The fluctuation theorem for currents in open quantum systems

Andrieux, David; Gaspard, Pierre; Monnai, Takaaki; Tasaki, Seiji

doi:10.1088/1367-2630/11/4/043014

Cited by 207 publications

(392 citation statements)

References 49 publications

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“…Full counting statistics of energy fluctuations in a driven quantum resonator is studied by Clerk [36]. The main focus in these papers was on the long-time limit and SSFT [37][38][39][40][41][42]. Using the NEGF method [43,44] and two-time measurement [40,41,45,46] concept, Wang et al [39] gave an explicit expression for the CGF which is valid for both transient and steady state regimes.…”

Section: Introductionmentioning

confidence: 99%

Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems

Agarwalla

Wang

2012

Phys. Rev. E

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We study the statistics of heat transferred in a given time interval tM , through a finite harmonic chain, called the center (C), which is connected with two heat baths, the left (L) and the right (R), that are maintained at two different temperatures. The center atoms are driven by an external time-dependent force. We calculate the cumulant generating function (CGF) for the heat transferred out of the left lead, QL, based on two-time measurement concept and using nonequilibrium Green's function (NEGF) method. The CGF can be concisely expressed in terms of Green's functions of the center and an argument-shifted self-energy of the lead. The expression of CGF is valid in both transient and steady state regimes. We consider three different initial conditions for the density operator and show numerically, for one-dimensional (1D) linear chains, how transient behavior differs from each other but finally approaches the same steady state, independent of the initial distributions. We also derive the CGF for the joint probability distribution P (QL, QR), and discuss the correlations between QL and QR. We calculate the total entropy flow to the reservoirs. In the steady state we explicitly show that the CGF obeys steady state fluctuation theorem (SSFT). Classical results are obtained by taking → 0. The method is also applied to the counting of the electron number and electron energy, for which the associated self-energy is obtained from the usual lead self-energy by multiplying a phase or shifting the contour time, respectively.

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Section: Introductionmentioning

confidence: 99%

Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems

Agarwalla

Wang

2012

Phys. Rev. E

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“…with the initial condition U F (0; B) = I [19]. In the Heisenberg representation, the observables evolve according to…”

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confidence: 99%

Quantum Work Relations and Response Theory

2008

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A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski equality is recovered in the case this observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity relations are deduced thereof in the linear response regime.Nonequilibrium work relations have recently attracted much interest [1,2]. They provide relations for the work dissipated in time-dependent driven systems, independently of the form of the driving. They are of great interest to evaluate free energies under general nonequilibrium conditions and they provide new methods to study nanosystems. In the nanoscopic world, the extension of these classical relations to quantum systems is of particular importance and different approaches have been proposed.A first scheme was introduced by Kurchan [3]. In this framework, a measurement of the system state is performed at the initial time. In the sequel, the system is perturbed by a time-dependent Hamiltonian before performing another measurement at the final time. The random work performed on the system is associated with the energy difference between the final and initial eigenstates. This setup leads to the quantum extension of Jarzynski equality and Crooks fluctuation theorem [4,5,6,7]. Another possibility is to introduce a quantum work operator which measures the energy difference [8], in which cases quantum corrections to the fluctuation theorem must be taken into account. On the other hand, quantum fluctuation theorems have been obtained in suitable limits where the dynamics admits a Markovian description, allowing in particular the applications to nonequilibrium steady states [9,10,11,12,13,14]. Yet, the connection between the quantum work relations and response theory is still an open question even in the linear regime.The purpose of the present paper is to derive a new type of work relations which involves a functional of an arbitrary observable. This generating functional can be related to another functional but averaged over the timereversed process. This new work relation turns out to be of great generality since we can recover known results such as Jarzynski equality as special cases. Furthermore, this universal work relation allows us to formulate the response theory, to derive the quantum linear response functions, the quantum Green-Kubo relations [15,16], as well as the Casimir-Onsager reciprocity relations [17,18] in the regime close to the thermodynamic equilibrium.Functional symmetry relations. We suppose that the system is described by a Hamiltonian operator H(t; B) which depends on the time t and the magnetic field B. The time-reversal operator Θ is an antilinear operator such that Θ 2 = I and which has the effect of changing the sign of all odd parameters such as magnetic fields:We first introduce the forward process. The system is initially in thermal equilibrium at the inverse temperature β...

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“…Here, the dissipated power is defined as ε d = Q d /τ and the injected power as ε i = Q i /τ . Note that ε d ≥ 0 as Q d is always positive by definition in equation (13), while ε i can take any value.…”

Section: Large Deviation Functionmentioning

confidence: 99%

Modified saddle-point integral near a singularity for the large deviation function

2013

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Abstract. Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibit rare but huge fluctuations. Work or heat production is such a quantity, of which the probability distribution function displays an exponential decay characterized by the large deviation function (LDF). The LDF is often deduced from the cumulant generating function through the inverse Fourier transformation. The saddle-point integration method is a powerful technique to obtain the asymptotic results in the Fourier integral, but a special care should be taken when the saddle point is located near a singularity of the integrand. In this paper, we present a modified saddle-point method to handle such a difficulty efficiently. We investigate the dissipated and injected heat production in equilibration processes with various initial conditions, as an example, where the generating functions contain branch-cut singularities as well as power-law ones. Exploiting the new modified saddle-point integrations, we obtain the leading finite-time corrections for the LDF's, which are confirmed by numerical results.

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The fluctuation theorem for currents in open quantum systems

Cited by 207 publications

References 49 publications

Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems

Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems

Quantum Work Relations and Response Theory

Modified saddle-point integral near a singularity for the large deviation function

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