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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.

It is commonly believed that γN → ΦN is a good reaction to study the Pomeron. By considering the existing data and the various properties associated with a pole, we show that it would be experimentally hard for this reaction to reveal departures from a pole-type Pomeron. For testing factorization and relative reality of all amplitudes, our claim uses the experimentally indicated approximate s-channel meson-helicity conservation and also, almost pure nature parity in the crossed channel.

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 letter, starting from recent experiments about the circular motion of a rotor with an absorber of photons emitted by a Mossbauer source, we want to underline some mathematical aspects in General Relativity framework. We do not want to discuss in detail the different physical interpretations of the experimental results proposed during the recent years and we do not want to propose a new one. Indeed, starting from a paper awarded to Gravity Research Competition 2018, the aim of our work is to analyze three different types of time involved in this experiment linking a term introduced in the above mentioned paper, to the difference between coordinate and physical velocity of light.

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 is a continuation of Paper I (Toutounji, 2017) of which motivation was testing the applicability of Morse oscillator propagator whose analytical form was derived by Duru (1983). This is because the Morse oscillator propagator was reported (Duru, 1983) in a triple-integral form of a functional of modified Bessel function of the first kind, which considerably limits its applicability. For this reason, I was prompted to find a regime under which Morse oscillator propagator may be simplified and hence be expressed in a closed-form. This was well accomplished in Paper I. Because Morse oscillator is of central importance and widely used in modelling vibrations, its propagator applicability will be extended to applications in quantum dynamics and spectroscopy as will be reported in this paper using the off-diagonal propagator of Morse oscillator whose analytical form is derived.

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.

In the present paper, we study rotating regular black hole (RBH) in the model of nonlinear electrodynamics (NED) in the framework of General Relativity (GR). The paper explores derivation of the generic form of rotating RBH solutions which can be written in Kerr-like form in Boyer-Lindquist coordinates. It is shown that RBH solutions depend on NED Lagrangian. Lastly, we also showed that Kerr–Newman-Taub-NUT spacetime, which is solution of Einstein-Maxwell equations, can be a candidate for one of exact analytical rotating RBH solution by calculating curvature invariants at origin r = 0 , as well as, Kerr-Taub-NUT and Taub-NUT spacetimes.

As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is the eigen-value of the canonical orbital angular momentum (OAM) operator of the electron. The eigen-energies of the system depend only on the first quantum number $n$, and the second quantum number $m$ does not correspond to any direct observables. This seems natural since the canonical OAM is generally believed to be a {\it gauge-variant} quantity, and observation of a gauge-variant quantity would contradict a fundamental principle of physics called the {\it gauge principle}. In recent researches, however, Bliohk et al. analyzed the motion of helical electron beam along the direction of a uniform magnetic field, which was mostly neglected in past analyses of the Landau states. Their analyses revealed highly non-trivial $m$-dependent rotational dynamics of the Landau electron, but the problem is that their papers give an impression that the quantum number $m$ in the Landau eigen-states corresponds to a genuine observable. This compatibility problem between the gauge principle and the observability of the quantum number $m$ in the Landau eigen-states was attacked in our previous letter paper. In the present paper, we try to give more convincing answer to this delicate problem of physics, especially by paying attention not only to the {\it particle-like} aspect but also to the {\it wave-like} aspect of the Landau electron., Slightly compactified version to appear in Annals of Physics

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

Over 80 years ago Samuel Wilks proposed that the “generalized variance” of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the “Wilks standard deviation” –the square root of the generalized variance–is indeed the standard deviation of a random vector. We further establish that the “uncorrelation index” –a derivative of the Wilks standard deviation–is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: “randomness measures” and “independence indices” of random vectors. In turn, these general notions give rise to “randomness diagrams”—tangible planar visualizations that answer the question: How random is a random vector? The notion of “independence indices” yields a novel measure of correlation for Levy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.

The study of the complex Ginzburg–Landau equation, which can describe the fiber laser system, is of significance for ultra-fast laser. In this paper, dromion-like structures for the complex Ginzburg–Landau equation are considered due to their abundant nonlinear dynamics. Via the modified Hirota method and simplified assumption, the analytic dromion-like solution is obtained. The partial asymmetry of structure is particularly discussed, which arises from asymmetry of nonlinear and dispersion terms. Furthermore, the stability of dromion-like structures is analyzed. Oscillation structure emerges to exhibit strong interference when the dispersion loss is perturbed. Through the appropriate modulation of modified exponent parameter, the oscillation structure is transformed into two dromion-like structures. It indicates that the dromion-like structure is unstable, and the coherence intensity is affected by the modified exponent parameter. Results in this paper may be useful in accounting for some nonlinear phenomena in fiber laser systems, and understanding the essential role of modified Hirota method.

