Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Green's functions techniques for computing the energy and particle statistics are presented.Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Green's functions techniques for computing the energy and particle statistics are presented.

arXiv:0811.3717Reviews of Modern PhysicsDec 2, 20091,414 citations

Out-of-equilibrium bosons on a one-dimensional optical random lattice

Thierry Platini, Rosemary J. Harris, Dragi Karevski

We study the transport properties of a one-dimensional hard-core boson lattice gas coupled to two particle reservoirs at different chemical potentials generating a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-κ(τ)\nabla ρ$ where $τ$ is a typical timescale of the lattice fluctuations and $\nabla ρ$ the density gradient imposed %on the system by the reservoirs.We study the transport properties of a one-dimensional hard-core boson lattice gas coupled to two particle reservoirs at different chemical potentials generating a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-κ(τ)\nabla ρ$ where $τ$ is a typical timescale of the lattice fluctuations and $\nabla ρ$ the density gradient imposed %on the system by the reservoirs.

arXiv:0811.3079Nov 19, 20080 citations

Complexity, Correlations and Fluctuations in Many-Particle Systems

Peter Carruthers

Recent Progress in Many-Body TheoriesJan 1, 19950 citations

Physics of many-particle systems : methods and problems

Emmanuel Meeron

Gordon and Breach eBooksJan 1, 196617 citations

Bosonic and fermionic transport phenomena of ultracold atoms in one-dimensional optical lattices

Chih-Chun Chien, Michael P. Zwolak, Massimiliano Di Ventra

Using the microcanonical picture of transport---a framework ideally suited to describe the dynamics of closed quantum systems such as ultracold atom experiments---we show that the exact dynamics of noninteracting fermions and bosons exhibits very different transport properties when the system is set out of equilibrium by removing the particles from half of the lattice. We find that fermions rapidly develop a finite quasisteady-state current reminiscent of electronic transport in nanoscale systems. This result is robust---it occurs with or without a harmonic confining potential and at zero or finite temperature. The zero-temperature bosonic current instead exhibits strong oscillatory behavior that decays into a steady-state of zero current only in the thermodynamic limit. These differences appear most strikingly in the different particle number fluctuations on half of the lattice as a consequence of the spin statistics. These predictions can be readily verified experimentally.Using the microcanonical picture of transport---a framework ideally suited to describe the dynamics of closed quantum systems such as ultracold atom experiments---we show that the exact dynamics of noninteracting fermions and bosons exhibits very different transport properties when the system is set out of equilibrium by removing the particles from half of the lattice. We find that fermions rapidly develop a finite quasisteady-state current reminiscent of electronic transport in nanoscale systems. This result is robust---it occurs with or without a harmonic confining potential and at zero or finite temperature. The zero-temperature bosonic current instead exhibits strong oscillatory behavior that decays into a steady-state of zero current only in the thermodynamic limit. These differences appear most strikingly in the different particle number fluctuations on half of the lattice as a consequence of the spin statistics. These predictions can be readily verified experimentally.

arXiv:1110.1646Physical Review AApr 10, 201244 citations

j=-κ(τ)\nabla ρ

where

τ

is a typical timescale of the lattice fluctuations and

\nabla ρ

the density gradient imposed %on the system by the reservoirs.