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Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in $n+2$ dimensions, equipped with its covariantly constant null Killing vector field. Reparametrization of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schr\"odinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaitre and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit., Comment: 34 pages, no figures. Minor corrections, some references added

This paper examines theoretically a novel mechanism of generating negative (pulling) radiation force for acoustic manipulation of spherical carriers equipped with piezoelectric actuators in its inner surface. In this mechanism, the spherical particle is handled by common plane progressive monochromatic acoustic waves instead of zero-/higher- order Bessel beams or standing waves field. The handling strategy is based on applying a spatially uniform harmonic electrical voltage at the piezoelectric actuator with the same frequency of handling acoustic waves, in order to change the radiation force effect from repulsive (away from source) to attractive (toward source). This study may be considered as a start point for development of contact-free precise handling and entrapment technology of active carriers which are essential in many engineering and medicine applications.

The difference in the theoretical structure between monatomic and polyatomic gases in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (MET) of rarefied gases, which is free from the local equilibrium assumption. The MET theories of these two types of gases are based on the moment balance equations with different hierarchy structures due to whether the internal degrees of freedom of a molecule are incorporated in their distribution functions or not. In particular, the number of balance equations in the MET theory of polyatomic gases is greater than the number in the corresponding theory of monatomic gases. The closure procedure for the system of balance equations of polyatomic gases obtained in a recent paper (Arima et al., 2014) is adopted. We prove that the solutions for polyatomic gases converge, in the limit where the degrees of freedom of a molecule D tend to 3, to the ones for monatomic gases provided that we impose appropriate initial conditions compatible with monatomic gases. Thus a MET theory of rarefied monatomic gases can be identified as a singular limit of the corresponding MET theory of rarefied polyatomic gases. As illustrative examples, the asymptotic behaviors when D → 3 in the dispersion relation of ultrasonic waves and in the shock wave structure are shown.

Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrodinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.

The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\it i.e.} $\R \times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${\cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.

Under investigation in this paper is a nonautonomous Kadomtsev–Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painleve analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

This paper investigates the possibility to extract optimum information about the momentum and position variables of a quantum mechanical system. For the observation we use a pair of independent detectors, which contribute their own noise to the recorded result. In the optimal case the setup measures the Q-distribution leading to antinormally ordered expectation values. The class of initial detector states to be used is discussed, and the relation to measurement theory is elucidated. The paper summarizes and unifies earlier works by Husimi, Arthurs, and Kelly and Braunstein, Caves and Milburn. A realization in quantum optics is suggested.

In this paper, by following the procedure of statistical mechanics we present the systematic calculational rules for evaluating the reaction rate of a generic dynamical process taking place in a heat bath. These rules are formulated within the framework of real-time thermal field theory (RTFT), in terms of the Feynman-like diagrams, the so-called circled diagrams. With the machinery developed in this paper we can establish the finite temperature generalization of the Cutkosky, or the cutting rules in quantum field theory at zero temperature. We have also studied the relation between the imaginary part of forward RTFT amplitude and the reaction rates; the imaginary part consists of various reaction rates. This is a finite temperature generalization of the optical theorem.

In this paper we investigate quasiparticles in graphene-based topological insulator with a wedge disclination in the presence of a uniform magnetic field. In particular, we consider a massive spinless model. The Landau levels are analytically found for the described system. We show that the Landau levels are lifted for a specific range of the parameter {\nu}. In addition, we also show that, for appropriate parameter values, one finds gapless and gapped states., Comment: 14 pages, 6 figures

The purpose of this paper is to develop the theory of asymptotic electromagnetic fields as presented in the classical paper by Goldberg and Kerr ( J. Math. Phys. 5 (1964), 172) in terms of retarded moments of the source 4-current involving integrals over null hyperplanes. The aspects of asymptotic electromagnetic fields which we discuss in some detail are: (i) the geometric optics approximation, (ii) the multipole expansion of the 4-potential, (iii) the arbitrary dependence of the electromagnetic field on a null coordinate, (iv) the comparison between the Goldberg-Kerr approach and the construction of asymptotic electromagnetic fields using sources defined with the aid of derivatives of Dirac delta functions, and (v) the two degrees of freedom of polarisation of the asymptotic electromagnetic field. Some of these topics are studied with a source having only retarded pole and dipole moments or having only retarded pole, dipole, and quadrupole moments. This is purely for the purpose of keeping the calculations within reasonable bounds. The extension of such calculations to sources possessing retarded multipole moments of higher orders will in most cases be obvious.

