arXiv subjects

D. M. Gitman

Publications and source records attributed to D. M. Gitman.

At least 19 recordsLinked to original sources

arXiv2026

Photon emission due to vacuum instability under the action of a quasi-constant electric field

Following a nonperturbative formulation of strong-field QED developed in our earlier works, we consider photon emission accompanying vacuum instability under the action of a quasi-constant strong electric field of finite duration T. We construct closed formulas for the total probabilities and study the photon emission accompanying an electron-positron pair creation from a vacuum. We establish the domain of the applicability of the locally constant field approximation (LCFA) for the photon emission. We study angular and polarization distribution of the emission as well as emission characteristics in a high-frequency approximations with respect of 1/T. The results presented in this work is suitable to a further development of the LCFA proposed in [Phys. Rev. D 95, 076013 (2017)].

hep-ph↗

arXiv2026

Non-commutative integration method and generalized coherent states

The relationship between states obtained by the non-commutative integration method of the Schrödinger equation on Lie groups and generalized coherent states is investigated. It is shown that such solutions belong to the class of generalized coherent states when the corresponding λ-representation is real.

quant-ph↗

arXiv2025

Classical scattering matrix for hard and soft Bose-excitations in a non-Abelian plasma within the Hamiltonian formalism

Within the framework of the Zakharov-Schulman approach, in close analogy with the methods of quantum field theory, the classical scattering matrix for the simplest process of interaction between hard and soft excitations in a quark-gluon plasma (QGP), is determined. The classical $\mathcal{S}$-matrix is defined in the form of the most general integro-power series expansion in the asymptotic values as $t\rightarrow-\infty$ of normal bosonic variables $c^{-\,a}_{\hspace{0.02cm}{\bf k}}(t)$ and $(c^{-\,a}_{\hspace{0.02cm}{\bf k}}(t))^{\ast}$, describing the soft gluon excitations of the system, and a color charge $\mathcal{Q}^{-\hspace{0.03cm}a}(t)$ of a hard particle. The first nontrivial contribution to this matrix is calculated. The quantum commutator of quantum field operators is replaced by the so-called Lie-Poisson bracket depending on the classical asymptotic variables. The developed approach is used to derive a general formula for energy loss of a fast color-charged particle during its scattering off soft bosonic excitations of QGP in the framework of the classical Hamiltonian formalism. For this purpose, the notion of an effective current of the scattering process under consideration is introduced and its relation to the classical $\mathcal{S}$-matrix is determined. With the help of the known form of the classical scattering matrix, the desired effective current is recovered, which in turn allowed us to determine the formula for energy loss of the hard color particle. The rough estimates of energy loss at the order-of-magnitude level is provided and their comparison with the well-known results on the radiation and collision losses is performed.

hep-th↗

arXiv2025

Semiclassical radiation spectrum from an electron in an external plane wave field

In this work, we study the electromagnetic energy and energy rate spectra produced by a point particle in the presence of plane wave fields. Our approach is based on a semiclassical formulation, in which the current distribution that generates electromagnetic radiation is treated classically while the radiation field is quantum. Unlike the classical energy spectrum--which exhibits divergences linked to the duration of interaction between the particle and the external field--the semiclassical spectrum is finite because radiation is produced during the quantum transition from an initial state without photons to the final state with photons at time $t$. In our formulation, we find that the maximum energy spectrum emitted by the particle is linearly proportional to time or phase, depending on the external field. This allowed us not only to extract the maximum energy rate spectra emitted by the particle but also to correlate them with energy rates derived in the framework of Classical Electrodynamics and Quantum Electrodynamics.

quant-ph↗

arXiv2025

Coherent states of finite-level systems

A method for constructing coherent states (CS) of finite-level systems with a given angular momentum is proposed. To this end we generalize the known spin equation (SE) to an infinite-dimensional Fock space. The equation describes a special quadratic system in the latter space. Its projections on $d$-dimensional subspaces, represent analogs of SE for $d$-dimensional systems in an external electromagnetic field which describe $d$-dimensional systems with a given angular moment. Using a modification of Malkin-Manko method developed in our earlier work, we construct the corresponding CS for the total quadratic system. Projections of the later CS on finite-dimensional subspaces we call angular moment CS (AMCS) of finite-level systems. The AMCS have a clear physical meaning, they obey the Schrödinger for a $d$-dimensional system with a given angular moment $j=\left(d-1\right)/2$ in an external electromagnetic field. Their possible exact solutions are constructed via exact solutions of the SE in $2$-dimensional space. The latter solutions can be found analytically and are completely described in our earlier works. A one subset of AMCS can be related to Perelomov spinning CS (PSCS). This reflects the fact that the set of possible AMCS is wider than the set of PSCS. AMCS states in a constant magnetic field are constructed. Some of them coincide with the Bloch CS.

