Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Correlation-Fluctuation Effects In Non-Equilibrium Quantum Gas

R. Katilius, S. V. Gantsevich, V. D. Kagan, M. I. Muradov, Mindaugas Ramonas, MASSIMO RUDAN, Massimo Macucci, Giovanni Basso

Published Jan 1, 2009• 1 citation
Publisher

Abstract

In the quasi‐classical approximation, the theory of fluctuations in a degenerate two‐or three‐dimensional non‐equilibrium electron gas is developed from first principles. It is shown that, thanks to the small‐angle character of the inter‐electron scattering, the theory takes a rather simple and transparent form, in contrast to other types of Fermi gases for which, due to exchange effects, the situation proves to be much more complicated.

DOI
10.1063/1.3140568

Related papers

FLUCTUATIONS IN NON-EQUILIBRIUM ELECTRON GAS: EFFECT OF QUANTUM STATISTICS

R. Katilius, S. V. Gantsevich, V. D. Kagan +1 more

Here we develop a mathematical apparatus to describe quasi-classical fluctuations in a non-equilibrium electron gas with electron-electron collisions. We substantiate the method by deriving, from general principles of quantum kinetics, an equation recently proposed by us for an equal-time electron-electron correlation function. The derivation is performed using the kinetic diagram technique. In degenerate non-equilibrium gas, the theory predicts that there exists a specific equal-time correlation between electrons. Due to the prevalence of small-angle electron-electron scattering, the equation in question takes a rather simple and treatable form (the Coulomb-type electron-electron interaction stands out against the background of all other types of interaction as one that does not generate, in the framework of quasi-classical approach, any direct exchange effects).

Fluctuation and Noise Letters•Jul 13, 2010•4 citations

Spin susceptibility in a two-dimensional electron gas

Sudhakar Yarlagadda, Gabriele F. Giuliani

The problem of the many-body enhancement of the static spin susceptibility at long wavelengths and its relation to the quasiparticle effective mass is investigated for a normal electron gas in two-dimensional space as a function of the electronic density. We start from a discussion of the results of the simple Hartree-Fock approximation for various interaction potentials and proceed to develop a complete theory. We find that the effects of the electron-electron interaction are significantly larger than in the familiar three-dimensional case. Our approach is based on a new self-consistent scheme which goes beyond the simple random-phase approximation by explicitly allowing for charge- and spin-fluctuation-induced vertex corrections of the Hubbard type. We show that when the latter are neglected, the many-body enhancement of the spin susceptibility can be cast in a remarkably simple and elegant analytic form.

Physical review. B, Condensed matter•Sep 15, 1989•45 citations

Beyond Gaussian pair fluctuation theory for strongly interacting Fermi gases

Brendan C. Mulkerin, Xia-Ji Liu, Hui Hu

Interacting Fermi systems in the strongly correlated regime play a fundamental role in many areas of physics and are of particular interest to the condensed matter community. Though weakly interacting fermions are understood, strongly correlated fermions are difficult to describe theoretically as there is no small interaction parameter to expand about. Existing strong-coupling theories rely heavily on the so-called many-body $T$-matrix approximation that sums ladder-type Feynman diagrams. Here, by acknowledging the fact that the effective interparticle interaction (i.e., the vertex function) becomes smaller above three dimensions, we propose an alternative way to reorganize Feynman diagrams and develop a theoretical framework for interacting Fermi gases beyond the ladder approximation. As an application, we solve the equation of state for three- and two-dimensional strongly interacting fermions and find excellent agreement with experimental [M. J. H. Ku et al., Science 335, 563 (2012)] and other theoretical results above temperatures of $0.5{T}_{F}$.

arXiv:1602.07391•Physical Review A•Jul 18, 2016•7 citations

Dynamics of Degenerate Electron Gas in a Magnetic Field

Amiram Ron

Some aspects of the correlations between interacting electrons in a magnetic field are studied by a quantum kinetic approach, taking into account the quantization of the orbital motion of the electrons. The treatment is based on the introduction of an hierarchy of equations of motion for the $s$-body density matrices and employing a decoupling scheme, valid in the self-consistent field approximation. In this way the dielectric function is introduced "naturally," and the response of the system to an applied field is calculated. The dielectric function reflects the two main effects of the correlations, i.e., the collective excitations of the system and the dynamical shielding. The dielectric function plays a role also in the "dressing" of the interacting electrons. This is shown by calculating the spectrum of the density fluctuations and the equation which governs the approach to equilibrium of the system. The method is not limited to systems in thermal equilibrium, but also applies to systems in other stationary equilibrium states.

Physical Review•Apr 6, 1964•15 citations

Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction

Julien Toulouse

A simple approximate expression in real and reciprocal spaces is given for the static exchange-correlation kernel of a uniform electron gas interacting with the long-range part only of the Coulomb interaction. This expression interpolates between the exact asymptotic behaviors of this kernel at small and large wave vectors which in turn requires, among other things, information from the momentum distribution of the uniform electron gas with the same interaction that have been calculated in the ${G}_{0}{W}_{0}$ approximation. This exchange-correlation kernel as well as its complement analog associated to the short-range part of the Coulomb interaction are more local than the Coulombic exchange-correlation kernel and constitute potential ingredients in approximations for recent adiabatic connection fluctuation-dissipation and/or density functional theory approaches of the electronic correlation problem based on a separate treatment of long- and short-range interaction effects.

arXiv:cond-mat/0505142•Physical Review B•Jul 14, 2005•21 citations

Low-energy effective theory of nonthermal fixed points in a multicomponent Bose gas