The vibrations inside diatomic molecules are well modeled by the Morse potential and, therefore, the Morse nonlinear coherent states can be considered as approximations of diatomic molecules coherent states. Currently, the experimental realization of nonlinear coherent states for molecular systems is an interesting subject of investigation. In this paper, we analyze the nonclassical properties of different coherent states for a particle in the Morse potential. We find that the s u ( 2 ) algebra can be generalized by using an appropriate monotonically increasing function and that the bound states of particular diatomic molecules can be well described by the introduced algebra. We construct two types of generalized s u ( 2 ) coherent states satisfying all necessary requirements, mainly the resolution of identity, for the molecule 27 Al 1 H . We notice an anti-bunching effect for both types of coherent states by analyzing the second order correlation function.

In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the energy-momentum tensor and the Lorentz force density are presented. For an electric point charge, the generalized Lienard-Wiechert potentials and the corresponding electromagnetic field strength tensor are given as retarded integral expressions. Explicit formulas for the electromagnetic potential vector and electromagnetic field strength tensor of a uniformly moving point charge are found without any singularity and discontinuity. In addition, a world-line integral expression for the self-force of a charged point particle is given. The relativistic equation of motion of a charged particle coupled with electromagnetic fields in second gradient electrodynamics is derived, which is an integro-differential equation with nonlocality in time. For a uniformly accelerated charge, explicit formulas of the self-force and the electromagnetic mass, being non-singular, are given. Moreover, the wave propagation and the dispersion relations in the vacuum of second gradient electrodynamics are analyzed. Three modes of waves were found: one non-dispersive wave as in Maxwell electrodynamics, and two dispersive waves similar to the wave propagation in a collisionless plasma., 22 pages, 5 figures

In this paper, we study the effects of thermal fluctuations on thermodynamics of charged rotating and accelerating anti-de Sitter black hole. We first derive exact expressions of thermodynamic quantities such as entropy, Hawking temperature and angular velocity for slowly accelerating black hole. We then compute Smarr–Gibbs–Dehum relation and thermodynamical volume in extended phase space. To discuss the impact of quantum fluctuations, we evaluate leading-order correction terms to entropy which modify other thermodynamical equations of state. Finally, we calculate specific heat to examine the local stability of this black hole. It is found that the logarithmic corrections originated from thermal fluctuations induce instability to small black holes.

In this paper, we investigate the effect of minimal length on Einstein model of a gas of two-level atoms in thermal equilibrium with blackbody radiation at temperature T. We reformulate the classical Hamiltonian describing the interaction of atomic electrons with the electromagnetic field of blackbody radiation by employing Kempf Algebra to obtain the Hamiltonian with a minimal length. In the electric dipole approximation, we obtain the modified transition rate relations, and modified Einstein coefficients for broadband excitation. We utilize the modified quantities to obtain the modified cross-section in the resonant laser excitation. We deduce the upper bounds for the deformation parameter and minimal length.

Multimode quantum correlation has important applications in the field of quantum information. In this paper, we propose a compact scheme to generate multiple quantum correlated beams based on energy-level cascaded four-wave mixing (EC-FWM) process in a single atomic medium of rubidium. Injecting two strong pump beams with different frequencies and one weak probe beam into one rubidium vapor, four possible parametrically amplified FWM (PA FWM) processes can coexist under different phase matching conditions. Within the scheme, the weak probe beam is amplified and three coherent beams are generated, which can also be seen as an eight-wave mixing (EWM) process when certain phase matching condition is satisfied. Based on the energy level system of the scheme, three different cascaded structure models are employed to study the quantum correlation between the four generated beams. Amplitude and phase quadratures squeezing and intensity squeezing of the three- and four-mode are calculated via the input–output relations of the system. We found versatile multimode squeezing can be generated in all the structures, but the degree of squeezing and its distribution among the modes are different, depending on the specific structure. Furthermore, the relation of the quantum correlation, as well as the eigenmodes and eigenvalues of the four-mode quantum states are studied.

