20 research outputs found
Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
We discuss the problem of heat conduction in quantum spin chain models. To
investigate this problem it is necessary to consider the finite open system
connected to heat baths. We describe two different procedures to couple the
system with the reservoirs: a model of stochastic heat baths and the quantum
trajectories solution of the quantum master equation. The stochastic heat bath
procedure operates on the pure wave function of the isolated system, so that it
is locally and periodically collapsed to a quantum state consistent with a
boundary nonequilibrium state. In contrast, the quantum trajectories procedure
evaluates ensemble averages in terms of the reduced density matrix operator of
the system. We apply these procedures to different models of quantum spin
chains and numerically show their applicability to study the heat flow.Comment: 13 pages, 5 figures, submitted to European Physics Journal Special
Topic
Magnetically Induced Thermal Rectification
We consider far from equilibrium heat transport in chaotic billiard chains
with non-interacting charged particles in the presence of non-uniform
transverse magnetic field. If half of the chain is placed in a strong magnetic
field, or if the strength of the magnetic field has a large gradient along the
chain, heat current is shown to be asymmetric with respect to exchange of the
temperatures of the heat baths. Thermal rectification factor can be arbitrarily
large for sufficiently small temperature of one of the baths.Comment: 4 pages, 5 figure
Entanglement Across a Transition to Quantum Chaos
We study the relation between entanglement and quantum chaos in one- and
two-dimensional spin-1/2 lattice models, which exhibit mixing of the
noninteracting eigenfunctions and transition from integrability to quantum
chaos. Contrary to what occurs in a quantum phase transition, the onset of
quantum chaos is not a property of the ground state but take place for any
typical many-spin quantum state. We study bipartite and pairwise entanglement
measures, namely the reduced Von Neumann entropy and the concurrence, and
discuss quantum entanglement sharing. Our results suggest that the behavior of
the entanglement is related to the mixing of the eigenfunctions rather than to
the transition to chaos.Comment: 14 pages, 14 figure
Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient
In this paper we study the distribution function of the
estimators , which optimise the least-squares fitting of the diffusion coefficient
of a single -dimensional Brownian trajectory . We pursue
here the optimisation further by considering a family of weight functions of
the form , where is a time lag and
is an arbitrary real number, and seeking such values of for
which the estimators most efficiently filter out the fluctuations. We calculate
exactly for arbitrary and arbitrary spatial dimension
, and show that only for the distribution
converges, as , to the Dirac delta-function centered at
the ensemble average value of the estimator. This allows us to conclude that
only the estimators with possess an ergodic property, so that the
ensemble averaged diffusion coefficient can be obtained with any necessary
precision from a single trajectory data, but at the expense of a progressively
higher experimental resolution. For any the distribution
attains, as , a certain limiting form with a finite variance,
which signifies that such estimators are not ergodic.Comment: 27 pages, 5 figure
Increasing thermoelectric efficiency towards the Carnot limit
We study the problem of thermoelectricity and propose a simple microscopic
mechanism for the increase of thermoelectric efficiency. We consider the cross
transport of particles and energy in open classical ergodic billiards. We show
that, in the linear response regime, where we find exact expressions for all
transport coefficients, the thermoelectric efficiency of ideal ergodic gases
can approach Carnot efficiency for sufficiently complex charge carrier
molecules. Our results are clearly demonstrated with a simple numerical
simulation of a Lorentz gas of particles with internal rotational degrees of
freedom.Comment: RevTex, 4 pages, 3 figure
Heat flux in one-dimensional systems
ACKNOWLEDGMENTS L.R. has been partially supported by Ministero dell'Istruzione dell'Università e della Ricerca (MIUR) Grant “Dipartimenti di Eccellenza 2018–2022”, Project No. E11G 18 000 35 000 1. C.M.M. thanks the Department of Mathematical Sciences of Politecnico di Torino for its hospitality and acknowledges financial support from the Spanish Government Grant No. PGC2018-099944-B-I00 (MCIU/AEI/FEDER, UE). This work started and developed while C.M.M. was a long-term Visiting Professor of Politecnico di Torino.Peer reviewedPublisher PD
Optimal protocols and optimal transport in stochastic thermodynamics
Thermodynamics of small systems has become an important field of statistical
physics. They are driven out of equilibrium by a control, and the question is
naturally posed how such a control can be optimized. We show that optimization
problems in small system thermodynamics are solved by (deterministic) optimal
transport, for which very efficient numerical methods have been developed, and
of which there are applications in Cosmology, fluid mechanics, logistics, and
many other fields. We show, in particular, that minimizing expected heat
released or work done during a non-equilibrium transition in finite time is
solved by Burgers equation of Cosmology and mass transport by the Burgers
velocity field. Our contribution hence considerably extends the range of
solvable optimization problems in small system thermodynamics.Comment: 5 pages, RevTex4-1 forma
Foundations and applications of non-equilibrium statistical mechanics
The full text of this article is available in the PDF provided
Dynamical Mechanisms Leading to Equilibration in Two-component Gases
Demonstrating how microscopic dynamics cause large systems to approach thermal equilibrium remains an elusive, longstanding, and actively pursued goal of statistical mechanics. We identify here a dynamical mechanism for thermalization in a general class of two-component dynamical Lorentz gases and prove that each component, even when maintained in a nonequilibrium state itself, can drive the other to a thermal state with a well-defined effective temperature
Optimal fits of diffusion constants from single-time data points of Brownian trajectories
Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution