Anomalous Heat Conduction

Lepri, Stefano; Livi, Roberto; Politi, Antonio

doi:10.1002/9783527622979.ch10

Cited by 76 publications

(149 citation statements)

References 54 publications

(51 reference statements)

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“…The divergence of the heat conductivity coefficient as N µ with µ ≈ 0.37 was observed in the numerical studies of the FPU β model [8,9,11,12]. This result is very close to estimation (33).…”

Section: The Long Time Behavior Of the Correlation Functionsupporting

confidence: 85%

“…It is now well established by computer simulations that the heat conductivity in FPU lattices diverges when the size of the lattice goes to infinity [8,9,10,11,12]. The simulations give a power law dependence of the heat conductivity on the number of particles N as approximately N 2/5 .…”

Section: Introductionmentioning

confidence: 90%

“…So far the most careful computer simulation [11] fail to confirm this claim. At present, therefore, this issue remains unsettled.…”

Section: The Long Time Behavior Of the Correlation Functionmentioning

confidence: 99%

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Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

2003

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The Peierls equation is considered for the Fermi-Pasta-Ulam β lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal mode energy as a function of wave vector k is estimated to be proportional to k 5/3 . This leads to the t −3/5 long time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained through the mode coupling theory our estimations give the same k dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam β lattice may lead to finite heat conductivity in this model.

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Section: The Long Time Behavior Of the Correlation Functionsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 90%

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Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

2003

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“…Any solid thermal insulator or weak conductor, can, in principle, be used as a substrate. A prototype could be a disordered harmonic lattice [11]. Among the possible applications of this study, one can think of biological molecules.…”

mentioning

confidence: 97%

“…These efforts mainly focused on the possibility to derive the Fourier law of heat conduction on purely dynamical grounds without recourse to any statistical assumption [2][3][4][5][6][7][8][9][10][11]. In spite of relevant progresses, several problems remain open and we are still far from a complete understanding [5][6][7][8][9][10][11].…”

mentioning

confidence: 99%

Controlling the Energy Flow in Nonlinear Lattices: A Model for a Thermal Rectifier

2002

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We address the problem of heat conduction in 1-D nonlinear chains; we show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the chain by the same amount. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.In recent years a renewed attention has been directed to the energy transport in dynamical systems, a problem which has been denoted by Peierls as one of the outstanding unsolved problems of modern physics [1]. These efforts mainly focused on the possibility to derive the Fourier law of heat conduction on purely dynamical grounds without recourse to any statistical assumption [2][3][4][5][6][7][8][9][10][11]. In spite of relevant progresses, several problems remain open and we are still far from a complete understanding [5][6][7][8][9][10][11].In this paper we investigate a different and important problem namely the possibility to control the energy transport inside a nonlinear 1D chain connecting two thermostats at different temperatures. We show that we can parametrically control the heat flux through the system by acting on a small central part of the chain. Even more interestingly, we show that it is possible to adjust the heat flux by varying the temperatures of both thermostats, keeping constant the temperature difference. Thus we provide a simple mechanism to change the properties of the system, from a normal conductor obeying Fourier law, down to an almost perfect insulator. Controlling heat conduction by nonlinearity opens new possibilities, such as the design of a lattice that carries heats preferentially in one direction, i.e. a thermal rectifier.We consider the Hamiltonianwhich describes a chain of N particles with harmonic coupling of constant K and a Morse on-site potential V n (y n ) = D n (e −αnyn − 1) 2 . This model was introduced for DNA chains where m is the reduced mass of a base pair, y n denotes the stretching from equilibrium position of the hydrogen bonds connecting the two bases of the n-th pair and p n is its momentum [12][13][14]. In the context of the present study, model (1) can simply be viewed as a generic system of anharmonic coupled oscillators, the onsite potential arising from interactions with other parts of the system, not included in the model. The Morse potential is simply an example of a highly anharmonic soft potential, which has a frequency that decreases drastically when the amplitude of the motion increases.In this paper we consider the out-of-equilibrium properties of model (1) by numerically simulating the dynamics of the N particle chain, coupled, at the two ends, with thermal baths at different temperatures T 1 and T 2 . We thermalize at T 1 and T 2 the first and the last L particles by using Nosé-Hoover thermostats chains [15,16],...

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Thermal and Thermoelectric Properties of Molecular Junctions

Wang

Meyhöfer

Reddy

2019

Adv Funct Materials

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Molecular junctions (MJs) represent an ideal platform for studying charge and energy transport at the atomic and molecular scale and are of fundamental interest for the development of molecular‐scale electronics. While tremendous efforts have been devoted to probing charge transport in MJs during the past two decades, only recently advances in experimental techniques and computational tools have made it possible to precisely characterize how heat is transported, dissipated, and converted in MJs. This progress is central to the design of thermally robust molecular circuits and high‐efficiency energy conversion devices. In addition, thermal and thermoelectric studies on MJs offer unique opportunities to test the validity of classical physical laws at the nanoscale. A brief survey of recent progress and emerging experimental approaches in probing thermal and thermoelectric transport in MJs is provided, including thermal conduction, heat dissipation, and thermoelectric effects, from both a theoretical and experimental perspective. Future directions and outstanding challenges in the field are also discussed.

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Anomalous Heat Conduction

Cited by 76 publications

References 54 publications

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Fermi-Pasta-Ulamβlattice: Peierls equation and anomalous heat conductivity

Controlling the Energy Flow in Nonlinear Lattices: A Model for a Thermal Rectifier

Thermal and Thermoelectric Properties of Molecular Junctions

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