Abstract The Hubbard model is a prototype for strongly correlated electrons in condensed matter, for molecules and fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the excitation and relaxation dynamics following a perturbation of the system are only poorly explored. Here, we present results for the dynamics of electrons following nonlinear strong excitation that are based on a nonequilibrium Green functions approach. We focus on small systems—“Hubbard nano‐clusters”—that contain just a few particles where, in addition to the correlation effects, finite size effects and spatial inhomegeneity can be studied systematically. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)Abstract The Hubbard model is a prototype for strongly correlated electrons in condensed matter, for molecules and fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the excitation and relaxation dynamics following a perturbation of the system are only poorly explored. Here, we present results for the dynamics of electrons following nonlinear strong excitation that are based on a nonequilibrium Green functions approach. We focus on small systems—“Hubbard nano‐clusters”—that contain just a few particles where, in addition to the correlation effects, finite size effects and spatial inhomegeneity can be studied systematically. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

arXiv:1309.4574Contributions to Plasma PhysicsDec 1, 201322 citations

Finite-size effects on critical diffusion and relaxation towards metastable equilibrium

Wulf Koch, V. Dohm

We present an analytic study of finite-size effects on critical diffusion above and below ${T}_{c}$ of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below ${T}_{c}.$ Two universal dynamic amplitude ratios at ${T}_{c}$ are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte Carlo simulations.We present an analytic study of finite-size effects on critical diffusion above and below ${T}_{c}$ of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below ${T}_{c}.$ Two universal dynamic amplitude ratios at ${T}_{c}$ are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte Carlo simulations.

arXiv:cond-mat/9802206Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsAug 1, 199821 citations

``Bare'' Effective Mass in Finite Sized $ν= 1/2$ Systems``Bare'' Effective Mass in Finite Sized $ν= 1/2$ Systems

A. Raghav Chari, F. D. M. Haldane

In this note, we discuss the effective mass of quasiparticles in finite sized $ν= 1/2$ systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for $ν= 1/2$ systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.In this note, we discuss the effective mass of quasiparticles in finite sized $ν= 1/2$ systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for $ν= 1/2$ systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.

arXiv:cond-mat/9709081Sep 5, 19970 citations

We present an analytic study of finite-size effects on critical diffusion above and below

{T}_{c}

of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below

{T}_{c}.

Two universal dynamic amplitude ratios at

{T}_{c}

are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte Carlo simulations.

``Bare'' Effective Mass in Finite Sized

ν= 1/2

Systems

In this note, we discuss the effective mass of quasiparticles in finite sized

ν= 1/2

systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for

ν= 1/2

systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.