The motivation of this paper is based on the foundation of extended teleparallel gravity with matter coupling to prospect the accelerated expansion of the Universe. This theory based on the torsion scalar along with the trace term of energy stress tensor. We manipulate the spherical symmetric metric and anisotropic fluid to discuss the study of stellar structures. To interpret our research, we used the observational data of three stars. We adopt the process of parallelism of interior and exterior space-times to estimate the unspecified parameters used in the stellar discussion. Further, we discuss the stellar properties like energy density, progressive behavior of radial and tangential components of pressure, the anisotropic formation of the compact stars. We also analyze the physical presence of stars by discussing the energy conditions redshift and mass functions. We signify the stability of the system by examining the speed of sounds and EoS. We show the equilibrium of the system by analyzing the TOV equation. Finally, we show that our system in the discussion is physically stable and analytically viable.

In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. Here we consider an oscillator chain containing three-types of anharmonicity in the Fermi-Pasta-Ulam-Tsingou (FPUT) model: cubic $\alpha$- and quartic $\beta$-type nearest-oscillator interactions and the on-site (pinned) Klein-Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flow in different junctures of the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For $\alpha$-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and $\beta$-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flow become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Our perturbative calculations provide a measure of the strength of nonlinearity for nonlinear open quantum systems, which may help control the mesoscopic heat transport distinct from or close to linear transport. Furthermore, our results also give a benchmark for the numerical challenge of simulating heat transport. Our setup and predictions can be implemented and verified by investigating heat flow in an array of Josephson junctions in the limit of large Josephson energy with the platform of circuit QED., Comment: 44 pages, 11 figures. Close to the published version

This paper is concerned with the effect of anisotropic pressure in the mass–radius relation and dynamical stability for strongly magnetized white dwarfs using Bowers and Liang model. Strongly magnetized white dwarfs is hot topic where it is believed that it can be a progenitor for some peculiar type Ia supernovae that was observed recently. In order to get the equation of state we assumed that the internal magnetic field strength of the star is constant and strong enough to oblige the electrons to occupy the first Landau level. We dealt with the problem by using both relativistic and non-relativistic equilibrium equations. In non-relativistic formalism, the mass–radius relation of the star was investigated and it is found that the dynamical stability of the star does not depend on the radius but on the mass of the star. In relativistic formalism, it is found that the radius of the star decreases in comparison with non-relativistic case. Also the maximum mass limit of the star does not exceed the non-relativistic one in isotropic case. Unfortunately, in both cases the predicted internal magnetic field of the star always exceeds the magnetic field strength needed for the stability. This leads to weaken the stability of the star and making the star deviates from the spherical configuration to oblate spheroidal shape. Thus according to this model the magnetic white dwarfs configurations are unstable and unbound.

This paper is a manual with tips and tricks for programming tensor network algorithms with global S U ( 2 ) symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of codes, such as useful data structures to store the tensors, practical ways of manipulating them, and adapting typical functions for symmetric tensors. Here we do not restrict ourselves to any specific tensor network method, but keep always in mind that the implementation should scale well for simulations of higher-dimensional systems using, e.g., Projected Entangled Pair States, where tensors with many indices may show up. To this end, the structural tensors (or intertwiners) that arise in the usual decomposition of S U ( 2 ) -symmetric tensors are never explicitly stored throughout the simulation. Instead, we store and manipulate the corresponding fusion trees – an algebraic specification of the symmetry constraints on the tensor – in order to implement basic S U ( 2 ) -symmetric tensor operations. This fusion tree approach is readily extensible to anyonic systems, as we demonstrate for a chain of Fibonacci anyons.

We analyze a recent treatment of the interaction of a magnetic quadrupole moment with a radial electric field for a non-relativistic particle in a rotating frame and show that the derivation of the equations in the paper is anything but rigorous. The authors presented eigenvalues and eigenfunctions for two sets of quantum numbers as if they belonged to the same physical problem when they are solutions for two different models. In addition to it, the authors failed to comment on the possibility of multiple solutions for every set of quantum numbers.

This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie–Bohm, hydrodynamic, or stochastic models of quantum mechanics where the physical basis for single-valuedness has been questioned. It first constructs a large class of multi-valued wave functions based on knotted vortex filaments familiar in fluid mechanics, and then it argues that for free particles, these systems will likely radiate electromagnetic radiation if they are charged or have multipolar moments, and only if they are single-valued will they definitely be radiationless. Thus, it is proposed that electromagnetic radiation is possibly the mechanism that causes quantum wave functions to relax to states of single-valuedness, and that multi-valued states might possibly exist in nature for transient periods of time. If true, this would be a modification to the standard quantum mechanical formalism. A prediction is made that electrons in vector Aharonov–Bohm experiments should radiate energy at a rate dependent on the solenoid’s magnetic flux.

