Classical double-well systems coupled to finite baths

TL;DR

This study investigates the dynamics and energy distribution of classical double-well systems coupled to finite baths, revealing conditions for chaos and how stationary energy distributions depend on system and bath parameters.

Contribution

It provides a detailed numerical analysis of double-well systems coupled to finite baths, highlighting the factors influencing chaos and energy distribution properties.

Findings

Chaos occurs for small bath sizes ($ extless=100$) but not for larger ones ($ extgreater=500$).

Stationary energy distribution mainly depends on system size, coupling strength, and temperature.

Energy distribution fits a Gamma distribution and differs from harmonic oscillator systems.

Abstract

We have studied properties of a classical $N_S$-body double-well system coupled to an $N_B$-body bath, performing simulations of $2(N_S+N_B)$ first-order differential equations with $N_S \simeq 1 - 10$ and $N_B \simeq 1 - 1000$. A motion of Brownian particles in the absence of external forces becomes chaotic for appropriate model parameters such as $N_B$, $c_o$ (coupling strength), and $\{\omega_n\}$ (oscillator frequency of bath): For example, it is chaotic for a small $N_B$ ($\lesssim 100$) but regular for a large $N_B$ ($\gtrsim 500$). Detailed calculations of the stationary energy distribution of the system $f_S(u)$ ($u$: an energy per particle in the system) have shown that its properties are mainly determined by $N_S$, $c_o$ and $T$ (temperature) but weakly depend on $N_B$ and $\{\omega_n \}$. The calculated $f_S(u)$ is analyzed with the use of the $\Gamma$ distribution. Difference and similarity between properties of double-well and harmonic-oscillator systems coupled to finite bath are discussed.