arXiv subjects

Peter Talkner

Publications and source records attributed to Peter Talkner.

At least 37 records · Page 2Linked to original sources

arXiv2015

Quantum fluctuation theorems and power measurements

Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system's dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.

cond-mat.stat-mech↗

arXiv2014

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

cond-mat.soft↗

arXiv2014

Unitary dynamics and finite-time measurements: a case study

The inhibition of the decay of a quantum system by frequent measurements is known as quantum Zeno effect. Beyond the limit of projective measurements, the interplay between the unitary dynamics of the system and the coupling to a measurement apparatus becomes relevant. We explore this interplay by considering a quantum particle moving on a one-dimensional chain. A local measurement by coupling to an apparatus with a two-dimensional Hilbert space detects the presence of the particle on a specific chain site. The decay of the population is studied analytically for a two-site chain and numerically for a larger system as a function of the measurement time and the time between subsequent measurements. Particular attention is given to the shift of the energy of the measured site due to the coupling to the apparatus. The decay of the initial population can be hindered or accelerated, depending on the chosen system and the coupling parameters.

quant-ph↗

arXiv2014

Generalized energy measurements and modified transient quantum fluctuation theorems

Determining the work which is supplied to a system by an external agent, provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements, and even yields a projective measurement in the limit of infinite repetitions.

cond-mat.stat-mech↗

arXiv2014

Quantum fluctuation theorems and generalized measurements during the force protocol

Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by Campisi {\it et al.} [M. Campisi, P. Talkner, and P. Hänggi, Phys. Rev. Lett. {\bf 105}, 140601 (2010); Phys. Rev. E {\bf 83}, 041114 (2011)], we find that these fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a {\it joint} probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function {\it conditioned} on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed fluctuation theorems with an arbitrary number of intervening measurements are obtained.

cond-mat.stat-mech↗

arXiv2013

Transient quantum fluctuation theorems and generalized measurements

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far these theorems have been obtained under the assumption that the work is determined by projective measurements at the end and the beginning of each run of the protocols. We found that one can replace these projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. We illustrate our results by the example of a two-level system for different generalized measurements.

cond-mat.stat-mech↗

arXiv2013

Statistics of work and fluctuation theorems for microcanonical initial states

The work performed on a system in a microcanonical state by changes in a control parameter is characterized in terms of its statistics. The transition probabilities between eigenstates of the system Hamiltonians at the beginning and the end of the parameter change obey a detailed balance-like relation from which various forms of the microcanonical fluctuation theorem are obtained. As an example, sudden deformations of a two dimensional harmonic oscillator potential are considered and the validity of the microcanonical Jarzynski equality connecting the degrees of degeneracy of energy eigenvalues before and after the control parameter change is confirmed.

cond-mat.stat-mech↗

arXiv2012

Comparison of free energy estimators and their dependence on dissipated work

The estimate of free energy changes based on Bennett's acceptance ratio method is examined in several limiting cases and compared with other estimates based on the Jarzynski equality and on the Crooks relation. While the absolute amount of dissipated work, defined as the surplus of average work over the free energy difference, limits the practical applicability of Jarzynski's and Crooks' methods, the reliability of Bennett's approach is restricted by the difference of the dissipated works in the forward and the backward process. We illustrate these points by considering a Gaussian chain and a hairpin chain which both are extended during the forward and accordingly compressed during the backward protocol. The reliability of the Crooks relation predominantly depends on the sample size; for the Jarzynski estimator the slowness of the work protocol is crucial, and the Bennett method is shown to give precise estimates irrespective of the pulling speed and sample size as long as the dissipated works are the same for the forward and the backward process as it is the case for Gaussian work distributions. With an increasing dissipated work difference the Bennett estimator also acquires a bias which increases roughly in proportion to this difference. A substantial simplification of the Bennett estimator is provided by the 1/2-formula which expresses the free energy difference by the algebraic average of the Jarzynski estimates for the forward and the backward processes. It agrees with the Bennett estimate in all cases when the Jarzynski and the Crooks estimates fail to give reliable results.

cond-mat.stat-mech↗

arXiv2012

Reply to M. Meléndez and W. G. Hoover [arXiv:1206.0188v2]

In response to the recent critical comment by M. Meléndez and W. G. Hoover [arXiv:1206.0188v2] on our work [M. Campisi et al., Phys. Rev. Lett. 108, 250601 (2012)], we show that their molecular dynamics simulations do not disprove our theory but in fact convincingly corroborate it.

cond-mat.stat-mech↗

arXiv2012

Logarithmic oscillators: ideal Hamiltonian thermostats

A logarithmic oscillator (in short, log-oscillator) behaves like an ideal thermostat because of its infinite heat capacity: when it weakly couples to another system, time averages of the system observables agree with ensemble averages from a Gibbs distribution with a temperature T that is given by the strength of the logarithmic potential. The resulting equations of motion are Hamiltonian and may be implemented not only in a computer but also with real-world experiments, e.g., with cold atoms.

