Heat Transport in Harmonic Systems

Dhar, Abhishek; Saito, Keiji

doi:10.1007/978-3-319-29261-8_2

Cited by 8 publications

(15 citation statements)

References 86 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the linear chain it shows a nearly perfect plateau. As is known, a flat temperature profile evidences the anomalous heat transport in one-dimensional harmonic crystals, which have infinite conductivity and can not, therefore, support a temperature gradient [11,12].…”

Section: B Temperature Profiles and Total Heat Fluxmentioning

confidence: 99%

“…This indicates that these systems obey Fourier's law. In contrast, in the case of one-dimensional integrable systems, such as a harmonic chain and the Toda mono-atomic model, a temperature gradient is not established [11][12][13][14]. There are also onedimensional nonintegrable systems, such as the Fermi-Pasta-Ulam model [15][16][17] or the Toda diatomic chain [18], for which the thermal conductivity diverges with increasing system size.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Delocalization and heat transport in multidimensional trapped ion systems

2019

View full text Add to dashboard Cite

We study the connection between heat transport properties of systems coupled to different thermal baths in two separate regions and their underlying nonequilibrium dynamics. We consider classical systems of interacting particles that may exhibit a certain degree of delocalization, and whose effective dimensionality can be modified through the controlled variation of a global trapping potential. We focus on Coulomb crystals of trapped ions, which offer a versatile playground to shed light on the role that spatial constraints play on heat transport. We use a three-dimensional model to simulate the trapped ion system, and show in a numerically rigorous manner to what extent heat transport properties could be feasibly tuned across the structural phase transitions between the linear, planar zigzag and helical configurations. By solving the classical Langevin equations of motion, we analyze the steady state spatial distributions of the particles, the temperature profiles and total heat flux through the various structural phase transitions that the system may experience. The results evidence a clear correlation between the degree of delocalization of the internal ions and the emergence of a non-zero gradient in the temperature profiles. The signatures of the phase transitions in the total heat flux as well as the optimal spatial configuration for heat transport are shown.

show abstract

Section: B Temperature Profiles and Total Heat Fluxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Delocalization and heat transport in multidimensional trapped ion systems

2019

View full text Add to dashboard Cite

show abstract

“…According to Fourier's law, the local current is proportional to the local temperature gradient. Much research has studied the microscopic details of this picture in, for example, harmonic chains [74] and lattices [75,76,77,78], anharmonic chains [79,80] and lattices [81,78], disordered harmonic chains [82], elastically colliding unequal-mass particles [83], and Brownian oscillators [84]. We are unaware of any study of heat conduction in a system of interacting active particles.…”

Section: Introductionmentioning

confidence: 99%

Heat fluctuations in a harmonic chain of active particles

Gupta,

Sivak

2021

Preprint

View full text Add to dashboard Cite

One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role. Hitherto much theoretical and experimental research has focused on systems composed of passive Brownian particles. In this paper, we study the heat fluctuations in a system of interacting active particles. Specifically we consider a onedimensional harmonic chain of N active Ornstein-Uhlenbeck particles, with the chain ends connected to heat baths of different temperatures. We compute the momentgenerating function for the heat flow in the steady state. We employ our general framework to explicitly compute the moment-generating function for two example single-particle systems. Further, we analytically obtain the scaled cumulants for the heat flow for the chain. Numerical Langevin simulations confirm the long-time analytical expressions for first and second cumulants for the heat flow for a two-particle chain.

show abstract

“…In some cases such models allow one to obtain the analytical description of thermomechanical processes in solids [9][10][11][12][13][14][15]. In the literature, the problems concerning heat transfer in harmonic lattices are mostly considered in the stationary formulation [7,[16][17][18][19][20][21][22][23][24][25][26][27][28][29], the non-stationary heat propagation is discussed in [10,[30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

“…in the stationary formulation [7,[16][17][18][19][20][21][22][23][24][25][26][27][28][29], the non-stationary heat propagation is discussed in [10,[30][31][32][33][34][35][36].…”

mentioning

confidence: 99%

Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source

Гаврилов

Кривцов

2019

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system of stochastic ordinary differential equations. We perform a continualization procedure and derive an infinite system of linear partial differential equations for covariance variables. The most important results of the paper are the deterministic differential-difference equation describing non-stationary heat propagation in the lattice and the analytical formula in the integral form for its steady-state solution describing kinetic temperature distribution caused by a point heat source of a constant intensity. The comparison between numerical solution of stochastic equations and obtained analytical solution demonstrates a very good agreement everywhere except for the main diagonals of the lattice (with respect to the point source position), where the analytical solution is singular.Keywords ballistic heat transfer · 2D harmonic scalar lattice · kinetic temperature 1 Introduction At the macroscale, Fourier's law of heat conduction is widely and successfully used to describe heat transfer processes. However, recent experimental observations demonstrate that Fourier's law is violated at the microscale and nanoscale, in particular, in low-dimensional nanostructures [1][2][3][4][5][6], where the ballistic heat transfer is realized. The anomalous heat transfer also may be related with the spontaneous emergence of long-range correlations; the latter is typical for momentum-conserving systems [7,8]. The simplest theoretical approach to describe the ballistic heat propagation is to use harmonic lattice models. In some cases such models allow one to obtain the analytical description of thermomechanical processes in solids [9][10][11][12][13][14][15]. In the literature, the problems concerning heat transfer in harmonic lattices are mostly considered

show abstract

Heat Transport in Harmonic Systems

Cited by 8 publications

References 86 publications

Delocalization and heat transport in multidimensional trapped ion systems

Delocalization and heat transport in multidimensional trapped ion systems

Heat fluctuations in a harmonic chain of active particles

Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source

Contact Info

Product

Resources

About