Doped SrTiO$_3$, one of the most dilute bulk systems to display superconductivity, is perhaps the first example of an unconventional superconductor, as it does not fit into the standard BCS paradigm. More than five decades of research has revealed a rich temperature-carrier concentration phase diagram that showcases a superconducting dome, proximity to a putative quantum critical point, Lifshitz transitions, a multi-gap pairing state and unusual normal-state transport properties. Research has also extended beyond bulk SrTiO$_3$, ushering the new field of SrTiO$_3$-based heterostructures. Because many of these themes are also featured in other quantum materials of contemporary interest, recent years have seen renewed interest in SrTiO$_3$. Here, we review the challenges and recent progress in elucidating the superconducting state of this model system. At the same time that its extreme dilution requires to revisit several of the approximations that constitute the successful Migdal-Eliashberg description of electron-phonon superconductivity, including the suppression of the Coulomb repulsion via the Tolmachev-Anderson-Morel mechanism, it opens interesting routes for alternative pairing mechanisms whose applicability remains under debate. For instance, pairing mechanisms involving longitudinal optical phonons have to overcome the hurdles created by the anti-adiabatic nature of the pairing interaction, whereas mechanisms that rely on the soft transverse optical phonons associated with incipient ferroelectricity face challenges related to the nature of the electron-phonon coupling. Proposals in which pairing is mediated by plasmons or promoted locally by defects are also discussed. We finish by surveying the existing evidence for multi-band superconductivity and outlining promising directions that can potentially shed new light on the rich problem of superconductivity in SrTiO$_3$., review paper; submitted to the Annals of Physics special issue "Eliashberg 90"; revised version with updated references

The theory of triplet superconductivity in ferromagnetic metals based on electron-electron interaction by spin fluctuation exchange is developed. The equations for the upper critical field temperature dependence are derived. In contrast to the similar equations for the superconductivity in two band metals they contain the pairing amplitudes and the Fermi velocities depending on magnetic field. The critical field behaviour near the critical temperature and at T = 0 is established analytically., The paper targeted for the AoP special issue in honour of G.M.Eliashberg 90 jubilee (9pages,1figure)

This paper investigates the dynamical evolution of thin-shell developed from a class of d -dimensional black holes. The components of stress–energy tensor of surface matter at thin-shell are evaluated through the Lanczos equations. The corresponding equations of motion and effective potential describe the expansion, collapse and saddle points. It is found that expanding and collapsing characteristics of the shell are enhanced for higher-dimensional spacetimes. We also investigate the dynamics of thin-shell in the presence of massless and massive scalar fields. The evolutionary behavior of massless scalar shell is greatly affected by the black hole parameters. The massive scalar field indicates the oscillation of thin-shell for d = 5 with specific values of the parameters. This scalar shell shows collapse for higher-dimensional Schwarzschild–de Sitter and quintessence manifolds while it indicates expansion for higher-dimensional Reissner–Nordstrom black hole.

Recently, He and Ma introduced a generic method to generate static, circular symmetric regular black holes in 2+1-dimensional gravity minimally coupled to nonlinear electrodynamics (NED). In their formalism, they considered spacetimes filled with pure radial electric field and as examples four different cases were studied. In accordance with their method, in the weak field limit, the regular black holes are supposed to reduce to the charged BTZ black hole and the NED Lagrangian admits the Maxwell linear theory. Inspired from their paper, in this Letter we address a common feature of the NED Lagrangian which has not been noticed by the author. It will be shown that the NED Lagrangians are actually hybrid functions whose behaviors at weak and strong field regimes are different. This is in analogy with its 3+1-dimensional counterpart which has been pointed out long ago by Bronnikov.

