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

arXiv:1112.2575 · Annales Henri Poincaré

The Existence of the Thermodynamic Limit for the System of Interacting Quantum Particles in Random Media

Nikolaj A. Veniaminov

Published May 31, 2012• 11 citations
arXivHTMLPDF
DOI
10.1007/s00023-012-0186-8

Related papers

Electron random walk in ideal phonon gas. Exact dressed electron density matrix evolution equations

Yu. E. Kuzovlev

An original approach is suggested to analysis of full quantum Liouville equation for single electron (quantum particle) interacting with ideal phonon gas (harmonic boson thermostat). It is shown that under the thermodynamic limit this equation can be exactly reduced to a system of evolution equations connecting density matrix of the electron and its simplest irreducible correlations with amplitudes of one, two, three and more phonon modes. Possible application of these new equations to explanation of the electron mobility 1/f-type fluctuations in semiconductors and other media is discussed. The special case of electron in static disorder is also considered.

arXiv:1107.3240•Jul 16, 2011•0 citations

The existence of the thermodynamic limit of the cluster integrals for a quantum gas

Dick Bedeaux

Physica•Feb 1, 1970•8 citations

Quantum Beats in Many-Body Localized Systems

Bernard Faulend, Hrvoje Buljan, Antonio Štrkalj

Slow particle dynamics observed numerically even deep inside the many-body localized (MBL) regime has called the stability of MBL in the thermodynamic limit into question, and its microscopic origin remains unknown. Here, we show that this slow dynamics originates from many-body quantum beats that arise from the interaction-induced modulation of oscillations associated with single-particle hopping processes. We relate this mechanism to local integrals of motion (LIOMs) and show that it survives at arbitrarily large distances between LIOMs, is consistent with the stability of MBL in the thermodynamic limit, and is generic to many-body systems. We present new numerical results for quasiperiodic potentials and, based on the quantum beats mechanism, develop an analytical model that explains number entropy growth and quasiparticle spreading, as well as clarifies the distinct MBL phenomenology observed in quasiperiodic and random potentials. Lastly, we propose concrete signatures for observing many-body quantum beats in existing experimental platforms.

arXiv:2603.28721•Mar 30, 2026•0 citations

On the independence of the thermodynamic limit on the boundary conditions in quantum statistical mechanics

N. Angelescu, G. Nenciu

Communications in Mathematical Physics•Mar 1, 1973•25 citations

Exactness of the Bogoliubov approximation in random external potentials

Thomas Jaeck, Valentin Anatol'evich Zagrebnov

We investigate the validity of the Bogoliubov c-number approximation in the case of interacting Bose-gas in a homogeneous random media. To take into account the possible occurence of type III generalized Bose-Einstein condensation (i.e. the occurrence of condensation in an infinitesimal band of low kinetic energy modes without macroscopic occupation of any of them) we generalize the c-number substitution procedure to this band of modes with low momentum. We show that, as in the case of the one-mode condensation for translation-invariant interacting systems, this procedure has no effect on the exact value of the pressure in the thermodynamic limit, assuming that the c-numbers are chosen according to a suitable variational principle. We then discuss the relation between these c-numbers and the (total) density of the condensate.

•Aug 26, 2015•4 citations

On equilibrium distributions of systems of particles in quantum theory

V. N. Gorshenkov, Н. А. Денисова, V. L. Kon'kov +1 more

Theoretical and Mathematical Physics•May 1, 1973•1 citation
An original approach is suggested to analysis of full quantum Liouville equation for single electron (quantum particle) interacting with ideal phonon gas (harmonic boson thermostat). It is shown that under the thermodynamic limit this equation can be exactly reduced to a system of evolution equations connecting density matrix of the electron and its simplest irreducible correlations with amplitudes of one, two, three and more phonon modes. Possible application of these new equations to explanation of the electron mobility 1/f-type fluctuations in semiconductors and other media is discussed. The special case of electron in static disorder is also considered.
Slow particle dynamics observed numerically even deep inside the many-body localized (MBL) regime has called the stability of MBL in the thermodynamic limit into question, and its microscopic origin remains unknown. Here, we show that this slow dynamics originates from many-body quantum beats that arise from the interaction-induced modulation of oscillations associated with single-particle hopping processes. We relate this mechanism to local integrals of motion (LIOMs) and show that it survives at arbitrarily large distances between LIOMs, is consistent with the stability of MBL in the thermodynamic limit, and is generic to many-body systems. We present new numerical results for quasiperiodic potentials and, based on the quantum beats mechanism, develop an analytical model that explains number entropy growth and quasiparticle spreading, as well as clarifies the distinct MBL phenomenology observed in quasiperiodic and random potentials. Lastly, we propose concrete signatures for observing many-body quantum beats in existing experimental platforms.
We investigate the validity of the Bogoliubov c-number approximation in the case of interacting Bose-gas in a homogeneous random media. To take into account the possible occurence of type III generalized Bose-Einstein condensation (i.e. the occurrence of condensation in an infinitesimal band of low kinetic energy modes without macroscopic occupation of any of them) we generalize the c-number substitution procedure to this band of modes with low momentum. We show that, as in the case of the one-mode condensation for translation-invariant interacting systems, this procedure has no effect on the exact value of the pressure in the thermodynamic limit, assuming that the c-numbers are chosen according to a suitable variational principle. We then discuss the relation between these c-numbers and the (total) density of the condensate.