A. N. Mikheev, Christian-Marcel Schmied, Thomas Gasenzer

Nonthermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of nonthermal fixed points in a bosonic quantum many-body system by integrating out long-wavelength density fluctuations. The system consists of $N$ distinguishable spatially uniform Bose gases with $\text{U}(N)$-symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relative-phase excitations. It is similar in character to the nonlinear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal nonlocal coupling function depending, in the large-$N$ limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the nonthermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields $N$. Numerical results for $N=3$ allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The predicted and observed exponentially suppressed coherence at short distances takes the form of that of a quasicondensate in low-dimensional equilibrium systems. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.

arXiv:1807.10228•Physical Review A•Jun 24, 2019•38 citations
In the quasi‐classical approximation, the theory of fluctuations in a degenerate two‐or three‐dimensional non‐equilibrium electron gas is developed from first principles. It is shown that, thanks to the small‐angle character of the inter‐electron scattering, the theory takes a rather simple and transparent form, in contrast to other types of Fermi gases for which, due to exchange effects, the situation proves to be much more complicated.
Here we develop a mathematical apparatus to describe quasi-classical fluctuations in a non-equilibrium electron gas with electron-electron collisions. We substantiate the method by deriving, from general principles of quantum kinetics, an equation recently proposed by us for an equal-time electron-electron correlation function. The derivation is performed using the kinetic diagram technique. In degenerate non-equilibrium gas, the theory predicts that there exists a specific equal-time correlation between electrons. Due to the prevalence of small-angle electron-electron scattering, the equation in question takes a rather simple and treatable form (the Coulomb-type electron-electron interaction stands out against the background of all other types of interaction as one that does not generate, in the framework of quasi-classical approach, any direct exchange effects).
The problem of the many-body enhancement of the static spin susceptibility at long wavelengths and its relation to the quasiparticle effective mass is investigated for a normal electron gas in two-dimensional space as a function of the electronic density. We start from a discussion of the results of the simple Hartree-Fock approximation for various interaction potentials and proceed to develop a complete theory. We find that the effects of the electron-electron interaction are significantly larger than in the familiar three-dimensional case. Our approach is based on a new self-consistent scheme which goes beyond the simple random-phase approximation by explicitly allowing for charge- and spin-fluctuation-induced vertex corrections of the Hubbard type. We show that when the latter are neglected, the many-body enhancement of the spin susceptibility can be cast in a remarkably simple and elegant analytic form.
Interacting Fermi systems in the strongly correlated regime play a fundamental role in many areas of physics and are of particular interest to the condensed matter community. Though weakly interacting fermions are understood, strongly correlated fermions are difficult to describe theoretically as there is no small interaction parameter to expand about. Existing strong-coupling theories rely heavily on the so-called many-body TTT-matrix approximation that sums ladder-type Feynman diagrams. Here, by acknowledging the fact that the effective interparticle interaction (i.e., the vertex function) becomes smaller above three dimensions, we propose an alternative way to reorganize Feynman diagrams and develop a theoretical framework for interacting Fermi gases beyond the ladder approximation. As an application, we solve the equation of state for three- and two-dimensional strongly interacting fermions and find excellent agreement with experimental [M. J. H. Ku et al., Science 335, 563 (2012)] and other theoretical results above temperatures of 0.5TF0.5{T}_{F}0.5TF​.
Some aspects of the correlations between interacting electrons in a magnetic field are studied by a quantum kinetic approach, taking into account the quantization of the orbital motion of the electrons. The treatment is based on the introduction of an hierarchy of equations of motion for the sss-body density matrices and employing a decoupling scheme, valid in the self-consistent field approximation. In this way the dielectric function is introduced "naturally," and the response of the system to an applied field is calculated. The dielectric function reflects the two main effects of the correlations, i.e., the collective excitations of the system and the dynamical shielding. The dielectric function plays a role also in the "dressing" of the interacting electrons. This is shown by calculating the spectrum of the density fluctuations and the equation which governs the approach to equilibrium of the system. The method is not limited to systems in thermal equilibrium, but also applies to systems in other stationary equilibrium states.
A simple approximate expression in real and reciprocal spaces is given for the static exchange-correlation kernel of a uniform electron gas interacting with the long-range part only of the Coulomb interaction. This expression interpolates between the exact asymptotic behaviors of this kernel at small and large wave vectors which in turn requires, among other things, information from the momentum distribution of the uniform electron gas with the same interaction that have been calculated in the G0W0{G}_{0}{W}_{0}G0​W0​ approximation. This exchange-correlation kernel as well as its complement analog associated to the short-range part of the Coulomb interaction are more local than the Coulombic exchange-correlation kernel and constitute potential ingredients in approximations for recent adiabatic connection fluctuation-dissipation and/or density functional theory approaches of the electronic correlation problem based on a separate treatment of long- and short-range interaction effects.
Nonthermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of nonthermal fixed points in a bosonic quantum many-body system by integrating out long-wavelength density fluctuations. The system consists of NNN distinguishable spatially uniform Bose gases with U(N)\text{U}(N)U(N)-symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relative-phase excitations. It is similar in character to the nonlinear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal nonlocal coupling function depending, in the large-NNN limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the nonthermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields NNN. Numerical results for N=3N=3N=3 allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The predicted and observed exponentially suppressed coherence at short distances takes the form of that of a quasicondensate in low-dimensional equilibrium systems. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.