The aim of this paper is to propose a criterion of spontaneous symmetry breaking that makes reference to the properties of pure phases defined by a translationally invariant state. By avoiding any reference to the ground state, at the basis of the standard approach, this criterion applies to a wider class of models. An interesting application is the breaking of time translations. Indeed, we discuss explicit theoretical models which exhibit the prototypical features of quantum time crystals, without the need of a time-dependent Hamiltonian., 20 pages, published in Annals of Physics

In this paper, we study the relativistic quantum dynamics of spin- 1 2 particles interact with electromagnetic potentials in three-dimensional space–time. We solve the Dirac oscillator including the Aharonov–Bohm potential in (1+2)-dimensional rotational symmetry Gurses metric (Gurses, 1994), and analyze the Aharonov–Bohm effect on the energy eigenvalues.

The Newman-Janis (NJ) method is a prescription to derive the Kerr space-time from the Schwarzschild metric. The BTZ, Kerr and five-dimensional Myers-Perry (MP) black hole solutions have already been generated by different versions of the NJ method. However, it is not known how to generate the metric of higher-dimensional (d > 6) rotating black holes by this method. In this paper, we propose the simplest algorithm for generation of the five-dimensional MP metric with two arbitrary angular momenta by using the Kerr-Schild form of the metric and quaternions. Then, we present another new two-step version of the NJ approach without using quaternions that generate the five-dimensional MP metric with equal angular momenta. Finally, the extension of the later procedure is explained for the higher odd-dimensional rotating black holes (d > 5) with equal angular momenta., 9 pages

In this paper we present a new extended complex nonlinear Klein–Gordon Lagrangian density, which bears a single non-topological soliton solution with a specific rest frequency ω s in 1 + 1 dimensions. There is a proper term in the new Lagrangian density, which behaves like a massless spook that surrounds the single soliton solution and opposes any internal changes. In other words, any arbitrary variation in the single soliton solution leads to an increase in the total energy. Moreover, just for the single soliton solution, the general dynamical equations are reduced to those versions of a special type of the standard well-known complex nonlinear Klein–Gordon systems, as its dominant dynamical equations.

In a recent paper, Deguchi et al. (2019), the authors proposed an analysis of the damped quantum harmonic oscillator in terms of ladder operators. This approach was shown to be partly incorrect in Bagarello et al. (2019), via a simple no-go theorem. More recently, (Deguchi and Fujiwara, 2019), Deguchi and Fujiwara claimed that our results in Bagarello et al. (2019) are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistakes in Deguchi et al. (2019) and Deguchi and Fujiwara (2019). We also propose a very simple example clarifying the core of the problem.

The main aim of this paper is to obtain analytic relativistic anisotropic spherical solutions in f ( R , T ) scenario. To do so we use modified Durgapal–Fuloria metric potential and the pressure anisotropy condition is imposed in order to obtain the effective anisotropic factor Δ . Besides, a notable and viable election on f ( R , T ) gravity formulation is taken. The choice of f ( R , T ) function modifies the matter sector only, including new ingredients to the physical parameters that characterize the model such as density, pressure, subliminal speeds of sound, surface redshift etc. We analyze all the physical and mathematical general requirements of the configuration taking M = 1 . 04 M ⊙ and varying χ from − 0 . 1 to 0.1. It is shown by the graphical procedure that χ 0 yields a more compact object in comparison when χ ≥ 0 (where χ = 0 . 0 corresponds to general relativity) and increases the value of the surface redshift. However, negative values of χ introduce in the system an attractive anisotropic force (inward) and the configuration is completely unstable (corroborated employing Abreu’s criterion). Furthermore, the model in Einstein gravity theory presents cracking while for χ > 0 the system is fully stable. The relationship between effective radial pressure p r and effective density ρ is discussed and obtained. This is achieved by establishing the corresponding equation of state.

Using the small volume expansion the mass spectrum and deconfining temperature of 4 d non-Abelian gauge theory are evaluated. Including non-perturbative features by restoring symmetries which were broken in perturbation theory we obtain results which are valid up to intermediate volumes. The mass spectrum obtained is in good agreement with Luscher's small volume limit and with Monte Carlo Data for medium sized volumes. Asymmetric volumes enable us to calculate the deconfining temperature and we find reasonable agreement with Monte Carlo calculations. Paper I outlines the general concepts and presents results for the SU (2) gauge group. Paper II shall generalize the approach to SU (3).