quant-ph↗

arXiv2025

Coherent states of an accelerated particle

We construct generalized coherent states (GCS) of a massive accelerated particle. This example is an important step in studying coherent states (CS) for systems with an unbounded motion and a continuous spectrum. First, we represent quantum states of the accelerated particle both known and new ones obtained by us using the method of non-commutative integration of linear differential equations. A complete set of non-stationary states for the accelerated particle is obtained. This set is expressed via elementary functions and is characterized by a continuous real parameter $η$, which corresponds to the initial momentum of the particle. A connection is obtained between these solutions and stationary states, which are determined by the Airy function. We solved the problem of constructing GCS, in particular, semiclassical states describing the accelerated particle, within the framework of the consistent method of integrals of motion. We have found different representations, coordinate one and in a Fock space, analyzing in detail all the parameters entering in these representations.

quant-ph↗

arXiv2024

Schwinger mechanism of magnon-antimagnon pair production on magnetic field inhomogeneities and the bosonic Klein effect

Effective field theory of low-energy exitations-magnons that describes antiferromagnets is mapped into scalar electrodynamics of a charged scalar field interacting with an external electromagnetic potential. In the presence of a constant inhomogeneous external magnetic field the latter problem is technically reduced to the problem of charged-particle creation from the vacuum by an electric potential step (x step). Magnetic moment plays here the role of the electric charge, and magnons and antimagnons differ from each other in the sign of the magnetic moment. In the framework of such a consideration, it is important to take into account the vacuum instability (the Schwinger effect) under the magnon-antimagnon production on magnetic field inhomogeneities (an analog of pair creation from the vacuum by electric-like fields). We demonstrate how to use the strong field QED with x steps developed by the authors (SPG and DMG) to study the magnon-antimagnon pair production on magnetic field inhomogeneities. Characteristics of the vacuum instability obtained for some magnetic steps that allows exact solving the Klein-Gordon equation are presented. In particular, we consider examples of magnetic steps with very sharp field derivatives that correspond to a regularization of the Klein step. In the case of smooth-gradient steps, we describe an universal behavior of the flux density of created magnon pairs. We also note that since the low-energy magnons are bosons with small effective mass, then for the first time maybe the opportunity will arise to observe the Schwinger effect in the case of the Bose statistics, in particular, the bosonic Klein effect in laboratory conditions. Moreover, it turns out that in the case of the Bose statistics appears a new mechanism for amplifying the effect of the pair creation, which we call statistically assisted Schwinger effect.

cond-mat.mes-hall↗

arXiv2024

Group-theoretical classification of orientable objects and particle phenomenology

In our previous works, we have proposed a quantum description of relativistic orientable objects by a scalar field on the Poincaré group. This description is, in a sense, a generalization of ideas used by Wigner, Casimir and Eckart back in the 1930's in constructing a non-relativistic theory of a rigid rotator. The present work is a continuation and development of the above mentioned our works. The position of the relativistic orientable object in Minkowski space is completely determined by the position of a body-fixed reference frame with respect to the space-fixed reference frame, and can be specified by elements $q$ of the motion group of the Minkowski space - the Poincaré group $M(3,1)$. Quantum states of relativistic orientable objects are described by scalar wave functions $f(q)$ where the arguments $q=(x,z)$ consist of Minkowski space-time points $x$, and of orientation variables $z$ given by elements of the matrix $Z\in SL(2,C)$. Technically, we introduce and study the so-called double-sided representation $\boldsymbol{T}(\boldsymbol{g})f(q)=f(g_l^{-1}qg_r)$, $\boldsymbol{g}=(g_l,g_r)\in \boldsymbol{M}$, of the group $\boldsymbol{M}$, in the space of the scalar functions $f(q)$. Here the left multiplication by $g_l^{-1}$ corresponds to a change of space-fixed reference frame, whereas the right multiplication by $g_r$ corresponds to a change of body-fixed reference frame. On this basis, we develop a classification of the orientable objects and draw the attention to a possibility of connecting these results with the particle phenomenology. In particular, we demonstrate how one may identify fields described by linear and quadratic functions of $z$ with known elementary particles of spins $0$,$\frac{1}{2}$, and $1$. The developed classification does not contradict the phenomenology of elementary particles and, moreover, in some cases give its group-theoretic explanation.

physics.gen-ph↗

arXiv2024

Vacuum instability in QED with an asymmetric x-step. New example of exactly solvable case