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states and interacting via $k$-body interactions, we have EGUE($k$) and the embedding algebra is $U(N)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (same initial and final systems), nuclear beta and double beta decay (different initial and final systems), particle addition to/removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities, we have derived formulas for lower order bivariate moments of the strength densities generated by a variety of transition operators. For a spinless fermion system, using EGUE($k$) representation for Hamiltonian and an independent EGUE($t$) representation for transition operator, finite-$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. Moments formulas are also derived for transition operator that removes $k_0$ number of particles from $m$ fermion system. Numerical results obtained using the exact formulas for two-body ($k=2$) Hamiltonians (in some examples for $k=3,4$) and the asymptotic formulas clearly establish that in general the smoothed form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed., 65 pages, 5 figures, 4 tables; some sections of the paper overlap considerably with the arXiv papers 1106.0395, 1411.6391 and 1501.07670

We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state" (Verbatim from ref. 2). This was the starting point of the popular "black hole (BH) information paradox". In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schr\"odinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of an unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schr\"oedinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in an unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox., Comment: 18 pages, definitive version accepted for publication in Annals of Physics. Comments are welcome. The results in arXiv:1210.7747 have been partially reviewed. Dedicated to the memory of the latter IFM Secretary Franco Pettini

The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin–orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has non-trivial superconducting properties, if the k -dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l and l + 1 . In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.

This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle as well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelarations. We show that the incorporation of rotational accelerations requires a class of \emph{loop prolongations} of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-stablished framework for implementing symmetry transformations in quantum mechanics., Comment: 40 pages

In a previous paper, Grassi (2012) [39] , a new entropy form has been proposed for which it is possible to obtain a stationary solution of the Non-Linear Fokker–Planck equation (referred as NLFP) with coulombic-like potentials. In this paper we analyze the stationary solution of NLFP obtained by using pure coulombic potentials and we will use this solution to study an “atomic-like” system.

A contribution of virtual electron states with large wave numbers to the self-energy of an electron bound in the weak Coulomb field is analyzed in the context of the evaluation method suggested in the previous paper. The contribution is of the order α ( Z α ) 5 . The same value for this contribution is found here as the one found in the previous calculations using different evaluation methods. When we add the remaining terms of the order α ( Z α ) 5 to the calculation of the self-energy effect in hydrogen-like ions presented in the previous paper we find a very good agreement with numerical evaluations. The relative difference between present and numerical evaluations ranges from 2 parts in 10 6 for Z = 1 up to 6 parts in 10 4 for Z = 10 .

In this paper, a quantum transport theory for describing photonic dissipative transport dynamics in nanophotonics is developed. The nanophotonic devices concerned in this paper consist of on-chip all-optical integrated circuits incorporating photonic bandgap waveguides and driven resonators embedded in nanostructured photonic crystals. The photonic transport through waveguides is entirely determined from the exact master equation of the driven resonators, which is obtained by explicitly eliminating all the degrees of freedom of the waveguides (treated as reservoirs). Back-reactions from the reservoirs are fully taken into account. The relation between the driven photonic dynamics and photocurrents is obtained explicitly. The non-Markovian memory structure and quantum decoherence dynamics in photonic transport can then be fully addressed. As an illustration, the theory is utilized to study the transport dynamics of a photonic transistor consisting of a nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the external driven field is demonstrated.

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 paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative $\star$-product and the deformation of the Poisson bracket to an appropriate Lie bracket is the key element in introducing the quantization of classical Hamiltonian systems. The considered class of deformations and the corresponding $\star$-products contains as a special cases all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of $\star$-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the $\star$-multiplication. The most important result of the paper shows that developed formalism is more fundamental then the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally., Comment: to appear in Annals of Physics

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

In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we give details of the work. We start with Dyson’s Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.