It is known that the formal perturbation theory of spinor quantum electrodynamics in three space-time dimensions requires no ultraviolet renormalization. We introduce an ondelette cluster expansion (with an infrared cutoff) which converges without counter-terms for weak coupling, thus making the knowledge rigorous. Following the formalism of Lesniewski, we integrate out the bosons at the outset to make the genuine absence of a large-field problem transparent. The combinatoric part of the convergence proof—indeed the precise case-by-case definition of the inductive expansion—is reserved for a subsequent paper. In this paper we publicize the language of ondelette diagrams—originally introduced by Federbush—and describe the correspondence to Feynman diagrams.

In this paper thermal entanglement between two identical two-level atoms within a bichromatic cavity including Kerr nonlinear coupler is investigated. In this study, besides atom–field interaction, the field–field (via linear and Kerr-type couplings) and atomic dipole–dipole interactions are also included. It is also assumed that the cavity is held at a temperature T , so that all atom–photon states with probabilities defined by Boltzmann factor are present. Using a canonical transformation, the presented model is converted to a generalized form of Jaynes–Cummings model. After introducing Casimir operators of the system, it is shown that the Hamiltonian representation is block-diagonal. Diagonalizing each block, the thermal (Gibb’s) density matrix, written in the bases of total Hamiltonian, is obtained. The reduced atomic density matrix and consequently the concurrence, as a measure of entanglement, are obtained by partial tracing of thermal density matrix over the bichromatic photonic states. The concurrence vanishes at zero temperature, indicating that the ground state is separable, exhibits a maximal at a critical temperature and terminates at a finite temperature. The influences of coupler nonlinearities and dipole–dipole coupling on the thermal atom–atom entanglement are also addressed in detail.

In this work we offer an approach to protect the entanglement based on the anti-symmetric property of the hamiltonian. Our main objective is to protect the entanglement of a given initial three-qubit state which is governed by hamiltonian of a three-spin Ising chain in site-dependent transverse fields. We show that according to anti-symmetric property of the hamiltonian with respect to some operators mimicking the time reversal operator, the dynamics of the system can be effectively reversed. It equips us to control the dynamics of the system. The control procedure is implemented as a sequence of cyclic evolution; accordingly the entanglement of the system is protected for any given initial state with any desired accuracy an long-time. Using this approach we could control not only the multiparty entanglement but also the pairwise entanglement. It is also notable that in this paper although we restrict ourselves mostly within a three-spin Ising chain in site-dependent transverse fields, our approach could be applicable to any n-qubit spin system models., Comment: 13 pages, 4 figures

In this paper the Dirac and Faddeev–Jackiw formulation for Einstein’s theory in the G → 0 limit is performed; the fundamental Dirac’s and Faddeev–Jackiw brackets for the theory are obtained. First, the Dirac brackets are constructed by eliminating the second class constraints remaining the first class ones, then we fix the gauge and we convert the first class constraints into second class constraints and the new fundamental Dirac’s brackets are computed. Alternatively, we reproduce all relevant Dirac’s results by means of the symplectic method. We identify the Faddeev–Jackiw constraints and we prove that the Dirac and the Faddeev–Jackiw brackets coincide to each other.

The dependence of physical properties of the electrically charged monopole–antimonopole pair (MAP) solutions in the Higgs self-coupling constant is previously investigated. In this paper we study the three-poles monopole–antimonopole chain (MAC) solutions. The study includes ϕ -winding number n = 2 , 3 , and 4. For the case of n = 2 , no bifurcation and geometrical transition is detected for the interval of the study. For the case of n = 3 , two geometrical transitions happen along the fundamental solution. Also two bifurcations and one joining point is detected for the interval of study. The case of n = 4 includes one bifurcation. There is also a geometrical transition along the fundamental solution and two transitions along the Higher energy bifurcating branch. This study implies that during some specific kind of geometrical transition, a magnetic and electric charge transition occurs for the pole which is located at the origin.

