Statistics of heat transfer in mesoscopic circuits

Kindermann, Markus; Pilgram, Sebastian

doi:10.1103/physrevb.69.155334

Cited by 51 publications

(83 citation statements)

References 27 publications

(45 reference statements)

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“…One may also analyse the nonlinear transport properties through the full counting statistics (FCS) [31,[53][54][55][56][57][58][59]. More mathematically oriented investigations would be to obtain some rigorous results concerning the global composite scattering matrix S and consequently to prove the existence of the finite limit, lim N →∞ κ(N), which ensures the validity of Ohm and Fourier laws in our model.…”

Section: Discussionmentioning

confidence: 99%

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

Jacquet

2009

J Stat Phys

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We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, FermiDirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T L , µ L ) and (T R , µ R ), and adjust the parameters (T i , µ i ), for i = 1, . . . , N , so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.Mathematics Subject Classification 80A20, 81Q50, 81U20, 82C70

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Section: Discussionmentioning

confidence: 99%

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

Jacquet

2009

J Stat Phys

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“…The FCS of energy transfers concentrates on the probability P (E tr ,T ) to have energy transfer of E tr during time interval T [19,20]. In the low frequency limit of long T all statistical cumulants of the energy transfer are proportional to T and are determined from the generating function F (ξ ) = dE tr P (E tr ,T ) exp(iξ E tr ) ≈ exp[−Tf (ξ )].…”

Section: Definitions and Resultsmentioning

confidence: 99%

“…In our consideration of FCS of energy transfer, we follow the lines of reference [19,20]. We specify it to our situation where the interaction Hamiltonian between system X in thermal equilibrium and an arbitrary system Y is given bŷ H = nX nŶn .…”

Section: A Full Counting Statisticsmentioning

confidence: 99%

Exact correspondence between Renyi entropy flows and physical flows

Ansari

Nazarov

2015

Phys. Rev. B

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We present a universal relation between the flow of a Renyi entropy and the full counting statistics of energy transfers. We prove the exact relation for a flow to a system in thermal equilibrium that is weakly coupled to an arbitrary time-dependent and nonequilibrium system. The exact correspondence, given by this relation, provides a simple protocol to quantify the flows of Shannon and Renyi entropies from the measurements of energy transfer statistics. Exact correspondences between seemingly different concepts play an important role in all fields of physics. An example is the fluctuation-dissipation theorem, which states that the linear response of a system to externally applied forces corresponds to the system fluctuations [1,2]. In the last decade, the fluctuation-dissipation theorem has initiated important developments in quantum transport, quantum computation, and other similar phenomenological theories [3]. This theorem can be extended to nonlinear responses [4] and to full counting statistics (FCS) [5], giving more extended sets of such relations similar to Crooks' formula [6]. In this paper we present a relation similar to the fluctuation-dissipation theorem that provides an exact correspondence between the flows of Renyi entropy and FCS of energy transfers. DOIIn transport theory, stationary flow of a physical quantity can take place from a system into an infinitely large system. In the case a quantity is locally conserved in each system, its flow is determined only by interaction between the two systems [7]. The traditional examples include electric current, which is the flow of charge, and energy flow. Moreover, there are other conserved quantities which are not physical in a strict sense. An example is the generalization of entropy by Renyi into S M = n p M n , with p n being the probability to be in state n and arbitrary M > 0 [8]. Quantum generalization of the Renyi entropy is obviously conserved in a system under Hamiltonian evolution, with the Hamiltonian involving only the degrees of freedom of this system [9]. For a system in thermal equilibrium at temperature T this entropy corresponds to the difference of free energies, i.e., ln S M = F (T ) − F (T /M). In nonequilibrium thermodynamics, the Renyi entropies have already been considered [10]. They have been studied in strongly interacting systems [11,12], in particular spin chains [13,14].The Renyi entropies in quantum physics are considered unphysical, or nonobservable, due to their nonlinear dependence on density matrix. So is the Shannon entropy, which is derived from the Renyi entropy S = lim M→1 ∂S M /∂M [9]. Such quantities cannot be determined from immediate measurements; instead their quantification seems to be equivalent to determining the density matrix. This requires re-initialization of the density matrix between many successive measurements [15]. Therefore, the flows of Renyi entropy between systems F M ≡ −d ln S M /dt are the conserved measures of nonphysical quantities. The same pertains to Shannon entropy flow [9]. An interest...

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“…A convenient way to express and calculate the CGF of the energy current 42 for noninteracting electrons is in terms of the scattering matrix, S(ω; B),…”

Section: Full-counting Statisticsmentioning

confidence: 99%

Fluctuation theorem for heat transport probed by a thermal probe electrode

et al. 2014

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We analyze the full-counting statistics of the electric heat current flowing in a two-terminal quantum conductor whose temperature is probed by a third electrode ("probe electrode"). In particular we demonstrate that the cumulant-generating function obeys the fluctuation theorem in the presence of a constant magnetic field. The analysis is based on the scattering matrix of the three-terminal junction (comprising of the two electronic terminals and the probe electrode), and a separation of time scales: it is assumed that the rapid charge transfer across the conductor and the rapid relaxation of the electrons inside the probe electrode give rise to much slower energy fluctuations in the latter. This separation allows for a stochastic treatment of the probe dynamics, and the reduction of the three-terminal setup to an effective two-terminal one. Expressions for the lowest nonlinear transport coefficients, e.g., the linear-response heat-current noise and the second nonlinear thermal conductance, are obtained and explicitly shown to preserve the symmetry of the fluctuation theorem for the two-terminal conductor. The derivation of our expressions which is based on the transport coefficients of the three-terminal system explicitly satisfying the fluctuation theorem, requires the full calculations of vertex corrections.

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Statistics of heat transfer in mesoscopic circuits

Cited by 51 publications

References 27 publications

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

Exact correspondence between Renyi entropy flows and physical flows

Fluctuation theorem for heat transport probed by a thermal probe electrode

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