The present paper outlines a basic theoretical treatment of decoherence and dephasing effects in interferometry based on single component BEC in double potential wells, where two condensate modes may be involved. Results for both two mode condensates and the simpler single mode condensate case are presented. A hybrid phase space distribution functional method is used where the condensate modes are described via a truncated Wigner representation, and the basically unoccupied non-condensate modes are described via a positive P representation. The Hamiltonian for the system is described in terms of quantum field operators for the condensate and non-condensate modes. The functional Fokker-Planck equation for the double phase space distribution functional is derived. Equivalent Ito stochastic equations for the condensate and non-condensate fields that replace the field operators are obtained, and stochastic averages of products of these fields give the quantum correlation functions used to interpret interferometry experiments. The stochastic field equations are the sum of a deterministic term obtained from the drift vector in the functional Fokker-Planck equation, and a noise field whose stochastic properties are determined from the diffusion matrix in the functional Fokker-Planck equation. The noise field stochastic properties are similar to those for Gaussian-Markov processes in that the stochastic averages of odd numbers of noise fields are zero and those for even numbers of noise field terms are sums of products of stochastic averages associated with pairs of noise fields. However each pair is represented by an element of the diffusion matrix rather than products of the noise fields themselves. The treatment starts from a generalised mean field theory for two condensate mode. The generalized mean field theory solutions are needed for calculations using the Ito stochastic field equations., Comment: To be published in Annals of Physics. Full version of paper, including all Appendices. Journal version only includes Appendix A. Appendices are in online supplementary material. Cross references to material in Appendices improved in Version 2 (5 July 2010). Minor amendments made in Version 3 (23 Nov 2010), including reference to Takagi factorisation of complex symmetric matrices

This work aims to obtain the effective dielectric constant tensor of a warm plasma in the spirit of the derivation of a mixing law. The medium is made of non point-like ions immersed in an electron gas with usual conditions relating the various lengths which define the problem. In this paper the ion dielectric constants are taken from their RPA responses as developed in a previous paper [1]. Furthermore the treatment of the screening effects is made through a mathematical redefinition of the initial problem as proposed in Ref. [1]. Here the complete calculation of the T-matrix describing the scattering of an electromagnetic wave on an isolated ion immersed in an “effective medium” is given. It is used for building , in the spirit of a mixing law, a self-consistent effective medium theory for the plasma dielectric tensor. We then extend the results obtained in Ref. [1] to higher orders in ion or dielectric inclusion densities. The techniques presented are generic and can be used in areas such as elasticity, thermoelasticity, and piezoelectricity.

This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D. Jentschura, Ann. Phys. (N.Y.) 313 (2004), pp. 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order formulas are provided for the oscillators of degrees 3 to 8, which lead to subleading corrections to the leading factorial growth of the perturbative coefficients describing the resonance energies. Numerical results are provided, and higher-order terms are found to be numerically significant. The resonances are described by generalized expansions involving intertwined non-analytic exponentials, logarithmic terms and power series. Finally, we summarize spectral properties and dispersion relations of anharmonic oscillators, and their interconnections. The purpose is to look at one of the classic problems of quantum theory from a new perspective, through which we gain systematic access to the phenomenologically significant higher-order terms.

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.

We have discovered an error in the numerical calculations for the extraction of parameters from the nucleon mass “data” presented in Sections 4 and 5 of our paper [M.R. Schindler, D.R. Phillips, Ann. Phys. 324 (2009) 682. Available from: ]. We present the corrected results and discuss the implications. We stress that the material presented in Sections 1–3 of our paper [M.R. Schindler, D.R. Phillips, Ann. Phys. 324 (2009) 682. Available from: ] is unaffected.

The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined "anyons", may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation., Comment: Invited review for the Annals of Physics

In a previous paper this author examined the Born expansion and isolated those parts of the expansion that contribute most significantly to the scattering amplitude for large momentum transfer collisions in inelastic collisions from the ground state of both hydrogen and helium. It turned out that certain terms where the scattering electron interacts once with the nucleus and once with the other electron dominate. The physical reason is that large momentum transfer collisions require the nucleus to take the bulk of the incident momentum but require an interaction with the one of the bound electrons to change the state of the atom. The arguments are quite general and this paper will extend this analysis by comparing the inelastic results obtained by this method for hydrogen and helium to a close coupling calculation with many intermediate states. Further, we will extend this analysis to the correction to the 1st Born result for elastic electron–hydrogen and electron–helium collisions and provide some results for scattering from the initial metastable states of hydrogen for large momentum transfer collisions. A comparison of the results of this analytic approach will be made to the numerical close coupling approach and experiments where available. The agreement is remarkable.

