86 research outputs found
Charge-current correlation equalities for quantum systems far from equilibrium
We prove that a recently derived correlation equality between conserved
charges and their associated conserved currents for quantum systems far from
equilibrium [O.A. Castro-Alvaredo et al., Phys. Rev. X \textbf{6}, 041065
(2016)], is valid under more general conditions than assumed so far. Similar
correlation identities, which in generalized Gibbs ensembles give rise to a
current symmetry somewhat reminiscent of the Onsager relations, turn out to
hold also in the absence of translation invariance, for lattice models, and in
any space dimension, and to imply a symmetry of the non-equilibrium linear
response functions.Comment: 6 pages, major revision with extension to non-translation invariant
settin
Quantum Non-Equilibrium Steady States Induced by Repeated Interactions
We study the steady state of a finite XX chain coupled at its boundaries to
quantum reservoirs made of free spins that interact one after the other with
the chain. The two-point correlations are calculated exactly and it is shown
that the steady state is completely characterized by the magnetization profile
and the associated current. Except at the boundary sites, the magnetization is
given by the average of the reservoirs' magnetizations. The steady state
current, proportional to the difference in the reservoirs' magnetizations,
shows a non-monotonous behavior with respect to the system-reservoir coupling
strength, with an optimal current state for a finite value of the coupling.
Moreover, we show that the steady state can be described by a generalized Gibbs
state.Comment: to appear in Phys. Rev. Let
Comparative study of the critical behavior in one-dimensional random and aperiodic environments
We consider cooperative processes (quantum spin chains and random walks) in
one-dimensional fluctuating random and aperiodic environments characterized by
fluctuating exponents omega>0. At the critical point the random and aperiodic
systems scale essentially anisotropically in a similar fashion: length (L) and
time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents,
characterizing the singularities of average quantities, are found to be
universal functions of omega, whereas some others do depend on details of the
distribution of the disorder. In the off-critical region there is an important
difference between the two types of environments: in aperiodic systems there
are no extra (Griffiths)-singularities.Comment: 13 pages RevTeX, 10 eps-figures include
Fourier's law on a one-dimensional optical random lattice
We study the transport properties of a one-dimensional hard-core bosonic
lattice gas coupled to two particle reservoirs at different chemical potentials
which generate 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
where is a typical timescale of the lattice
fluctuations and the density gradient imposed by the reservoirs.Comment: 9 pages, 2 figure
Random and aperiodic quantum spin chains: A comparative study
According to the Harris-Luck criterion the relevance of a fluctuating
interaction at the critical point is connected to the value of the fluctuation
exponent omega. Here we consider different types of relevant fluctuations in
the quantum Ising chain and investigate the universality class of the models.
At the critical point the random and aperiodic systems behave similarly, due to
the same type of extreme broad distribution of the energy scales at low
energies. The critical exponents of some averaged quantities are found to be a
universal function of omega, but some others do depend on other parameters of
the distribution of the couplings. In the off-critical region there is an
important difference between the two systems: there are no Griffiths
singularities in aperiodic models.Comment: 4 pages RevTeX, 2 eps-figures include
Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
We consider the Ising model and the directed walk on two-dimensional layered
lattices and show that the two problems are inherently related: The zero-field
thermodynamical properties of the Ising model are contained in the spectrum of
the transfer matrix of the directed walk. The critical properties of the two
models are connected to the scaling behavior of the eigenvalue spectrum of the
transfer matrix which is studied exactly through renormalization for different
self-similar distributions of the couplings. The models show very rich bulk and
surface critical behaviors with nonuniversal critical exponents,
coupling-dependent anisotropic scaling, first-order surface transition, and
stretched exponential critical correlations. It is shown that all the
nonuniversal critical exponents obtained for the aperiodic Ising models satisfy
scaling relations and can be expressed as functions of varying surface magnetic
exponents.Comment: 22 pages, 8 eps-figures, uses RevTex and epsf, minor correction
Work fluctuations in quantum spin chains
We study the work fluctuations of two types of finite quantum spin chains
under the application of a time-dependent magnetic field in the context of the
fluctuation relation and Jarzynski equality. The two types of quantum chains
correspond to the integrable Ising quantum chain and the nonintegrable XX
quantum chain in a longitudinal magnetic field. For several magnetic field
protocols, the quantum Crooks and Jarzynski relations are numerically tested
and fulfilled. As a more interesting situation, we consider the forcing regime
where a periodic magnetic field is applied. In the Ising case we give an exact
solution in terms of double-confluent Heun functions. We show that the
fluctuations of the work performed by the external periodic drift are maximum
at a frequency proportional to the amplitude of the field. In the nonintegrable
case, we show that depending on the field frequency a sharp transition is
observed between a Poisson-limit work distribution at high frequencies toward a
normal work distribution at low frequencies.Comment: 10 pages, 13 figure
Historical and interpretative aspects of quantum mechanics: a physicists' naive approach
Many theoretical predictions derived from quantum mechanics have been
confirmed experimentally during the last 80 years. However, interpretative
aspects have long been subject to debate. Among them, the question of the
existence of hidden variables is still open. We review these questions, paying
special attention to historical aspects, and argue that one may definitively
exclude local realism on the basis of present experimental outcomes. Other
interpretations of Quantum Mechanics are nevertheless not excluded.Comment: 30 page
Lattice two-point functions and conformal invariance
A new realization of the conformal algebra is studied which mimics the
behaviour of a statistical system on a discrete albeit infinite lattice. The
two-point function is found from the requirement that it transforms covariantly
under this realization. The result is in agreement with explicit lattice
calculations of the Ising model and the dimensional spherical
model. A hard core is found which is not present in the continuum. For a
semi-infinite lattice, profiles are also obtained.Comment: 5 pages, plain Tex with IOP macros, no figure
Steps toward the foundations of statistical mechanics: in and out of equilibrium
The first part of the paper is devoted to the foundations, that is the mathematical and physical justification,
of equilibrium statistical mechanics. It is a pedagogical attempt, mostly based on Khinchin’s presentation,
which purpose is to clarify some aspects of the development of statistical mechanics. In the second part,
we discuss some recent developments that appeared out of equilibrium, such as fluctuation theorem and
Jarzynski equalit
- …