Session M44: Focus Session: Systems Far from Equiibrium III

Total cost of operating an information engine

We study a two-level system controlled in a discrete feedback loop, modeling both the system and the controller in terms of stochastic Markov processes. We find that the extracted work, which is known to be bounded from above by the mutual information acquired during measurement, has to be compensated by an additional energy supply during the measurement process itself, which is bounded by the mutual information from below. Our results confirm that the total cost to operate an information engine is in full agreement with the conventional second law of thermodynamics. We also consider the efficiency of the information engine in the finite-time case.   

Simulation of an epidemic model with vector transmission

We study a lattice model for vector-mediated transmission of a disease in a population consisting of two species, A and B, which contract the disease from one another. Individuals of species A are sedentary, while those of species B (the vector) diffuse in space. Examples of such diseases are malaria, dengue fever, and Pierce's disease in vineyards. The model exhibits a phase transition between an absorbing (infection free) phase and an active one as parameters such as infection rates and vector density are varied. We study the static and dynamic critical behavior of the model using initial spreading, initial decay, and quasistationary simulations. Simulations are checked against mean-field analysis. Although phase transitions to an absorbing state fall generically in the directed percolation universality class, this appears not to be the case for the present model.   

Equilibrium behavior of coarse-grained chaos

A wide variety of systems exhibiting spatiotemporal chaos have been shown to be extensive, in that their fractal dimensions grow linearly with volume. Ruelle argued that this extensivity is evidence that these systems can be viewed as a gas of weakly-interacting regions. We have tested this idea by performing large-scale computational studies of spatiotemporal chaos in the 1D complex Ginzburg-Landau equation, and we have found that aspects of the coarse-grained system are well-described not only as a gas, but as an {\it equilibrium} gas --- in particular, a Tonks gas (and variants) in the grand canonical ensemble. Furthermore, for small system sizes, the average number of particles in the corresponding Tonks gas exhibits oscillatory, decaying deviations from extensivity in agreement with deviations in the fractal dimension found by Fishman and Egolf. This result not only supports Ruelle's picture but also suggests that the coarse-grained behavior of this far-from-equilibrium system might be understood using equilibrium statistical mechanics.   

How to detect many body localization in experiments

The standard theory of many body localization (MBL) is framed in terms of exact eigenstates of perfectly isolated quantum systems. However, exact eigenstates can neither be prepared nor measured in the laboratory, and perfectly isolated quantum systems are equally unrealizable. In this talk I explain how MBL can be reformulated without invoking exact eigenstates or perfect isolation. I introduce a way to think about MBL in terms of correlation functions of local operators, evaluated in arbitrary states. This perspective reformulates the standard theory in terms of (in principle) experimentally measurable quantities. Moreover, this ``spectral'' perspective on MBL is far more robust than the conventional ``eigenstate'' perspective. Eigenstates thermalize upon arbitrarily weak coupling to an external environment, but the correlation functions (which are the physical observables) continue to show signatures of MBL as long as the coupling to the environment is weaker than the characteristic energy scales in the system Hamiltonian. I also show how this ``spectral perspective'' can be used to reveal additional structure in the MBL phase, and to make progress on otherwise intractable theory problems.   

Kinetics of Brownian Maxima

We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability $P(t)$ that the two maxima remain ordered up to time $t$, and find the algebraic decay $P\sim t^{-\beta}$ with exponent $\beta=1/4$. When the two particles have diffusion constants $D_1$ and $D_2$, the exponent depends on the mobilities, $\beta=\frac{1}{\pi}\arctan\sqrt{D_2/D_1}$. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.   

Attaining local temperatures close to absolute zero in a nonequilibrium quantum system

We consider a question motivated by the third law of thermodynamics: Can there be a local temperature arbitrarily close to absolute zero in a nonequilibrium quantum system? We consider ballistic quantum conductors with the source reservoir held at finite temperature and the drain held at or near absolute zero, a problem outside the scope of linear response theory.We obtain local temperatures close to absolute zero when electrons originating from the finite temperature reservoir undergo destructive quantum interference. We compute the local temperature by numerically solving a nonlinear system of equations describing equilibration of a scanning thermoelectric probe with the system, and obtain excellent agreement with analytic results derived using a method analogous to the Sommerfeld expansion.   

Local temperature of an interacting quantum system far from equilibrium

A theory of local temperature measurement of an interacting quantum electron system far from equilibrium via a floating thermoelectric probe is developed [1]. A number of relations are derived relating the probe temperature (and chemical potential) to the local properties of the nonequilibrium system, including a fluctuation-dissipation relation [2]. It is shown that the measured local electron temperature of a steady-state system arbitrarily far from equilibrium is consistent with the zeroth, first, second, and third laws of thermodynamics, provided the probe-system coupling is weak and broad band (ideal temperature measurement). For general probe-system couplings, there are corrections to the zeroth and first laws that are higher-order in the Sommerfeld expansion. The corrections to the zeroth and first laws are related, and can be interpreted in terms of the error of a non-ideal temperature measurement. [1] C. A. Stafford, arXiv:1409.3179; [2] J. Meair, J. P. Bergfield, C. A. Stafford, Ph. Jacquod, Phys. Rev. B 90, 035407 (2014)   

Thermodynamics of Maximum Transition Entropy for Quantum Assemblies

We present one possible unifying framework for the statistics of driven quantum systems in terms of a stochastic propagator for the density matrix. Its classical limit [Rogers, Beck and Rempe, J. Stat. Phys 145:385, 2011] takes the form of a Langevin equation with an associated large-deviation functional intimately related to the partition function of statistical mechanics. Surprising results of this quantum theory are that work is a measurable quantity, and that a precise form of the second law of thermodynamics can be stated for dynamical systems. Numerical results are presented for the time-course of work and heat production for trapped 1D particles. Properties of the large deviation functional are discussed in the context of the quantum measurement problem.   