This is the first of two papers in which we study real and virtual photon-proton scattering in a nonperturbative framework. We classify different contributions to this process and identify the leading contributions at high energies. We then study the renormalisation of the photon-quark-antiquark vertex that occurs in the leading contributions. We find something like the dipole picture in one of these contributions but also find two correction terms which can potentially become large at small photon virtualities. In the second paper we will discuss the additional approximations and assumptions that are necessary to obtain the dipole model of high energy scattering from the results found here., 38 pages, 14 figures; v2: minor changes, references added, matches journal version

This paper follows in the tradition of direct-action versions of electromagnetism having the aim of avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass so as to arrive at a finite observed value. However, the direct-action approach ultimately failed in that respect because its initial exclusion of self-action was later found to be untenable in the relativistic domain. Pursing the same end, this paper examines instead a version of electromagnetism wherein mechanical action is excluded and self-action is retained. It is shown that the resulting theory is effectively interacting due to the presence of infinite forces. A vehicle for the investigation is a pair of classical point charges in a positronium-like arrangement for which the orbits are found to be self-sustaining and naturally quantized.

The purpose of this paper was to justify the fact that deterministic corpuscular description of a free particle can be made reconciled with its dual probabilistic wave description in complex space. It is found that the known wave-particle duality can be best manifested in complex space by showing that the wave motion associated with a material particle is just the phenomenon of projection of its complex motion into real space. To verify this new interpretation of matter wave, the equation of motion for a particle moving in complex space is derived first, then it is solved to reveal how the interaction between the real and imaginary motion can produce the particle’s wave motion observed in real space. The derived complex equation of motion for a “free” particle indicates that a so-called free particle is only free from classical potential, but not free from the complex quantum potential. Due to the action of this complex quantum potential, a free particle may move either right or left in a classical way retaining its corpuscular property, or may oscillate between the two directions producing a non-local wave motion. A propagation criterion is derived in this paper to determine when a particle follows a classical corpuscular motion and when it follows a quantum wave motion. Based on this new interpretation, the internal mechanism producing polarization of matter wave and the formation of interference fringes can all be understood from the particle’s motion in complex space, and the reason why wave function can be served as a probability density function also becomes clear.

This is the second in a series of two papers. While in Paper I we derive semiclassical Boltzmann transport equations and study their flow terms, here we address the collision terms. We use a model Lagrangean, in which fermions couple to scalars through Yukawa interactions and approximate the self-energies by the one-loop expressions. This approximation already contains important aspects of thermalization and scatterings required for quantitative studies of transport in plasmas. We compute the CP-violating contributions to both the scalar and the fermionic collision term., Comment: 52 pages, 12 figures; continuation of hep-ph/0312110; accepted for publication in Annals of Physics

We review in detail the construction of {\em all} stable static fermion bags in the 1+1 dimensional Gross-Neveu model with $N$ flavors of Dirac fermions, in the large $N$ limit. In addition to the well known kink and topologically trivial solitons (which correspond, respectively, to the spinor and antisymmetric tensor representations of O(2N)), there are also threshold bound states of a kink and a topologically trivial soliton: the heavier topological solitons (HTS). The mass of any of these newly discovered HTS's is the sum of masses of its solitonic constituents, and it corresponds to the tensor product of their O(2N) representations. Thus, it is marginally stable (at least in the large $N$ limit). Furthermore, its mass is independent of the distance between the centers of its constituents, which serves as a flat collective coordinate, or a modulus. There are no additional stable static solitons in the Gross-Neveu model. We provide detailed derivation of the profiles, masses and fermion number contents of these static solitons. For pedagogical clarity, and in order for this paper to be self-contained, we also included detailed appendices on supersymmetric quantum mechanics and on reflectionless potentials in one spatial dimension, which are intimately related with the theory of static fermion bags. In particular, we present a novel simple explicit formula for the diagonal resolvent of a reflectionless Schr\"odinger operator with an arbitrary number of bound states. In additional appendices we summarize the relevant group representation theoretic facts, and also provide a simple calculation of the mass of the kinks., Comment: A review paper, 95 pages, 1 eps figure. Latex Final version, accepted for publication in the Annals of Physics

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.

