761 research outputs found
Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
We study the transport of cold fermionic atoms trapped in optical lattices in
the presence of artificial Abelian or non-Abelian gauge potentials. Such
external potentials can be created in optical lattices in which atom tunneling
is laser assisted and described by commutative or non-commutative tunneling
operators. We show that the Hall-like transverse conductivity of such systems
is quantized by relating the transverse conductivity to topological invariants
known as Chern numbers. We show that this quantization is robust in non-Abelian
potentials. The different integer values of this conductivity are explicitly
computed for a specific non-Abelian system which leads to a fractal phase
diagram.Comment: 6 pages, 2 figure
Heat transport in stochastic energy exchange models of locally confined hard spheres
We study heat transport in a class of stochastic energy exchange systems that
characterize the interactions of networks of locally trapped hard spheres under
the assumption that neighbouring particles undergo rare binary collisions. Our
results provide an extension to three-dimensional dynamics of previous ones
applying to the dynamics of confined two-dimensional hard disks [Gaspard P &
Gilbert T On the derivation of Fourier's law in stochastic energy exchange
systems J Stat Mech (2008) P11021]. It is remarkable that the heat conductivity
is here again given by the frequency of energy exchanges. Moreover the
expression of the stochastic kernel which specifies the energy exchange
dynamics is simpler in this case and therefore allows for faster and more
extensive numerical computations.Comment: 21 pages, 5 figure
On the derivation of Fourier's law in stochastic energy exchange systems
We present a detailed derivation of Fourier's law in a class of stochastic
energy exchange systems that naturally characterize two-dimensional mechanical
systems of locally confined particles in interaction. The stochastic systems
consist of an array of energy variables which can be partially exchanged among
nearest neighbours at variable rates. We provide two independent derivations of
the thermal conductivity and prove this quantity is identical to the frequency
of energy exchanges. The first derivation relies on the diffusion of the
Helfand moment, which is determined solely by static averages. The second
approach relies on a gradient expansion of the probability measure around a
non-equilibrium stationary state. The linear part of the heat current is
determined by local thermal equilibrium distributions which solve a
Boltzmann-like equation. A numerical scheme is presented with computations of
the conductivity along our two methods. The results are in excellent agreement
with our theory.Comment: 19 pages, 5 figures, to appear in Journal of Statistical Mechanics
(JSTAT
Quantum work relations and response theory
A universal quantum work relation is proved for isolated time-dependent
Hamiltonian systems in a magnetic field as the consequence of
microreversibility. This relation involves a functional of an arbitrary
observable. The quantum Jarzynski equality is recovered in the case this
observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity
relations are deduced thereof in the linear response regime
Thermodynamic time asymmetry in nonequilibrium fluctuations
We here present the complete analysis of experiments on driven Brownian
motion and electric noise in a circuit, showing that thermodynamic entropy
production can be related to the breaking of time-reversal symmetry in the
statistical description of these nonequilibrium systems. The symmetry breaking
can be expressed in terms of dynamical entropies per unit time, one for the
forward process and the other for the time-reversed process. These entropies
per unit time characterize dynamical randomness, i.e., temporal disorder, in
time series of the nonequilibrium fluctuations. Their difference gives the
well-known thermodynamic entropy production, which thus finds its origin in the
time asymmetry of dynamical randomness, alias temporal disorder, in systems
driven out of equilibrium.Comment: to be published in : Journal of Statistical Mechanics: theory and
experimen
Thermodynamics of Quantum Jump Trajectories
We apply the large-deviation method to study trajectories in dissipative
quantum systems. We show that in the long time limit the statistics of quantum
jumps can be understood from thermodynamic arguments by exploiting the analogy
between large-deviation and free-energy functions. This approach is
particularly useful for uncovering properties of rare dissipative trajectories.
We also prove, via an explicit quantum mapping, that rare trajectories of one
system can be realized as typical trajectories of an alternative system.Comment: 5 pages, 3 figure
Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems
We calculate the spectrum of Lyapunov exponents for a point particle moving
in a random array of fixed hard disk or hard sphere scatterers, i.e. the
disordered Lorentz gas, in a generic nonequilibrium situation. In a large
system which is finite in at least some directions, and with absorbing boundary
conditions, the moving particle escapes the system with probability one.
However, there is a set of zero Lebesgue measure of initial phase points for
the moving particle, such that escape never occurs. Typically, this set of
points forms a fractal repeller, and the Lyapunov spectrum is calculated here
for trajectories on this repeller. For this calculation, we need the solution
of the recently introduced extended Boltzmann equation for the nonequilibrium
distribution of the radius of curvature matrix and the solution of the standard
Boltzmann equation. The escape-rate formalism then gives an explicit result for
the Kolmogorov Sinai entropy on the repeller.Comment: submitted to Phys Rev
Persistence effects in deterministic diffusion
In systems which exhibit deterministic diffusion, the gross parameter
dependence of the diffusion coefficient can often be understood in terms of
random walk models. Provided the decay of correlations is fast enough, one can
ignore memory effects and approximate the diffusion coefficient according to
dimensional arguments. By successively including the effects of one and two
steps of memory on this approximation, we examine the effects of
``persistence'' on the diffusion coefficients of extended two-dimensional
billiard tables and show how to properly account for these effects, using walks
in which a particle undergoes jumps in different directions with probabilities
that depend on where they came from.Comment: 7 pages, 7 figure
Bohr-Sommerfeld Quantization of Periodic Orbits
We show, that the canonical invariant part of corrections to the
Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be
computed by the Bohr-Sommerfeld quantization rules, which usually apply for
integrable systems. We argue that the information content of the classical
action and stability can be used more effectively than in the usual treatment.
We demonstrate the improvement of precision on the example of the three disk
scattering system.Comment: revte
Understanding deterministic diffusion by correlated random walks
Low-dimensional periodic arrays of scatterers with a moving point particle
are ideal models for studying deterministic diffusion. For such systems the
diffusion coefficient is typically an irregular function under variation of a
control parameter. Here we propose a systematic scheme of how to approximate
deterministic diffusion coefficients of this kind in terms of correlated random
walks. We apply this approach to two simple examples which are a
one-dimensional map on the line and the periodic Lorentz gas. Starting from
suitable Green-Kubo formulas we evaluate hierarchies of approximations for
their parameter-dependent diffusion coefficients. These approximations converge
exactly yielding a straightforward interpretation of the structure of these
irregular diffusion coeficients in terms of dynamical correlations.Comment: 13 pages (revtex) with 5 figures (postscript
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