We present a new exactly solvable case in strong-field QED with one-dimensional step potential (x-step). The corresponding x-step is given by an analytic asymmetric with respect to the axis x reflection function. The step can be considered as a certain analytic "deformation" of the symmetric Sauter field. Moreover, it can be treated as a new regularization of the Klein step field. We study the vacuum instability caused by this x-step in the framework of a nonperturbative approach to strong-field QED. Exact solutions of the Dirac equation used in the corresponding nonperturbative calculations, are represented in the form of stationary plane waves with special left and right asymptotics and identified as components of initial and final wave packets of particles. We show that in spite of the fact that the symmetry with respect to positive and negative bands of energies is broken, distribution of created pairs and other physical quantities can be expressed via elementary functions. We consider the processes of transmission and reflection in the ranges of the stable vacuum and study physical quantities specifying the vacuum instability. We find the differential mean numbers of electron-positron pairs created from the vacuum, the components of current density and energy-momentum tensor of the created electrons and positrons leaving the area of the strong field under consideration. Besides, we study the particular case of the particle creation due to a weakly inhomogeneous electric field and obtain explicitly the total number, the current density and energy-momentum tensor of created particles. Unlike the symmetric case of the Sauter field the asymmetric form of the field under consideration causes the energy density and longitudinal pressure of created electrons to be not equal to the energy density and longitudinal pressure of created positrons.

hep-th↗

arXiv2023

Singular electromagnetic fields in nonlinear electrodynamics with a constant background field

When exploring equations of nonlinear electrodynamics in effective medium formed by mutually parallel external electric and magnetic fields, we come to special static axial-symmetric solutions of two types. The first are comprised of fields referred to as electric and magnetic responses to a point-like electric charge when placed into the medium. In electric case, this is a field determined by the induced charge density. In magnetic case, this is a field carrying no magnetic charge and determined by an induced current. Fields of second type require presence of pseudoscalar constants for their existence. These are singular on the axis drawn along the external fields. In electric case this is a field of an inhomogeneously charged infinitely thin thread. In magnetic case this is the magnetic monopole with the Dirac string supported by solenoidal current. In both cases the necessary pseudoscalar constant is supplied by field derivatives of nonlinear Lagrangian taken on external fields. There is also a magnetic thread solution dual to electric thread with null total magnetic charge.

hep-th↗

arXiv2023

Resonant entanglement of photon beams by a magnetic field

In spite of the fact that photons do not interact with an external magnetic field, the latter field may indirectly affect photons in the presence of a charged environment. This opens up an interesting possibility to continuously control the entanglement of photon beams without using any crystalline devices. We study this possibility in the framework of an adequate QED model. In an approximation it was discovered that such entanglement has a resonant nature, namely, a peak behavior at certain magnetic field strengths, depending on characteristics of photon beams direction of the magnetic field and parameters of the charged medium. Numerical calculations illustrating the above-mentioned resonant behavior of the entanglement measure and some concluding remarks are presented.

quant-ph↗

arXiv2023

Electromagnetic radiation of accelerated charged particle in the framework of a semiclassical approach

We address the problem of the electromagnetic radiation produced by charge distributions in the framework of a semiclassical approach proposed in the work by Bagrov, Gitman, Shishmarev and Farias [J. Synchrotron Rad. (2020). 27, 902-911]. In this approach, currents, generating the radiation are considered classically, while the quantum nature of the radiation is kept exactly. Quantum states of the electromagnetic field are solutions of Schrödinger's equation and relevant quantities to the problem are evaluated with the aid of transition probabilities. This construction allows us to introduce the quantum transition time in physical quantities and assess its role in radiation problems by classical currents. We study radiated electromagnetic energies in detail and present a definition for the rate at which radiation is emitted from sources. In calculating the total energy and rate radiated by a pointlike charged particle accelerated by a constant and uniform electric field, we discover that our results are compatible with results obtained by other authors in the framework of the classical radiation theory under an appropriate limit. We also perform numerical and asymptotic analysis of the results.

quant-ph↗

arXiv2023

Photon emission in the graphene under the action of a quasiconstant external electric field

Following a nonperturbative formulation of strong-field QED developed in our earlier works, and using the Dirac model of the graphene, we construct a reduced QED_{3,2} to describe one species of the Dirac fermions in the graphene interacting with an external electric field and photons. On this base, we consider the photon emission in this model and construct closed formulas for the total probabilities. Using the derived formulas, we study probabilities for the photon emission by an electron and for the photon emission accompanying the vacuum instability in the quasiconstant electric field that acts in the graphene plane during the time interval T. We study angular and polarization distribution of the emission as well as emission characteristics in a high frequency and low frequency approximations. We analyze the applicability of the presented calculations to the graphene physics in laboratory conditions. In fact, we are talking about a possible observation of the Schwinger effect in these conditions.

