]. However, constructing SIC-POVMs is notoriously hard. Although some SIC-POVMs have been constructed numerically, there does not exist an infinite class of them. In this paper, we propose two constructions of approximately SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. We employ difference sets to present the first construction and the dimension of the approximately SIC-POVMs is q + 1 , where q is a prime power. Notably, the dimension of this framework is new. The second construction is based on partial geometric difference sets and works whenever the dimension of the framework is a prime power.

The entropic force has been recently argued to be responsible for dissociation of heavy quarkonia. In this paper, we analyze $R^2$ corrections and $R^4$ corrections to the entropic force, respectively. It is shown that for $R^2$ corrections, increasing $\lambda_{GB}$ (Gauss-Bonnet factor) leads to increasing the entropic force. While for $R^4$ corrections, increasing $\lambda$ ('t Hooft coupling) leads to decreasing the entropic force. Also, we discuss how the entropic force changes with the shear viscosity to entropy density ratio, $\eta/s$, at strong coupling., Comment: 8 pages, 2 figures

This paper investigates the geometry of static traversable wormhole through Noether symmetry approach in f ( R ) gravity. We take perfect fluid distribution and formulate symmetry generators with associated conserved quantities corresponding to general form, power-law and exponential f ( R ) models. In each case, we evaluate wormhole solutions using constant and variable red-shift functions. We analyze the behavior of shape function, viability of constructed f ( R ) model and stability of wormhole solutions graphically. The physical existence of wormhole solutions can be examined through null/weak energy conditions of perfect fluid and null energy condition of the effective energy–momentum tensor. The graphical interpretation of constructed wormhole solutions ensures the existence of physically viable and traversable wormholes for all models. It is concluded that the constructed wormholes are found to be stable in most of the cases.

Quantum coherence is an essential feature of quantum mechanics and is an important physical resource in quantum information. Recently, the resource theory of quantum coherence has been established parallel with that of entanglement. In the resource theory, a resource can be well defined if given three ingredients: the free states, the resource, the (restricted) free operations. In this paper, we study the resource theory of coherence in a different light, that is, we consider the total coherence defined by the basis-free coherence maximized among all potential basis. We define the distillable total coherence and the total coherence cost and in both the asymptotic regime and the single-copy regime show the reversible transformation between a state with certain total coherence and the state with the unit reference total coherence. Extensively, we demonstrate that the total coherence can also be completely converted to the total correlation with the equal amount by the free operations. We also provide the alternative understanding of the total coherence, respectively, based on the entanglement and the total correlation in a different way.

In this paper, we investigate the localization of a bulk gravitino field on the scalar-tensor branes and compare the result with that in the Randall–Sundrum-1 (RS1) model. The coupled chiral equations for the Kaluza–Klein (KK) modes of the gravitino field are obtained by fixing the gauge Ψ 5 = 0 and using the chiral KK decompositions. It is shown that, in the RS1 model for the left- and right-handed zero modes of the gravitino field, only one of them can be localized near one brane. For the massive modes, both chiral modes survive and the lower KK modes are localized near the IR brane from the four-dimensional physical coordinate point of view. However, for the scalar-tensor brane model, the localization of the gravitino chiral zero modes depends on the coupling parameter λ , and they will be not localized around anyone brane within a certain range of the parameter λ , which is quite different from the RS1 model. Furthermore, we also give the corresponding mass spectra of the massive KK gravitinos in the scalar-tensor model.

In this paper we introduce the p -deformed fermion algebra as a kind of generalization of the ordinary fermion algebra. We discuss the p -fermion algebra and its representation. We also find the generalized Pauli matrices related to the p -fermion algebra. As applications we discuss the thermodynamics in the canonical ensemble of the p -fermion and the p -fermion gas model.

In this paper we investigate the influence of thermal photons as an inevitable source of damping on the dynamics of a quantum optomechanics system consisting of a suspended membrane in an optical cavity. The membrane is putted inside the cavity, in such a way that it plays the role of a movable mirror for each subcavity. In this respect, we investigate about the tunnelling of the photons between the two subcavities as well as the dynamics of membrane position in the mean-field approximation. In particular, the influences of thermal photons (in the presence of ”photon” and ”phonon” loss rates) on the time evolution of the above-mentioned quantities are evaluated and studied through which it is observed that the thermal photons considerably affects on the population inversion of photons number whenever the square coupling constant of cavity–membrane is weak. Inversely, the influence of thermal photons on the position of membrane is more visible for strong square coupling. Furthermore, it is demonstrated that generally the discussed properties can be appropriately adjusted by tuning the involved damping parameters.