Fourier’s Law from Schrödinger Dynamics

Michel, M.; Mahler, G.; Gemmer, Jochen

doi:10.1103/physrevlett.95.180602

Cited by 117 publications

(127 citation statements)

References 20 publications

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“…Recently, there are several ideas of how to approach Fourier's law from fundamental principles [26,27,28,29,30]. Here we will show that the appropriately defined flux operator naturally leads to the discrete form of the law.…”

Section: Formal Fourier's Lawmentioning

confidence: 99%

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Energy flux operator, current conservation and the formal Fourier's law

Wu¹,

Segal²

2008

J. Phys. A: Math. Theor.

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By revisiting previous definitions of the heat current operator, we show that one can define a heat current operator that satisfies the continuity equation for a general Hamiltonian in one dimension. This expression is useful for studying electronic, phononic and photonic energy flow in linear systems and in hybrid structures. The definition allows us to deduce the necessary conditions that result in current conservation for general-statistics systems. The discrete form of the Fourier's Law of heat conduction naturally emerges in the present definition.

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Section: Formal Fourier's Lawmentioning

confidence: 99%

“…Derivation of the Fourier's law from fundamental principles, classical [24,25,26,27], or quantum [28,29,30], is a great challenge in theoretical physics. Model calculations manifested that the onset of diffusional behavior delicately depends on the details of the system.…”

Section: Introductionmentioning

confidence: 99%

Energy flux operator, current conservation and the formal Fourier's law

Wu¹,

Segal²

2008

J. Phys. A: Math. Theor.

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“…That means the model does not show normal transport. According to (27) this happens if the coupling becomes to strong. This fact might be missed by simply evaluating the KF: Since C(ω) completely scales with the square of the overall interaction strength (at least for C(ω) evaluated in the interaction picture), the distinction between normal and non-normal transport cannot be made by simply looking at the features of C(ω) (this will be demonstrated in more detail in Sect.…”

Section: Local Energy Currents As a Response To Local Temperature mentioning

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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“…Here we extend our single mode model and present a realization of a molecular chain that can lead to normal Fourier conduction, provided that the molecule is highly anharmonic, independently of the molecule-baths coupling strengths. We emphasize that we bypass the difficult task of showing how normal diffusion emerges in the system [16], and simply assume non-correlated hopping motion between molecular units. Our sole mission here is to construct from the single mode result (54) a model that supplies normal conduction.…”

Section: Fourier Law Of Conductionmentioning

confidence: 99%

“…An outstanding problem in statistical physics is to find out the necessary and sufficient conditions for attaining this normal (Fourier) law of heat conductivity in low dimensional systems [11,12,13,14,15,16]. Among the crucial requirements explored is that the molecular potential energy should constitute strong anharmonic interactions.…”

Section: Introductionmentioning

confidence: 99%

Heat flow in nonlinear molecular junctions: Master equation analysis

2006

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We investigate the heat conduction properties of molecular junctions comprising anharmonic interactions. We find that nonlinear interactions can lead to novel phenomena: negative differential thermal conductance and heat rectification. Based on analytically solvable models we derive an expression for the heat current that clearly reflects the interplay between anharmonic interactions, strengths of coupling to the thermal reservoirs, and junction asymmetry. This expression indicates that negative differential thermal conductance shows up when the molecule is strongly coupled to the thermal baths, even in the absence of internal molecular nonlinearities. In contrast, diode like behavior is expected for a highly anharmonic molecule with an inherent structural asymmetry.Anharmonic interactions are also necessary for manifesting Fourier type transport. We briefly present an extension of our model system that can lead to this behavior.

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Fourier’s Law from Schrödinger Dynamics

Cited by 117 publications

References 20 publications

Energy flux operator, current conservation and the formal Fourier's law

Energy flux operator, current conservation and the formal Fourier's law

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

Heat flow in nonlinear molecular junctions: Master equation analysis

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