This paper looks for an entropy-like quantity having a monotonic time development. In the case of spontaneous emission, the final state usually consists of a single ground state assigning zero to the ordinary expressions for entropy. Thus entropy ceases to be a monotonic measure of the direction of time. The point is illustrated by a simple test case consisting of three levels coupled by spontaneous emission. It is shown how this case allows the definition of a monotonic function. Using the theory of non-Hermitian operators, the paper shows how such a function may be constructed in the general case, and it explores the main consequences of the expressions suggested. The generalization of the entropy concept is found to relate to time-reversal properties of the dynamics. The paper concludes by discussing open questions and possible further explorations.

The tunneling effect in multidimensional systems may be greatly influenced by the underlying chaotic dynamics which is generic in more than one-dimensional systems. Aiming at a classical dynamical description of chaotic tunneling, we have developed in the present paper a basic formulation for the complex-domain semiclassical wave-matrix of systems with 1.5 degrees of freedom, namely, periodically time-dependent 1D-scattering systems, which can be regarded as a minimal model of multidimensional systems. Using an autonomous 2D system equivalent to the periodically time-dependent system, the semiclassical expression of the wave-matrix described in the 1D time-dependent picture is derived. In the latter half of the paper, our semiclassical formulation is examined with two simple examples, i.e., an oscillating wall and an oscillating barrier. The semiclassical wave-matrix is constructed, paying particular attention to some problems which emerge by extending classical dynamics to complex domain, and the results are compared with the fully quantum counterparts. The semiclassical results agree quite well with the corresponding quantal results if complex classical trajectories are fully taken into account. The relationship between the semiclassical wave-matrix and Miller's classical S-matrix is also discussed.

The one-dimensional molecular-crystal model of polaron motion, described in the preceding paper, is here analyzed for the case in which the electronic-overlap term of the total Hamiltonian is a small perturbation. In zeroth order—i.e., in the absence of this term—the electron is localized at a given site, p. The vibrational state of the system is specified by a set of quantum-numbers, Nk, giving the degree of excitation of each vibration-mode; the latter differ from the conventional modes in that in each of them, the equilibrium displacement, about which the system oscillates, depends upon the location of the electron. The presence of a nonvanishing electronic-overlap term gives rise to transitions in which the electron jumps to a neighboring site (p→p±1), and in which either all of the Nk remain unaltered (“diagonal” transitions) or in which some of them change by ±1 (“nondiagonal” transitions). The two types of transitions play fundamentally different roles. At sufficiently low temperatures, the diagonal transitions are dominant. They give rise to the formation of Bloch-type bands whose widths (see Eq. 37) are each given by the product of the electronic-overlap integral, and a vibrational overlap-integral, the latter being an exponentially falling function of the Nk (and, hence, of temperature). In this low-temperature domain, the role of the non- diagonal transitions is essentially one of scattering. In the absence of other scattering mechanisms, such as impurity scattering, they determine the lifetimes of the polaron-band states and, hence, the mean free path for typical transport quantities, such as electron diffusivity. With rising temperature, the probability of the off-diagonal transitions goes up exponentially. This feature, together with the above-mentioned drop in bandwidth, results, e.g., in an exponentially diminishing diffusivity. Eventually, a temperature, Tt∼ 1 2 the Debye Θ, is reached at which the energy uncertainty, ℏ/τ, associated with the finite lifetime of the states, is equal to the bandwidth. At this point, the Bloch states lose their individual characteristics (in particular, those which depend upon electronic wave number); the bands may then be considered as “washed out.” For temperatures >Tt, electron motion is predominantly a diffusion process. The elementary steps of this process consist of the random-jumps between neighboring sites associated with the nondiagonal transitions. In conformance with this picture, the electron diffusivity is, apart from a numerical factor, the product of the square of the lattice distance and the total non-diagonal transition probability, and is therefore an exponentially rising function of temperature. The limit, Jmax, of the magnitude of the electronic overlap term, beyond which the perturbation treatment of the present paper becomes inapplicable, is investigated. For representative values of the parameters entering into the theory, Jmax∼0.12 ev and 0.035 ev for the extreme cases of (a) width of the ground-state polaron-band and (b) high-temperature site-jump probabilities (these numbers correspond to electronic bandwidths of 0.24 ev and 0.07 ev, respectively). For electronic bandwidths in excess of these limits, a treatment based on the adiabatic approach is required; preliminary results of such a treatment are given for the above two cases.