In this paper, a higher-order ( 2 + 1 ) -dimensional nonlinear Schrodinger-type equation is investigated, which describes the nonlinear spin dynamics of the ( 2 + 1 ) -dimensional Heisenberg ferromagnetic spin chain with bilinear and biquadratic interaction. Lax pair and infinite-number conservation laws are constructed, which could prove the existence of the multi-soliton solutions. Via the auxiliary function, bilinear forms and dark-soliton solutions are derived. Properties and interaction patterns for the dark solitons are investigated: (i) Effects on the dark solitons arising from the bilinear interaction, biquadratic interaction and lattice parameter are discussed. (ii) Through the asymptotic analysis, elastic and inelastic interaction between the two solitons is discussed analytically and graphically, respectively. Due to the elastic interaction, amplitudes and velocities of the two dark solitons remain unchanged with the distortion of the interaction area, except for certain phase shifts. However, in virtue of the inelastic interaction, amplitudes of the dark solitons reduce to zero, without the distortion. (iii) Elastic interaction among the three dark solitons is investigated, which implies that the properties of the elastic interaction among the three are similar to that between the two, except for the more complicated distortion. Inelastic–elastic interaction is also investigated, which implies that the interaction between the inelastic region and the dark soliton is elastic. (iv) Linear stability analysis is proposed, which is used to analyze the properties of modulation instability and proves that the dark solitons are modulationally stable.

In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2 + 1 -dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.

The study of Majorana fermions is of great importance for the implementation of a quantum computer. These modes are topologically protected and very stable. It is now well known that a p -wave superconducting wire can sustain, in its topological non-trivial phase, Majorana quasi-particles at its ends. Since this type of superconductor is not found in nature, many methods have been devised to implement it. Most of them rely on the spin–orbit interaction. In this paper we study the superconducting properties of a two-band system in the presence of antisymmetric hybridization. We consider inter-band attractive interactions and also an attractive interaction in one of the bands. We show that superconducting fluctuations with p -wave character are induced in the non-interacting band due to the combined effects of inter-band coupling and hybridization. In the case of a wire, this type of induced superconductivity gives rise to four Majorana modes at its ends. The long range correlation between the different charge states of these modes offers new possibilities for the implementation of protected q -bits.

In this paper, we study the $\alpha$th power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations related to the $\alpha$th power of negativity and the Convex- Roof Extended Negativity are obtained for N-qubit states. We also give a tighter bound of hierarchical monogamy inequality for the entanglement of formation. We find that the GHZ state and W state can be used to distinguish the $\alpha$th power the concurrence for $0, Comment: 6 pages, 2 figures

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity shows very much different result., Comment: 16 pages, 1 figure, version to match published version in Annals of Physics

In the present paper we show that the complete list of special Killing forms on the 5-dimensional Sasaki–Einstein spaces Y p , q can be extracted using the symplectic potential and the classical Delzant construction. The results achieved here agree with previous ones obtained by direct computation, proving the reliability of the method which stands in fact as a general algorithm for toric Sasaki–Einstein manifolds. Finally, we discuss the integrability of geodesic motion in Y p , q spaces.

In this work the conservative system of N identical two-level atoms coupled with a quantized electromagnetic field, prepared via a single photon Fock state, is investigated. The non-zero initial detuning of the Fock state is under consideration. The present paper reveals and investigates the certain fundamental problems concerning the application of the dipole approximation for the “interaction” of the quantized electromagnetic field with the many-body system. Here, we do not restrict ourselves to any boundary conditions and do not apply the “Weisskopf–Wigner” and “Markovian” approximations. We developed technique to estimate the most “problematic” integral expressions appearing in the quantum optic theory of a photon scattering by a polyatomic system. The Laplace transformation was applied in order to solve the corresponding N -particle evolution equations. It was shown, the dipole approximation, that is determined by a gauge non-invariant Hamiltonian, can result in certain irreversible processes during the system evolution with time. Namely, possible collective (coherent) modes for the probability amplitudes decay with time. At the same time, the mode corresponding to the field detuning frequency does not vanish. However, the ability to decay vanishes for the collective (coherent) modes, when the used inverse Laplace transformation undergoes a commutation in the specific limits of the problem. The investigated here structure of the solutions for the evolution equations therefore raises the fundamental problem about the correct representation of a damping phenomena in the commonly accepted approximations. The corresponding N -particle state amplitudes are calculated for the several space configurations of the closed conservative system. The elaborated theory allows to describe analytically the evolution of the system components with time for any space configurations, including the cases with relative distances between atoms shorter or larger than the emission wavelength.

