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

Boltzmann relaxation dynamics in strongly interacting quantum lattice systems

Friedemann Queißer, Ralf Schützhold

Published Dec 20, 2018• 0 citations
OpenAlex

Abstract

Via the hierarchy of correlations, we study strongly interacting fermions on a lattice and derive a quantum Boltzmann equation describing their relaxation dynamics. Interestingly, in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. Therefore, the relaxation towards equilibrium strongly depends on what kind of excitations (particles or holes or both) are present.

Related papers

Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice

Friedemann Queißer, Sebastian Schreiber, Peter Kratzer +1 more

Motivated by the recent interest in nonequilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium. The derivation is carried out by inspecting the hierarchy of correlations within the framework of the $1/Z$ expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions---in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation timescales strongly depend on the type of excitations (particles or holes or both) that are initially present.

arXiv:1909.12802•Physical review. B./Physical review. B•Dec 5, 2019•8 citations

Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model

Friedemann Queißer, Ralf Schützhold

Via the hierarchy of correlations, we study the Mott insulator phase of the Fermi-Hubbard model in the limit of strong interactions and derive a quantum Boltzmann equation describing its relaxation dynamics. In stark contrast to the weakly interacting case, we find that the scattering cross sections strongly depend on the momenta of the colliding quasiparticles and holes. Therefore, the relaxation towards equilibrium crucially depends on the spectrum of excitations. For example, for particle-hole excitations directly at the minimum of the (direct) Mott gap, the scattering cross sections vanish such that these excitations can have a very long lifetime.

arXiv:1812.08581•Physical Review A•Nov 19, 2019•14 citations

On the weak coupling limit of quantum many-body dynamics and the quantum Boltzmann equation

Xuwen Chen, Yan Guo

The rigorous derivation of the Uehling-Uhlenbeck equation from morefundamental quantum many-particle systems is a challenging open problem inmathematics. In this paper, we exam the weak coupling limit of quantum $N$-particle dynamics. We assume the integral of the microscopic interaction iszero and we assume $W^{4,1}$ per-particle regularity on the coresspondingBBGKY sequence so that we can rigorously commute limits and integrals. Weprove that, if the BBGKY sequence does converge in some weak sense, thenthis weak-coupling limit must satisfy the infinite quantum Maxwell-Boltzmannhierarchy instead of the expected infinite Uehling-Uhlenbeck hierarchy,regardless of the statistics the particles obey. Our result indicates that,in order to derive the Uehling-Uhlenbeck equation, one must work withper-particle regularity bound below $W^{4,1}$.

arXiv:1412.1775•Kinetic and Related Models•Jan 1, 2015•12 citations

Quantum Boltzmann equation for fermions: An attempt to calculate the NMR relaxation and decoherence times using quantum field theory techniques

Hassan Manshouri, Ahmad Hoseinpour, Moslem Zarei

Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse (decoherence) relaxation times from the collision term by considering the nucleon-nucleon scattering.

arXiv:2009.01917•Physical review. D/Physical review. D.•May 21, 2021•5 citations

Relaxation of weakly interacting electrons in one dimension

Zoran Ristivojević, К. А. Матвеев

We consider the problem of relaxation in a one-dimensional system of interacting electrons. In the limit of weak interactions, we calculate the decay rate of a single-electron excitation, accounting for the nonlinear dispersion. The leading processes that determine the relaxation involve scattering of three particles. We elucidate how particular forms of Coulomb interaction, unscreened and screened, lead to different results for the decay rates and identify the dominant scattering processes responsible for relaxation of excitations of different energies. Interestingly, temperatures much smaller than the excitation energy strongly affect the rate. At higher temperatures the quasiparticle relaxes by exciting copropagating electron-hole pairs, whereas at lowest temperatures the relaxation proceeds via excitations of both copropagating and counterpropagating pairs.

arXiv:1301.3908•Physical Review B•Apr 5, 2013•24 citations

Quantum Boltzmann equation for fermions: an attempt to calculate the NMR relaxation times using the quantum field theory techniques

Hassan Manshouri, Ahmad Hoseinpour, Moslem Zarei

Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse relaxation times from the collision term by considering the nucleon-nucleon scattering.

•Sep 3, 2020•1 citation
Via the hierarchy of correlations, we study strongly interacting fermions on a lattice and derive a quantum Boltzmann equation describing their relaxation dynamics. Interestingly, in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. Therefore, the relaxation towards equilibrium strongly depends on what kind of excitations (particles or holes or both) are present.
Motivated by the recent interest in nonequilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium. The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z1/Z1/Z expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions---in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation timescales strongly depend on the type of excitations (particles or holes or both) that are initially present.
Via the hierarchy of correlations, we study the Mott insulator phase of the Fermi-Hubbard model in the limit of strong interactions and derive a quantum Boltzmann equation describing its relaxation dynamics. In stark contrast to the weakly interacting case, we find that the scattering cross sections strongly depend on the momenta of the colliding quasiparticles and holes. Therefore, the relaxation towards equilibrium crucially depends on the spectrum of excitations. For example, for particle-hole excitations directly at the minimum of the (direct) Mott gap, the scattering cross sections vanish such that these excitations can have a very long lifetime.
The rigorous derivation of the Uehling-Uhlenbeck equation from morefundamental quantum many-particle systems is a challenging open problem inmathematics. In this paper, we exam the weak coupling limit of quantum NNN-particle dynamics. We assume the integral of the microscopic interaction iszero and we assume W4,1W^{4,1}W4,1 per-particle regularity on the coresspondingBBGKY sequence so that we can rigorously commute limits and integrals. Weprove that, if the BBGKY sequence does converge in some weak sense, thenthis weak-coupling limit must satisfy the infinite quantum Maxwell-Boltzmannhierarchy instead of the expected infinite Uehling-Uhlenbeck hierarchy,regardless of the statistics the particles obey. Our result indicates that,in order to derive the Uehling-Uhlenbeck equation, one must work withper-particle regularity bound below W4,1W^{4,1}W4,1.
Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse (decoherence) relaxation times from the collision term by considering the nucleon-nucleon scattering.
We consider the problem of relaxation in a one-dimensional system of interacting electrons. In the limit of weak interactions, we calculate the decay rate of a single-electron excitation, accounting for the nonlinear dispersion. The leading processes that determine the relaxation involve scattering of three particles. We elucidate how particular forms of Coulomb interaction, unscreened and screened, lead to different results for the decay rates and identify the dominant scattering processes responsible for relaxation of excitations of different energies. Interestingly, temperatures much smaller than the excitation energy strongly affect the rate. At higher temperatures the quasiparticle relaxes by exciting copropagating electron-hole pairs, whereas at lowest temperatures the relaxation proceeds via excitations of both copropagating and counterpropagating pairs.
Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse relaxation times from the collision term by considering the nucleon-nucleon scattering.