In a recent paper (Struchtrup, Annals of Physics, 257, 1997) we set up an extended moment method for radiative transfer problems, which involves matrices of mean absorption and scattering coefficients. In the present paper, we examine the resulting moment equations for one-dimensional radiative transfer problems. In particular we are interested in the number of moments which one has to choose in order to have satisfactory agreement between solutions of the moment equations and solutions of the radiative transfer equation. We show that the moment theory will describe a one-dimensional beam properly, if moments with a tensorial rank of about 30 are taken into account. 1998 Academic Press

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.

The transport theory of ions and electrons in an oscillating electric field, typically at radio frequencies, is of interest both as a problem in basic physics and for its potential for application to modern technology, e.g., plasma processing. Our research has been motivated by both these considerations, but the present paper concerns theory and focuses on Boltzmann's kinetic equation in particular. We note that as far as kinetic theory is concerned, any substantial advances on the pioneering work of Margenau and Hartmann nearly fifty years ago have been remarkably limited in comparison with the extensive, systematic development of d.c. transport theory over the past two decades. Our goal has been to develop a comprehensive theory of a.c. charged particle transport, at a level of sophistication comparable with the d.c. theory, and the first steps are reported in the present paper, which deals with theoretical foundations and phenomenology. After examining the broader implications of space-time symmetries, namely, parity and phase-reversal invariance, we proceed through low-order moments of Boltzmann's equation, with collision terms approximated in the same way as for d.c. momentum-transfer theory, and look for relationships, however approximate, connecting experimentally measurable quantities, and otherwise attempt to shed light on transport phenomena peculiar to harmonically varying electric fields. In this way we obtain: (a) A full set of momentum-energy balance equations for both ions and electrons, to be solved simultaneously with Poisson's equation where appropriate; (b) A generalisation of Wannier's energy relation for ion swarms in an a.c. field; (c) Generalised Einstein relations for cycle-averaged electron swarm diffusion coefficients; (d) Information about a.c. negative differential conductivity and the anomalous character of anisotropic diffusion in a.c. fields; (e) A procedure for adaptation of d.c. experimental swarm data to a.c. swarms and r.f. discharges. The discussion is at the semiquantitative level, with emphasis on physical understanding.

This article has been withdrawn at the request of the Editors. Soon after the publication of this paper was announced, several experts in the field contacted the Editors to report errors. After extensive review, the Editors unanimously concluded that the results are in obvious conflict with a proven scientific fact, i.e., violation of local realism that has been demonstrated not only theoretically but experimentally in recent experiments. On this basis, the Editors decided to withdraw the paper. As a consequence, pages 67–79 originally occupied by the withdrawn article are missing from the printed issue. The publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy .

The purpose of the present paper is to investigate whether dissipation can be self-organized in quantum systems with a small number (precisely, equal to or greater than three) of degrees of freedom, such as nuclei, polyatomic molecules, micro-clusters, provided that the system is classically chaotic. To be more concrete we examine the above problem in the context of the light absorption process. The paper is composed of three parts as follows: First, numerically computable models representing multi-dimensional (more than 2) classically chaotic quantum systems with which the whole process of light absorption experiment can be simulated are proposed. The main part of our model is equivalent to a quantum map defined on a torus and it is coupled with a small number of linear oscillators. The former, which is called the host system , models the "bright mode" and is directly coupled by a light field with an effective ground state set outside of the system, while the latter oscillators, called the helper modes , represent the "dark modes" which form an environment of the host. Second, a simulation of light absorption is carried out with the above models, and it reveals that dissipation characterized by stationary light absorption is realized through a phase transition if and only if the system is classically chaotic. In the dissipative state the absorption spectrum becomes mainly composed of a continuous component. It is further accompanied by an anomalous quantum component with a fractal peak structure, which can never be decomposed into a line spectrum at any higher resolution. A relationship between the appearance of dissipation and unidentifiability of spectral peak positions is suggested, and the effect of finite dimensionality of the Hilbert space on dissipation is also discussed. Third, a semiclassical theory of multidimensional quantum map system based upon the path-integral method is developed, and it is applied to the light absorption problem. It turns out that the semiclassical theory can precisely describe the fully dissipative state. Moreover, the semiclassical theory provides a natural basis for the interpretation of the transition to the dissipative state in terms of a competition between a remarkable growth of correlation among an exponentially increasing number of classical trajectories and a correlation-canceling mechanism originated from short-time-scale chaotic fluctuations fed back to the host system through the helper modes. This interpretation leads to a qualitative explanation of the spectral features in the fully dissipative regime.

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.