A Wigner Quasi-distribution Function for Charged Particles in Classical Electromagnetic Fields

Levanda, M; Fleurov, V.

doi:10.1006/aphy.2001.6170

Cited by 37 publications

(40 citation statements)

References 70 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The transposition of (72) toward the ξ-integrated representation of the quasi-classical Green function is straightforward, except for the collision integral which we discuss now separately. If we suppose the disorder to be weakly and isotropically interacting with the electrons and randomly distributed along the sample, a convenient approximation to describe it is the Born approximation (66). There, we substitute d 3 p/ (2π ) 3 ≈ N 3d 0 dξ p dΩ p /4π in 3D, d 2 p/ (2π ) 2 ≈ N 2d 0 dξ p dΩ p /2π in 2D or dp/2π = N 1d 0 dξ p in 1D, with Ω p the solid-angle in the momentum space and N 3d 0 = mp F /2π 2 3 , N 2d 0 = m/2π 2 or N 1d 0 = m/p F 2π the density of state in the normal metal in 3D, 2D and 1D, respectively.…”

Section: Eilenberger Equationmentioning

confidence: 99%

Transport equations for superconductors in the presence of spin interaction

Konschelle

2014

Eur. Phys. J. B

View full text Add to dashboard Cite

Quasi-classical theory of superconductivity provides a powerful and yet simple description of the superconductivity phenomenology. In particular, the Eilenberger and Usadel equations provide a neat simplification of the description of the superconducting state in the presence of disorder and electromagnetic interaction. However, the modern aspects of superconductivity require a correct description of the spin interaction as well. Here, we generalize the transport equations of superconductivity in order to take into account space-time dependent electromagnetic and spin interactions on equal footing. Using a gauge-covariant Wigner transformation for the Green-Gor'kov correlation functions, we establish the correspondence between the Dyson-Gor'kov equation and the quasiclassical transport equation in the time-dependent phase-space. We give the expressions for the gauge-covariant current and charge densities (quasi-particle, electric and spin) in the transport formulation. The generalized Eilenberger and Usadel limits of the transport equation are given, too. This study is devoted to the formal derivation of the equations of motion in the electromagnetic plus spin plus particle-hole space. The studies of some specific systems are postponed to future works. [5,6] and Nambu [7,8] is a masterpiece of condensed matter in particular, and quantum field theory in general. It consists in a few concepts -a second-order phase transition due to electron-phonon interaction, or a classical gaugesymmetry breaking in high-energy language -together with a predictive power which provided breakthrough discoveries all along the second half of the 20-th century. Among others, the BCS theory and its close parent the Ginzburg-Landau model [9,10] The balance between a few concepts involved in a large number of novel effects is certainly due to the robustness of the quasi-classical description of superconductivity [18][19][20][21]. Indeed, most superconductors are characterized by a relevant energy scale, namely the gap parameter energy, much smaller than the Fermi energy. Then it becomes possible to adapt for superconductors the quasiclassical theory developed for normal metals [22,23].Due to its success describing such vast problems as vortex in bulk, Josephson and proximity effect in mesoscopic systems as well as the competition between superconductivity and disorder, the quasi-classical description of superconductivity was naturally extended to discuss the competition between superconductor and magnetic orders. There, the quasi-classical description opened a new era of discoveries, which are too numerous to be listed here. We just mention that their possible domain of applicability ranges from spintronic effects to some proposed fundamental phases in neutron stars and in the early universe, passing through original vortex states and new electronic devices based on novel Josephson effects, see e.g. [24][25][26][27] and references therein.Whereas the first studies discussing the competing effect between superconductivity and spin coupl...

show abstract

Section: Eilenberger Equationmentioning

confidence: 99%

Transport equations for superconductors in the presence of spin interaction

Konschelle

2014

Eur. Phys. J. B

View full text Add to dashboard Cite

show abstract

“…Moreover also the Wigner distribution function (Levanda and Fleurov, 2001), although providing significant information about the quantum states, presents conceptual difficulties: It cannot be really regarded like a probability distribution in the classical sense, rather it is a quasi-probability that can take even negative values; moreover it can represent the average value of an observable but not, in general, also its higher power moments. Both these difficulties are bypassed exploiting the statistical formulation of the quantum uncertainty, regarded as a fundamental assumption itself; it reads in one space dimension:…”

Section: Quantum Backgroundmentioning

confidence: 99%

Quantum Approach to the Gravitational Waves

Tosto¹

2013

Physics International

View full text Add to dashboard Cite

The study proposes a quantum approach to explain existence and main features of the gravitational waves radiated by an isolated two body orbiting system. The quantum eigenvalues of such a system are calculated with the help of the space-time quantum uncertainty, without additional hypotheses via an "ab initio" model. The approach is deliberately non-relativistic: The model does not implement any relativistic assumption and shows that the mere quantum approach is enough to get energy loss and orbit radius contraction coincident with that early inferred by Einstein. However the outcomes of the model also show features typical of the quantum systems, which are purposely discussed.

show abstract

“…The properties of the GIWF have been detailed in [4,5]. Nevertheless for completeness we discuss some of them once again.…”

Section: Basic Properties Of the Gauge Invariant Wigner Functionmentioning

confidence: 99%

Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

Haas¹,

Zamanian

Marklund

et al. 2010

New J. Phys.

View full text Add to dashboard Cite

The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner function is shown to produce inconsistencies, if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and shown to be in agreement with the kinetic theory in the long wavelength approximation, provided an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.

show abstract

A Wigner Quasi-distribution Function for Charged Particles in Classical Electromagnetic Fields

Cited by 37 publications

References 70 publications

Transport equations for superconductors in the presence of spin interaction

Transport equations for superconductors in the presence of spin interaction

Quantum Approach to the Gravitational Waves

Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

Contact Info

Product

Resources

About