The classical limit of the relativistic Vlasov-Maxwell system

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

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About the Use of Entropy Production for the Landau–Fermi–Dirac Equation

Journal of Statistical Physics ◽

10.1007/s10955-021-02751-z ◽

2021 ◽

Vol 183 (1) ◽

Author(s):

R. Alonso ◽

V. Bagland ◽

L. Desvillettes ◽

B. Lods

Keyword(s):

Dirac Equation ◽

Classical Limit ◽

Large Time ◽

A Priori Estimates ◽

Landau Equation ◽

A Priori ◽

Time Behaviour ◽

Entropy Dissipation ◽

Priori Estimates ◽

Potential Case

AbstractIn this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

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Nonrelativistic near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills with SU(1, 1) symmetry

Journal of High Energy Physics ◽

10.1007/jhep02(2021)188 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Stefano Baiguera ◽

Troels Harmark ◽

Nico Wintergerst

Keyword(s):

Classical Limit ◽

Particle Number ◽

Matrix Theory ◽

Companion Paper ◽

Positive Definite ◽

Normal Ordering ◽

Yang Mills ◽

Three Sphere ◽

Dilatation Operator ◽

Definite Expressions

Abstract We consider limits of $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory that approach BPS bounds and for which an SU(1,1) structure is preserved. The resulting near-BPS theories become non-relativistic, with a U(1) symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the SU(1,1—1) near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a SU(2,1) structure is preserved.

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The Semiclassical Limit of the Gailitis Formula Applied to Electron Impact Broadening of Spectral Lines of Ionized Atoms

Atoms ◽

10.3390/atoms9020029 ◽

2021 ◽

Vol 9 (2) ◽

pp. 29

Author(s):

Sylvie Sahal-Bréchot

Keyword(s):

Electron Impact ◽

Classical Limit ◽

Semiclassical Limit ◽

Spectral Lines ◽

Stark Broadening ◽

Feshbach Resonances

The present paper revisits the determination of the semi-classical limit of the Feshbach resonances which play a role in electron impact broadening (the so-called “Stark“ broadening) of isolated spectral lines of ionized atoms. The Gailitis approximation will be used. A few examples of results will be provided, showing the importance of the role of the Feshbach resonances.

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Fields Connected with Particles in Terms of Complex-Riemannian Geometry

Zeitschrift für Naturforschung A ◽

10.1515/zna-1990-0201 ◽

1990 ◽

Vol 45 (2) ◽

pp. 81-94

Author(s):

Julian Ławrynowicz ◽

Katarzyna Kędzia ◽

Leszek Wojtczak

Keyword(s):

Field Potential ◽

Riemannian Metrics ◽

Interaction Matrix ◽

Explicit Calculation ◽

Maxwell System ◽

Curved Space ◽

Starting Point ◽

Autocorrelation Time ◽

The Fourier Transform ◽

Convolution Equations

AbstractA complex analytical method of solving the generalised Dirac-Maxwell system has recently been proposed by two of us for a certain class of complex Riemannian metrics. The Dirac equation without the field potential in such a metric appeared to be equivalent to the Dirac-Maxwell system including the field potentials produced by the currents of a particle in question. The method proposed is connected with applying the Fourier transform with respect to the electric charge treated as a variable, with the consideration of the mass as an eigenvalue, and with solving suitable convolution equations. In the present research an explicit calculation based on linearization of the spinor connections is given. The conditions for the motion are interpreted as a starting point to seek selection rules for curved space-times corresponding to actually existing particles. Then the same method is applied to solids. Namely, by a suitable transformation of the configuration space in terms of elements of the interaction matrix corresponding to the Coulomb, exchange, and dipole integrals, the interaction term in the hamiltonian becomes zero, thus leading to experimentally verificable formulae for the autocorrelation time

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