Fourier's Law confirmed for a class of small quantum systems
TLDR
Within the Lindblad formalism, the authors considered an interacting spin chain coupled locally to heat baths and investigated the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength.Abstract:
Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength. For a large class of couplings we find a normal heat conduction and confirm Fourier's Law. In a fully quantum mechanical approach linear transport behavior appears to be generic even for small quantum systems.read more
Citations
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Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions
TL;DR: In this article, a survey of recent advances and an understanding of physical mechanisms of energy transport in nanostructures focusing mainly on molecular junctions and atomic wires is presented, and basic issues such as thermal conductivity, thermoelectricity, local temperature and heating are examined.
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Third quantization: a general method to solve master equations for quadratic open Fermi systems
TL;DR: In this paper, the Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n?4n matrix, provided that all bath operators are linear in the fermionic variables.
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Third quantization: a general method to solve master equations for quadratic open Fermi systems
TL;DR: In this article, the Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided that all bath operators are linear in the fermionic variables.
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Finite-temperature transport in one-dimensional quantum lattice models
Bruno Bertini,Fabian Heidrich-Meisner,Christoph Karrasch,Tomaž Prosen,Robin Steinigeweg,Marko Žnidarič +5 more
TL;DR: In this paper, a review of the current understanding of transport in one-dimensional lattice models, in particular in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, is reviewed, as well as state-of-theart theoretical methods, including both analytical and computational approaches.
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Matrix product simulations of non-equilibrium steady states of quantum spin chains
Tomaz Prosen,Marko Znidaric +1 more
TL;DR: In this paper, a time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends.
References
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Quantum theory of solids
Rudolf Peierls,Louis D. Roberts +1 more
TL;DR: In this article, the interaction of light with non-conducting crystals has been studied in the context of crystal lattices and its applications in general theory and applications, such as semi-conductivity and superconductivity.
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On the anomalous thermal conductivity of one-dimensional lattices
TL;DR: In this paper, the divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated and the divergence law is consistently determined with two different numerical approaches based on equilibrium and nonequilibrium simulations, and a possible explanation in the framework of linear response theory is also presented, which traces back the physical origin of this anomaly to the slow diffusion of the energy of long-wavelength Fourier modes.
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Quantum Approach to a Derivation of the Second Law of Thermodynamics
TL;DR: It is shown that for typical (degenerate or nondegenerate) thermodynamical systems almost all states within the allowed region of Hilbert space have a local von Neumann entropy S close to the maximum and a purity P close to its minimum, respectively.
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Strong evidence of normal heat conduction in a one-dimensional quantum system
TL;DR: In this article, the authors investigated how the normal energy transport is realized in one-dimensional quantum systems using a quantum spin system and found that the autocorrelation function in the Green-Kubo formula decays as t−1.5 to a finite value which vanishes rapidly with the increase of the system size.