# Thermalization in Harmonic Particle Chains with Velocity Flips

@article{Lukkarinen2013ThermalizationIH, title={Thermalization in Harmonic Particle Chains with Velocity Flips}, author={Jani Lukkarinen}, journal={Journal of Statistical Physics}, year={2013}, volume={155}, pages={1143-1177} }

We propose a new mathematical tool for the study of transport properties of models for lattice vibrations in crystalline solids. By replication of dynamical degrees of freedom, we aim at a new dynamical system where the “local” dynamics can be isolated and solved independently from the “global” evolution. The replication procedure is very generic but not unique as it depends on how the original dynamics are split between the local and global dynamics. As an explicit example, we apply the scheme…

## 8 Citations

### Harmonic Chain with Velocity Flips: Thermalization and Kinetic Theory

- Physics
- 2016

We consider the detailed structure of correlations in harmonic chains with pinning and a bulk velocity flip noise during the heat relaxation phase which occurs on diffusive time scales, for…

### Heat Flow in a Periodically Forced, Thermostatted Chain

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We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic…

### Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities

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We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total…

### Harmonic Chain with Velocity Flips: Thermalization and Kinetic Theory

- PhysicsJournal of Statistical Physics
- 2016

We consider the detailed structure of correlations in harmonic chains with pinning and a bulk velocity flip noise during the heat relaxation phase which occurs on diffusive time scales, for…

### A new approach to Boltzmann’s ergodic hypothesis

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The worst (in the sense of convergence to an equilibrium) many-particle Hamiltonian system is considered, namely, a linear system of dimension 2N for which there is an N-parameter family of invariant…

### Liouville ergodicity of linear multi-particle hamiltonian system with one marked particle velocity flips

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We consider multi-particle systems with linear deterministic hamiltonian dynamics. Besides Liouville measure it has continuum of invariant tori and thus continuum of invariant measures. But if one…

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In this manuscript, we provide a non-asymptotic process level control between the telegraph process and the Brownian motion with suitable diffusivity constant via a Wasserstein distance with…

### A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

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(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1…

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