Fourier's Law confirmed for a class of small quantum systems

Michel, M.; Hartmann, Michael J.; Gemmer, Jochen; Mahler, Guenter

doi:10.1140/epjb/e2003-00228-x

Cited by 76 publications

(142 citation statements)

References 16 publications

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“…Particularly, in analogy with the studies at the classical level the relation between the validity of Fourier law and the onset of quantum chaos has been investigated in recent years [123,105,102,137,115,116].…”

Section: Fourier Law In Quantum Mechanicsmentioning

confidence: 99%

From Thermal Rectifiers to Thermoelectric Devices

Benenti

Casati

Mejía‐Monasterio

et al. 2016

Thermal Transport in Low Dimensions

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We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.

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Section: Fourier Law In Quantum Mechanicsmentioning

confidence: 99%

From Thermal Rectifiers to Thermoelectric Devices

Benenti

Casati

Mejía‐Monasterio

et al. 2016

Thermal Transport in Low Dimensions

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“…Thus it has often been pointed out that those concepts do not provide a rigorous justification of the KF for thermal conduction 5,11,12,13,14,15,16 which remains an open question. Furthermore, the KF has been counterchecked only for few concrete systems, see Refs.…”

Section: Introductionmentioning

confidence: 99%

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

2006

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The Kubo formula describes a current as a response to an external field. In the case of heat conduction there is no such external field. We analyze why and to what extend it is nevertheless justified to describe heat conduction in modular quantum systems by the Kubo formula. "Modular" we call systems that may be described as consisting of weakly coupled identical subsystems. We explain in what sense this description applies to a large class of systems. Furthermore, we numerically evaluate the Kubo formula for some finite modular systems. We compare the results with data obtained from the direct numerical solution of the corresponding time-dependent Schrödinger equation.

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“…Refs [25][26][27]. Using timedependent density matrix renormalization group (t-DMRG) to study nonequilibrium steady state (NESS), in particular the scaling of spin current with system size, we are able to reach considerably larger systems of up to L = 400 spins, allowing us to study all the length scales involved in the problem.…”

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confidence: 99%

Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System

2016

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We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.Introduction.-There are ever increasing technological capabilities in simulating isolated quantum systems through cold atomic gases [1] and, recently, through coupled, controlled superconducting qubits [2]. While there is a commensurately good theoretical handle on capturing ground state properties of such systems [3], understanding their dynamical properties, especially away from the ground state, is fraught with analytical and numerical challenges.Despite this, in the recent years we have witnessed a change in paradigm in the study of isolated quantum systems, in particular with regard to the role that disorder plays in such systems. The turning point came about from the study of Anderson localization [4] in interacting, many-body quantum systems [5]. The observation that disorder and quantum effects can hinder transport (of energy, charge or spin) even at an infinite temperature and in the presence of interactions [6] opened the door to a new phenomenology of a so-called manybody localized (MBL) phase exhibiting many unique and interesting properties. Slow growth of entanglement [7,8], emergent integrability [9], protection of symmetries [10], and change in the properties of eigenstates [11][12][13] are a few of the peculiar properties of this newly identified phase; see review [14] for a comprehensive list. The implications of the new MBL physics, being inherently robust, are far reaching, going from fundamental physics to the theory of quantum computation [15], some of which have already been experimentally probed [16].While the deep MBL region (in one dimensional systems) is well understood, much remains to be said about the conducting regime and the transition to it. Although both aspects are important, here we focus on characterizing the conducting phase, in particular its transport properties, in, what is by now, an archetypal model that harbors the MBL phase, i.e., the one dimensional anisotropic Heisenberg model.Generic arguments and numerical evidence on very small systems (about 20 spins) have been put forward for the existence of subdiffusive transport of spin [17][18][19][20] and energy [18,21,22]. A number of recent works have analyzed its sp...

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Fourier's Law confirmed for a class of small quantum systems

Cited by 76 publications

References 16 publications

From Thermal Rectifiers to Thermoelectric Devices

From Thermal Rectifiers to Thermoelectric Devices

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System

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