# Nonintegrability and thermalization of one-dimensional diatomic lattices.

@article{Fu2019NonintegrabilityAT, title={Nonintegrability and thermalization of one-dimensional diatomic lattices.}, author={Weicheng Fu and Yong Zhang and Hong Zhao}, journal={Physical review. E}, year={2019}, volume={100 5-1}, pages={ 052102 } }

Nonintegrability is a necessary condition for the thermalization of a generic Hamiltonian system. In practice, the integrability can be broken in various ways. As illustrating examples, we numerically studied the thermalization behaviors of two types of one-dimensional (1D) diatomic chains in the thermodynamic limit. One chain was the diatomic Toda chain whose nonintegrability was introduced by unequal masses. The other chain was the diatomic Fermi-Pasta-Ulam-Tsingou-β chain whose…

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## References

SHOWING 1-10 OF 78 REFERENCES

Universal scaling of the thermalization time in one-dimensional lattices.

- PhysicsPhysical review. E
- 2019

We show that, in the thermodynamic limit, a one-dimensional (1D) nonlinear lattice can always be thermalized for arbitrarily small nonlinearity, thus proving the equipartition theorem for a class of…

Universal route to thermalization in weakly-nonlinear one-dimensional chains

- PhysicsMathematics in Engineering
- 2019

We apply Wave Turbulence theory to describe the dynamics on nonlinear one-dimensional chains. We consider $\alpha$ and $\beta$ Fermi-Pasta-Ulam-Tsingou (FPUT) systems, and the discrete nonlinear…

Thermal conductivity of one- and two-dimensional lattices

- Physics
- 1989

Numerical experiments were conducted to study the energy transfer through one- and two-dimensional nonlinear lattices, with various anharmonicities and diatomic mass ratios, when they are placed…

Nonintegrability and the Fourier heat conduction law.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is found that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as themass ratio tends to one, this range may expand rapidly.

Universal law of thermalization for one-dimensional perturbed Toda lattices

- Physics, MathematicsNew Journal of Physics
- 2019

The Toda lattice is a nonlinear but integrable system. Here we study the thermalization problem in one-dimensional, perturbed Toda lattices in the thermodynamic limit. We show that the thermalization…

Thermal conductivity in the diatomic Toda lattice

- Physics
- 1983

The diatomic Toda lattice, a linear chain with exponential interaction and alternating masses, is coupled to different heat baths at the two ends. The non-integrability of the system leads to a…

Heat conduction in the diatomic Toda lattice revisited

- Physics
- 1999

Department of Pure and Applied Sciences, University of Tokyo, Komaba, Tokyo 153-0041, Japan(February 1, 2008)The problem of the diverging thermal conductivity in one-dimensional (1-D) lattices is…

Time-Scales to Equipartition in the Fermi–Pasta–Ulam Problem: Finite-Size Effects and Thermodynamic Limit

- Physics
- 2011

We investigate numerically the common α+β and the pure β FPU models, as well as some higher order generalizations. We consider initial conditions in which only low-frequency normal modes are excited,…

Finite times to equipartition in the thermodynamic limit.

- Physics, MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

A theory of the scaling of the time scale T to equipartition with E/N is presented and compared to the numerical results in the range 0.03<or=E/N <or=0.8.

Dynamic form factors of the diatomic Toda lattice

- Physics
- 1985

Dynamic displacement-displacement correlation functions are calculated in normal coordinates for the diatomic Toda lattice at low temperatures. The corresponding spectral densities evaluated for a…