This paper is devoted to the theory of quantum electromagnetic field in an optically dense medium. Self-consistent equations describing interaction between a quantum field and a quantum dielectric medium are obtained from the first principles, i.e., outside a phenomenological description. Using these equations, we found a transformation (of the Bogoliubov transformation type) that converts the operators of the “vacuum” field into operators of collective perturbations of the field and an ensemble of atoms, that is, photons in the medium. Transformation parameter is the refractive index of the wave mode considered. It is shown that besides the energy of the collective electromagnetic field, the energy of photons in the medium includes the energy of the internal degrees of freedom of the substance and the energy of near-field dipole interaction between atoms in the polarized medium. The concept of negative energy photons is introduced on the basis of self-consistent equations.

Dyson–Schwinger equations determine the Green functions G r ( α , L ) in quantum field theory. Their solutions are triangular series in a coupling constant α and an external scale parameter L for a chosen amplitude r , with the order in L bounded by the order in the coupling. Perturbation theory calculates the first few orders in α . On the other hand, Dyson–Schwinger equations determine next-to { j } -leading log expansions, G r ( α , L ) = 1 + ∑ j = 0 ∞ ∑ M p j M α j M ( u ) . ∑ M sums for any finite j a finite number of functions M in u . Here, u is the one-loop approximation to G r , for example, for the (inverse) propagator in massless Yukawa theory, u = α L / 2 . The leading logs come then from the trivial representation, e.g. M ( u ) = 1 − 1 − 2 u in massless Yukawa theory. The respective period at j = 0 is p 0 M ( u ) = 1 . All non-leading logs are organized by corresponding suppressions in powers α j . We describe an algebraic method to derive all next-to { j } -leading log terms from the knowledge of the first ( j + 1 ) terms in perturbation theory and their filtrations. This implies the calculation of the functions M ( u ) and periods p j M . In the first part of our paper, we investigate the structure of Dyson–Schwinger equations and develop a method to filter their solutions. Applying renormalized Feynman rules maps each filtered term to a certain power of α and L in the log-expansion. Based on this, the second part derives the next-to { j } -leading log expansions. Our method is general. Here, we exemplify it using the examples of the propagator in Yukawa theory and the photon self-energy in quantum electrodynamics. In particular, we give explicit formulas for the leading log, next-to-leading log and next-to-next-to-leading log orders in terms of at most three-loop Feynman integrals. The reader may apply our method to any (set of) Dyson–Schwinger equation(s) appearing in renormalizable quantum field theories.

Experiments of multi-photon entanglement have been performed by several groups. Obviously, an increase on the photon number for fidelity estimation and quantum state tomography causes a dramatic increase in the elements of the positive operator valued measures (POVMs), which results in a great consumption of time in measurements. In practice, we wish to obtain a good estimation of fidelity and quantum states through as few measurements as possible for multi-photon entanglement. Phaselift provides such a chance to estimate fidelity for entangling states based on less data. In this paper, we would like to show how the Phaselift works for six qubits in comparison to the data given by Pan’s group, i.e., we use a fraction of the data as input to estimate the rest of the data through the obtained density matrix, and thus goes beyond the simple fidelity analysis. The fidelity bound is also provided for general Schrodinger Cat state. Based on the fidelity bound, we propose an optimal measurement approach which could both reduce the copies and keep the fidelity bound gap small. The results demonstrate that the Phaselift can help decrease the measured elements of POVMs for six qubits. Our conclusion is based on the prior knowledge that a pure state is the target state prepared by experiments.

Under investigation in this paper are the inhomogeneous nonlinear Schrodinger Maxwell–Bloch (INLS-MB) equations which model the propagation of optical waves in an inhomogeneous nonlinear light guide doped with two-level resonant atoms. Higher-order nonautonomous breather as well as rogue wave solutions in terms of the determinants for the INLS-MB equations are presented via the n -fold variable-coefficient modified Darboux transformation. The interactions among two nonautonomous breathers are graphically discussed, including the fundamental breather, bound breather, two-breather compression and two-breather evolution, etc. Moreover, several patterns of the higher-order rogue waves are also exhibited, such as the square rogue wave, two- and three-order periodic rogue waves, periodic fission and fusion, two-order stationary rogue waves, and recurrence of the two-order rogue waves. The character of the trajectory of the two-order periodic rogue wave is analyzed. Additionally, a novel type of interaction, namely, the collision between the breather and long-lived rogue waves, is found to be elastic. Our results could be useful for controlling the nonautonomous optical breathers and rogue waves in the inhomogeneous erbium doped fiber.

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.

Under investigation in this paper is a fifth-order nonlinear Schrodinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-on and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.