Entropy Production in Isolated Quantum Many-Body Systems

Beginning with the Liouville-von Neumann equation for the density matrix of an isolated quantum many-body system, and applying well-known projection-operator techniques, we derive an equation of motion for the rate of change of the thermodynamic entropy, valid to arbitrary order in the perturbation deviating the system from equilibrium. To lowest order, a balance equation is obtained which coincides with the one defining the entropy production in irreversible thermodynamics. A connection with fluctuation theorems is mentioned, as well as an application of the results to clarify the ``thermalization problem'' in the Jaynes-Cummings model.   

Spin Noise Spectroscopy Beyond Thermal Equilibrium and Linear Response

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of 41K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.   

Finite N corrections to Vlasov dynamics and the range of pair interactions

We explore [1] the conditions on a pair interaction for the validity of the Vlasov equation to describe the dynamics of an interacting N particle system in the large N limit. Using a coarse-graining in phase space of the exact Klimontovich equation for such a system, we evaluate the scalings with N of the terms describing the corrections to the Vlasov equation for the coarse-grained one particle phase space density. Considering an interaction with radial pair force \textit{F(r) $\sim$ 1/r}$^{a}$, regulated to a bounded behavior below a ``softening'' scale $l$, we find that there is an essential qualitative difference between the cases \textit{a\textless d} (i.e. the spatial dimension) and \textit{a\textgreater d}, i.e., depending on the the integrability at large distances of $F(r)$. For \textit{a\textless d} the corrections to the Vlasov dynamics for a given coarse-grained scale are essentially insensitive to the softening parameter $l$, while for \textit{a\textgreater d} the corrections are directly regulated by $l$, i.e. by the small scale properties of the interaction, in agreement with the Chandrasekhar approach [2]. This gives a simple physical criterion for a basic distinction between long-range (\textit{a\textless d}) and short range (\textit{a\textgreater d}) interactions, different from the thermodynamic one (\textit{a\textless d-1} or \textit{a\textgreater d-1}). This alternative classification, based purely on dynamical arguments, is relevant notably to understanding the conditions for the existence of so-called quasi-stationary states in long-range interacting systems. \\[4pt] [1] A. Gabrielli et al., \underline {arxiv.org/abs/1408.0999}, to appear in PRE (2014)\\[0pt] [2] A. Gabrielli et al., PRL, \textbf{115}, 210602 (2010)   

Molecular dynamics study on a nonequilibrium motion of a colloidal particle driven by an external torque

We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use the molecular dynamics simulation that is alternative to the simulation based on the Langevin equation and is expected to mimic an experiment more realistically. We choose a heat bath composed of about a thousand particles interacting to each other through the Lenard-Jones potential and impose the Langevin thermostat to maintain it in equilibrium. We prepare a colloidal particle to interact with the particles of the heat bath also by the Lenard-Jones potential while any dissipative force and noise are not employed explicitly. We study the stochastic properties of the nonequilibrium fluctuation for work and heat produced incessantly in the steady state. We accurately confirm the fluctuation theorem for the work production. We also investigate the motion beyond the overdamped limit by varying the mass of the particle. We compare our result with a previous theoretical result in the overdamped limit based on the Langevin equation\footnote[1]{C. Kwon, J. D. Noh, and H. Park, Phys. Rev. E {\bf 83}, 061145 (2011).}.   

Transient Orthogonality Catastrophe in a Time Dependent Nonequilibrium Environment

We study the response of a highly-excited time dependent quantum many-body state to a sudden local perturbation, a sort of orthogonality catastrophe problem in a transient non-equilibrium environment. To this extent we consider, as key quantity, the overlap between time dependent wave-functions, that we write in terms of a novel two-time correlator generalizing the standard Loschmidt Echo. We discuss its physical meaning, general properties, and its connection with experimentally measurable quantities probed through non-equilibrium Ramsey interferometry schemes. Then we present explicit calculations for a one dimensional interacting Fermi system brought out of equilibrium by a sudden change of the interaction, and perturbed by the switching on of a local static potential. We show that different scattering processes give rise to remarkably different behaviors at long times, quite opposite from the equilibrium situation. In particular, while the forward scattering contribution retains its power law structure even in the presence of a large non-equilibrium perturbation, with an exponent that is strongly affected by the transient nature of the bath, the backscattering term is a source of non-linearity which generates an exponential decay in time of the Loschmidt Echo, reminiscent of