Emergence of Boltzmann Subspaces in Open Quantum Systems Far from Equilibrium.

Single molecule junctions are important examples of complex out-of-equilibrium many-body quantum systems. We identify a nontrivial clustering of steady state populations into distinctive subspaces with Boltzmann-like statistics, which persist far from equilibrium. Such Boltzmann subspaces significantly reduce the information needed to describe the steady state, enabling modeling of high-dimensional systems that are otherwise beyond the reach of current computations. The emergence of Boltzmann subspaces is demonstrated analytically and numerically for fermionic transport systems of increasing complexity.

Nonuniform convergence in moment expansions of integral work relations.

Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit nonuniform convergence in certain singular limits. The first example is a simple model of a process with measurement and feedback. In this example, the limit of interest is that of error-free measurements. The second system we study is an ideal gas particle inside an (infinitely) fast expanding piston. Both examples show qualitative similarities; the low-order moments are close to their limiting value, while high-order moments strongly deviate from their limit. As the limit is approached the transition between the two groups of moments is pushed toward higher and higher moments. Our findings highlight the importance of the ordering of limits in certain nonequilibrium-related calculations.

Experimental Realization of an Information Machine with Tunable Temporal Correlations.

We experimentally realize a Maxwell's demon that converts information gained by measurements to work. Our setup is composed of a colloidal particle in a channel filled with a flowing fluid. A barrier made by light prevents the particle from being carried away by the flow. The colloidal particle then performs biased Brownian motion in the vicinity of the barrier. The particle's position is measured periodically. When the particle is found to be far enough from the barrier, feedback is applied by moving the barrier upstream while maintaining a given minimal distance from the particle. At steady state, the net effect of this measurement and feedback loop is to steer the particle upstream while applying very little direct work on it. This clean example of a Maxwell's demon is also naturally operated in a parameter regime where correlations between outcomes of consecutive measurements are important. Interestingly, we find a tradeoff between output power and efficiency. The efficiency is maximal at quasistatic operating conditions, whereas both the power output and rate of information gain are maximal for very frequent measurements.

Nonequilibrium free-energy estimation conditioned on measurement outcomes.

The Jarzynski equality is one of the most influential results in the field of nonequilibrium statistical mechanics. This celebrated equality allow the calculation of equilibrium free-energy differences from work distributions of nonequilibrium processes. In practice, such calculations often suffer from poor convergence due to the need to sample rare events. Here we examine if the inclusion of measurement and feedback can improve the convergence of nonequilibrium free-energy calculations. A modified version of the Jarzynski equality in which realizations with a given outcome are kept, while others are discarded, is used. We find that discarding realizations with unwanted outcomes can result in improved convergence compared to calculations based on the Jarzynski equality. We argue that the observed improved convergence is closely related to Bennett's acceptance ratio method, which was developed without any reference to measurements or feedback.

Kinetic discrimination of a polymerase in the presence of obstacles.

One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single-stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motor's fidelity does not depend on details of the motor-junction interaction, such as whether the interaction is passive or active. Analysis of the copying fidelity can still be used as a tool for investigating the junction kinetics.

Validity of the no-pumping theorem in systems with finite-range interactions between particles.

The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle systems with zero-range interactions. Interestingly, it is known that the theorem is violated by systems with exclusion interactions. These two paradigmatic interactions differ by two qualitative aspects: the range of interactions and the dependence of branching fractions on the state of the system. In this work two different models are studied in order to identify the qualitative property of the interaction that leads to breakdown of no pumping. A model with finite-range interaction is shown analytically to satisfy no pumping. In contrast, a model in which the interaction affects the probabilities of reaching different sites, given that a particle is making a transition, is shown numerically to violate the no-pumping theorem. The results suggest that systems with interactions that lead to state-dependent branching fractions do not satisfy the no-pumping theorem.

Integral fluctuation theorems for stochastic resetting systems.

We study the stochastic thermodynamics of resetting systems. Violation of microreversibility means that the well-known derivations of fluctuations theorems break down for dynamics with resetting. Despite that we show that stochastic resetting systems satisfy two integral fluctuation theorems. The first is the Hatano-Sasa relation describing the transition between two steady states. The second integral fluctuation theorem involves a functional that includes both dynamical and thermodynamic contributions. We find that the second law-like inequality found by Fuchs et al. for resetting systems [Europhys. Lett. 113, 60009 (2016)EULEEJ0295-507510.1209/0295-5075/113/60009] can be recovered from this integral fluctuation theorem with the help of Jensen's inequality.

No-pumping theorem for many particle stochastic pumps.

Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett. 101, 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfies an additional no-pumping theorem.

Nonequilibrium steady state and induced currents of a mesoscopically glassy system: interplay of resistor-network theory and Sinai physics.

We introduce an explicit solution for the nonequilibrium steady state (NESS) of a ring that is coupled to a thermal bath, and is driven by an external hot source with log-wide distribution of couplings. Having time scales that stretch over several decades is similar to glassy systems. Consequently there is a wide range of driving intensities where the NESS is like that of a random walker in a biased Brownian landscape. We investigate the resulting statistics of the induced current I. For a single ring we discuss how sign of I fluctuates as the intensity of the driving is increased, while for an ensemble of rings we highlight the fingerprints of Sinai physics on the distribution of the absolute value of I.

Multidimensional measures of impulsively driven stochastic systems based on the Kullback-Leibler distance.

