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:cond-mat/0405523

Non-exponential relaxations in disordered conductors

Gilles Montambaux, Éric Akkermans

Published May 21, 2004• 0 citations
arXivHTMLPDF

Abstract

We show that, in low dimensional conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In quasi-one dimension, they scale as $e^{- (t/τ_N)^{3/2}}$ where the characteristic time $τ_{in}$, identical for both processes, is a power $T^{2/3}$ of the temperature. This result implies a distribution of relaxation times.

DOI
10.48550/arxiv.cond-mat/0405523

Related papers

Nonexponential Quasiparticle Decay and Phase Relaxation in Low-Dimensional Conductors

Gilles Montambaux, Éric Akkermans

We show that in low-dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one-dimensional case, both behave at small time as e(-(t/tau(in))3/2) where the inelastic time, tau(in), identical for both processes, is a power T-2/3 of the temperature. The nonexponential quasiparticle decay results from a modified derivation of the Fermi golden rule. This result implies the existence of an unusual distribution of relaxation times.

arXiv:cond-mat/0404361•Physical Review Letters•Jun 29, 2005•16 citations

Dynamic scaling and non exponential relaxations in the presence of disorder. Application to spin glasses

B. Castaing, Jean Souletie

Assuming that hierarchical procedure governs the evolution from one to the next step of Kadanoff's renormalization in the presence of some disorder one finds that the dynamic response is described by a log-normal distribution of the relaxation times. There are two natural limits to the model which restitute either the dynamic scaling or the activated dynamic hypotheses. This provides the basis for a simple justification to the success of the usual fits by a stretched exponential or by a Cole-Cole law which are commonly made to the non-exponential responses observed in the time or in the frequency domains in spin glasses. We provide expressions for the temperature dependences of the parameters which control these laws. We also propose a model for freezing which is based on the idea that $\partial$ ln $\tau/\partial(1/T)$ should be continuous at the freezing point. We discuss available data in spin glasses but our conclusions should be very general.

Journal de Physique I•Mar 1, 1991•30 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 quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time

Ehsan Khatami, Marcos Rigol, Armando Relaño +1 more

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.

arXiv:1103.0787•Physical Review E•May 15, 2012•79 citations

Universal long-time relaxation on lattices of classical spins: Markovian behavior on non-Markovian timescales

Boris V. Fine

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two-, and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.

•Jan 1, 2003•17 citations

Equilibration of a one-dimensional quantum liquid

К. А. Матвеев

We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low temperatures, the relaxation of the gas of excitations toward full equilibrium is exponentially slow. In electronic Luttinger liquids, these relaxation processes involve backscattering of electrons and give rise to interesting corrections to the transport properties of one-dimensional conductors. We focus on the phenomenological theory of the equilibration of a quantum liquid and obtain an expression for the relaxation rate in terms of the excitation spectrum.

arXiv:1304.6012•Journal of Experimental and Theoretical Physics•Sep 1, 2013•10 citations
We show that, in low dimensional conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In quasi-one dimension, they scale as e−(t/τN)3/2e^{- (t/τ_N)^{3/2}}e−(t/τN​)3/2 where the characteristic time τinτ_{in}τin​, identical for both processes, is a power T2/3T^{2/3}T2/3 of the temperature. This result implies a distribution of relaxation times.
We show that in low-dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one-dimensional case, both behave at small time as e(-(t/tau(in))3/2) where the inelastic time, tau(in), identical for both processes, is a power T-2/3 of the temperature. The nonexponential quasiparticle decay results from a modified derivation of the Fermi golden rule. This result implies the existence of an unusual distribution of relaxation times.
Assuming that hierarchical procedure governs the evolution from one to the next step of Kadanoff's renormalization in the presence of some disorder one finds that the dynamic response is described by a log-normal distribution of the relaxation times. There are two natural limits to the model which restitute either the dynamic scaling or the activated dynamic hypotheses. This provides the basis for a simple justification to the success of the usual fits by a stretched exponential or by a Cole-Cole law which are commonly made to the non-exponential responses observed in the time or in the frequency domains in spin glasses. We provide expressions for the temperature dependences of the parameters which control these laws. We also propose a model for freezing which is based on the idea that ∂\partial∂ ln τ/∂(1/T)\tau/\partial(1/T)τ/∂(1/T) should be continuous at the freezing point. We discuss available data in spin glasses but our conclusions should be very general.
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.
We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.
The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two-, and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.
We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low temperatures, the relaxation of the gas of excitations toward full equilibrium is exponentially slow. In electronic Luttinger liquids, these relaxation processes involve backscattering of electrons and give rise to interesting corrections to the transport properties of one-dimensional conductors. We focus on the phenomenological theory of the equilibration of a quantum liquid and obtain an expression for the relaxation rate in terms of the excitation spectrum.