cond-mat.stat-mech↗

arXiv2012

Deterministic transport of particles in a micro-pump

We study the drift of suspended micro-particles in a viscous liquid pumped back and forth through a periodic lattice of pores (drift ratchet). In order to explain the particle drift observed in such an experiment, we present an one-dimensional deterministic model of Stokes' drag. We show that the stability of oscillations of particle is related to their amplitude. Under appropriate conditions, particles may drift and two mechanisms of transport are pointed out. The first one is due to an spatio-temporal synchronization between the fluid and particle motions. As results the velocity is locked by the ratio of the space periodicity over the time periodicity. The direction of the transport may switch by tuning the parameters. Noteworthy, its emergence is related to a lattice of 2-periodic orbits but not necessary to chaotic dynamics. The second mechanism is due to an intermittent bifurcation and leads to a slow transport composed by long time oscillations following by a relative short transport to the next pore. Both steps repeat in a quasi-periodic manner. The direction of this last transport is strongly dependent on the pore geometry.

physics.flu-dyn↗

arXiv2012

Reply to W. G. Hoover [arXiv:1204.0312v2]

In response to W. G. Hoover's comment [arXiv:1204.0312v2] on our work [arXiv:1203.5968], we show explicitly that the divergence of the velocity field associated with the Nosé-Hoover equations is nonzero, implying that those equations are not volume preserving, and hence, as often stated in the literature, are not Hamiltonian. We further elucidate that the trajectories {q(t)} generated by the Nosé-Hoover equations are generally not identical to those generated by Dettmann's Hamiltonian. Dettmann's Hamiltonian produces the same trajectories as the Nosé-Hoover equations only on a specific energy shell, but not on the neighboring ones. This fact explains why the Nosé-Hoover equations are not volume preserving. The Hamiltonian that we put forward with [arXiv:1203.5968] instead produces thermostated dynamics irrespective of the energy value. The main advantage of our Hamiltonian thermostat over previous ones is that it contains kinetic energy terms that are of standard form with coordinate-independent masses and consequently is readily matched in laboratory experiments.

cond-mat.stat-mech↗

arXiv2012

Work fluctuations for Bose particles in grand canonical initial states

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the initial equilibrium state, the exponentiated work average (EWA) defined in the context of the Crooks relation and the Jarzynski equality may diverge if the trap becomes wider. We investigate how the probability distribution function (PDF) of the work signals this divergence. It is shown that at low temperatures the PDF is highly asymmetric with a steep fall off at one side and an exponential tail at the other side. For high temperatures it is closer to a symmetric distribution approaching a Gaussian form. These properties of the work PDF are discussed in relation to the convergence of the EWA and to the existence of the hypothetical equilibrium state to which those thermodynamic potential changes refer that enter both the Crooks relation and the Jarzynski equality.

cond-mat.stat-mech↗

arXiv2012

Transport of flexible chiral objects in a uniform shear flow

The transport of slightly deformable chiral objects in a uniform shear flow is investigated. Depending on the equilibrium configuration one finds up to four different asymptotic states that can be distinguished by a lateral drift velocity of their center of mass, a rotational motion about the center of mass and deformations of the object. These deformations influence the magnitudes of the principal axes of the second moment tensor of the considered object and also modify a scalar index characterizing its chirality. Moreover, the deformations induced by the shear flow are essential for the phenomenon of dynamical symmetry breaking: Objects that are achiral under equilibrium conditions may dynamically acquire chirality and consequently experience a drift in the lateral direction.

cond-mat.soft↗

arXiv2012

Beyond Zeno: Approaching Infinite Temperature upon Repeated Measurements

The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied in dependence of the time lag $τ$ between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponential in the case of finite Hilbert space dimension. The rate characterizing this approach undergoes a sharp transition from a monotonically increasing to an erratically varying function of the time between subsequent measurements.

quant-ph↗

arXiv2011

Colloquium. Quantum Fluctuation Relations: Foundations and Applications

Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars we guide the reader through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)-linear response theory. We also attempt to clarify a number of fundamental issues which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.

cond-mat.stat-mech↗

arXiv2011

Nonequilibrium work statistics of an Aharonov-Bohm flux

We investigate the statistics of work performed on a noninteracting electron gas confined into a ring as a threaded magnetic field is turned on. For an electron gas initially prepared in a grand canonical state it is demonstrated that the Jarzynski equality continues to hold in this case, with the free energy replaced by the grand potential. The work distribution displays a marked dependence on the temperature. While in the classical (high temperature) regime, the work probability density function follows a Gaussian distribution and the free energy difference entering the Jarzynski equality is null, the free energy difference is finite in the quantum regime, and the work probability distribution function becomes multimodal. We point out the dependence of the work statistics on the number of electrons composing the system.

cond-mat.stat-mech↗

arXiv2011

First passage time statistics of Brownian motion with purely time dependent drift and diffusion

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model for water availability from surface runoff in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated.

cond-mat.stat-mech↗