By subjecting a dynamical system to a series of short pulses and varying several time delays, we can obtain multidimensional characteristic measures of the system. Multidimensional Kullback-Leibler response function (KLRF), which are based on the Kullback-Leibler distance between the initial and final states, are defined. We compare the KLRF, which are nonlinear in the probability density, with ordinary response functions obtained from the expectation value of a dynamical variable, which are linear. We show that the KLRF encode different level of information regarding the system's dynamics. For overdamped stochastic dynamics two-dimensional KLRF shows a qualitatively different variation with the time delays between pulses, depending on whether the system is initially in a steady state or in thermal equilibrium.

Stimulated coherent anti-Stokes Raman spectroscopy (CARS) resonances originate from double-slit interference of two-photon Stokes pathways.

Coherent anti-Stokes Raman spectroscopy (CARS) uses vibrational resonances to study nuclear wavepacket motions and is widely used in cell imaging and other applications. The resonances usually lie on top of a parametric component that involves no change in the molecular state and creates an undesirable background which reduces the sensitivity of the technique. Here, by examining the process from the perspective of the molecule, rather than the field, we are able to separate the two components and recast each resonance as a modulus square of a transition amplitude which contains an interference between two Stokes pathways, each involving a different pair of field modes. We further propose that dissipative signals obtained by measuring the total absorption of all field modes in a convenient collinear pulse geometry can eliminate the parametric component and retain the purely resonant contributions. Specific vibrational resonances may then be readily detected using pulse shapers through derivatives with respect to pulse parameters.

Manipulating stimulated coherent anti-Stokes Raman spectroscopy signals by broad-band and narrow-band pulses.

A transition-amplitude based representation of heterodyne detected coherent anti-Stokes Raman signals is used to separate them into a parametric component that involves no change in the material and dissipative processes associated with various transitions between states. Qualitatively different contributions from the two processes are predicted for the signal generated by an overlapping narrow (picosecond) and broad-band (femtosecond) pulse.

Directed flow in nonadiabatic stochastic pumps.

We analyze the operation of a molecular machine driven by the nonadiabatic variation of external parameters. We derive a formula for the integrated flow from one configuration to another, obtain a "no-pumping theorem" for cyclic processes with thermally activated transitions, and show that in the adiabatic limit the pumped current is given by a geometric expression.

Ehrenfest time and the coherent backscattering off ballistic cavities.

If the Ehrenfest time tau(E) of a ballistic cavity is not negligible in comparison to its dwell time tau(D), the weak localization correction to the cavity's transmission is suppressed proportional to exp(-tau(E/tau(D). At the same time, quantum interference enhances the probability of reflection into the mode of incidence by a factor two. This "enhanced backscattering" does not depend on the Ehrenfest time. We show that, in addition to the diagonal enhanced backscattering, there are off-diagonal contributions to coherent backscattering that become relevant if tau(E) > or = tau(D).

Spectral form factor near the Ehrenfest time.

We calculate the Ehrenfest-time dependence of the leading quantum correction to the spectral form factor of a ballistic chaotic cavity using periodic orbit theory. For the case of broken time-reversal symmetry, when the quantum correction to the form factor involves two small-angle encounters of classical trajectories, our result differs from that previously obtained using field-theoretic methods [Tian and Larkin, Phys. Rev. B 70, 035305 (2004)]. While we believe that the existing field-theoretic calculation is technically flawed, the question whether the field theoretic and periodic-orbit approaches agree when more than one small-angle encounter of classical orbits is involved remains unanswered.

Ehrenfest-time dependence of weak localization in open quantum dots.

Semiclassical theory predicts that the weak localization correction to the conductance of a ballistic chaotic cavity is suppressed if the Ehrenfest time exceeds the dwell time in the cavity [I. L. Aleiner and A. I. Larkin, Phys. Rev. B 54, 14423 (1996)]. We report numerical simulations of weak localization in the open quantum kicked rotator that confirm this prediction. Our results disagree with the "effective random matrix theory" of transport through ballistic chaotic cavities.

Time-independent approximations for periodically driven systems with friction.

The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency omega) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the slow part is found to be described by a time-independent equation that is derived as an expansion in orders of omega(-1) (in this paper terms to the order omega(-3) are calculated explicitly). This time-independent equation is used to calculate the attracting fixed points and their basins of attraction. The results are found to be in excellent agreement with numerical solutions of the original time-dependent problem.

Time independent description of rapidly oscillating potentials.

The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency (omega) to order omega(-4). The work is an extension of the classical result for the Kapitza pendulum, which was calculated in the past to order omega(-2). The analysis makes use of an implementation of the method of separation of time scales and of a quantum gauge transformation in the framework of Floquet theory. The effective time independent Hamiltonian enables one to explore the dynamics in the presence of rapidly oscillating fields, in the framework of theories that were developed for systems with time independent Hamiltonians. The results are relevant, in particular, for exploring the dynamics of cold atoms.

Localized perturbations of integrable quantum billiards.

The statistics of energy levels of a rectangular billiard that is perturbed by a strong localized potential are studied analytically and numerically, when this perturbation is at the center or at a typical position. Different results are found for these two types of position. If the scatterer is at the center, the symmetry leads to additional contributions, some of which are related to the angular dependence of the potential. The limit of the delta-like scatterer is obtained explicitly. The form factor, which is the Fourier transform of the energy-energy correlation function, is calculated analytically, in the framework of the semiclassical geometrical theory of diffraction, and numerically. Contributions of classical orbits that are nondiagonal are calculated and are found to be essential.