cond-mat.mes-hall↗

arXiv2022

Calculation of the wave functions of a quantum asymmetric top using the noncommutative integration method

In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative reduction of the Schrodinger equation leads to the Lame equation. The resulting set of solutions is determined by the Lame polynomials in a complex parameter, which is related to the geometry of the orbits of the coadjoint representation of the rotation group. The spectrum of an asymmetric top is obtained from the condition that the solutions are invariant with respect to a special irreducible $λ$-representation of the rotation group.

quant-ph↗

arXiv2022

Calculations of vacuum mean values of spinor field current and energy-momentum tensor in a constant electric background

In the framework of strong-field QED with $x$-steps, we study vacuum mean values of the current density and energy--momentum tensor of the quantized spinor field placed in the so-called $L$-constant electric background. The latter background can be, for example, understood as the electric field confined between capacitor plates, which are separated by a sufficiently large distance $L$. First, we reveal peculiarities of nonperturbative calculating of mean values in strong-field QED with $x$-steps in general and, in the $L$-constant electric field, in particular. We propose a new renormalization and volume regularization procedures that are adequate for these calculations. We find necessary representations for singular spinor functions in the external background under consideration. With their help, we calculate the above mentioned vacuum means. In the obtained expressions, we show how to separate global contributions due to the particle creation and local ones due to the vacuum polarization. We demonstrate how these contributions can be related to the renormalized effective Heisenberg-Euler Lagrangian.

hep-th↗

arXiv2022

Noncommutative reduction of the nonlinear Schrödinger equation on Lie groups

We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations. The main idea is to apply the method of noncommutative integration to the linear part of a nonlinear equation, which allows one to find bases in the space of solutions of linear partial differential equations with a set of noncommuting symmetry operators. The approach is implemented for the generalized nonlinear Schrödinger equation on a Lie group in curved space with local cubic nonlinearity. General formalism is illustrated by the example of noncommutative reduction of the nonstationary nonlinear Schrödinger equation on the motion group $E(2)$ of the two-dimensional plane $\mathbb{R}^{2}$. In the particular case, we come to the usual ($1+1$) dimensional nonlinear Schrödinger equation with the soliton solution. Another example provides the noncommutative reduction of the stationary multidimensional nonlinear Schrödinger equation on the four-dimensional exponential solvable group.

math-ph↗

arXiv2022

Light beam interacting with electron medium. Exact solutions of the model and their possible applications to photon entanglement problem

We consider a model for describing a QED system consisting of a photon beam interacting with quantized charged spinless particles. We restrict ourselves by a photon beam that consists of photons with two different momenta moving in the same direction. Photons with each moment may have two possible linear polarizations. The exact solutions correspond to two independent subsystems, one of which corresponds to the electron medium and another one is described by vectors in the photon Hilbert subspace and is representing a set of some quasi-photons that do not interact with each other. In addition, we find exact solution of the model that correspond to the same system placed in a constant magnetic field. As an example, of possible applications, we use the solutions of the model for calculating entanglement of the photon beam by quantized electron medium and by a constant magnetic field. Thus, we calculate the entanglement measures (the information and the Schmidt ones) of the photon beam as functions of the applied magnetic field and parameters of the electron medium.

quant-ph↗

arXiv2021

Vacuum instability due to the creation of neutral Fermion with anomalous magnetic moment by magnetic-field inhomogeneities

We study neutral Fermions pair creation with anomalous magnetic moment from the vacuum by time-independent magnetic-field inhomogeneity as an external background. We show that the problem is technically reduced to the problem of charged-particle creation by an electric step, for which the nonperturbative formulation of strong-field QED is used. We consider a magnetic step given by an analytic function and whose inhomogeneity may vary from a "gradual" to a "sharp" field configuration. We obtain corresponding exact solutions of the Dirac-Pauli equation with this field and calculate pertinent quantities characterizing vacuum instability, such as the differential mean number and flux density of pairs created from the vacuum, vacuum fluxes of energy and magnetic moment. We show that the vacuum flux in one direction is formed from fluxes of particles and antiparticles of equal intensity and with the same magnetic moments parallel to the external field. Backreaction to the vacuum fluxes leads to a smoothing of the magnetic-field inhomogeneity. We also estimate critical magnetic field intensities, near which the phenomenon could be observed.

hep-th↗