Surprise ballistic and scaling inverted dynamics of a system coupled to a Hamiltonian thermostat

We study the induced generalized Brownian dynamics of a Hamiltonian thermostat, and specifically the diffusive properties. For a tagged particle regulated by a logarithmic-oscillator thermostat and moving in an external logarithmic potential, we reveal a distinct inversion of the scaling exponents for the mean-squared displacement ⟨Delta x (2)(t)⟩ similar to t ( lambda ) around the exponent lambda = 2 - alpha covering regimes from ballistic diffusion to confinement motion (i.e. 0 <= alpha <= 2). This behavior contrasts with the expanding behavior associated with superdiffusive processes in a tilted periodic potential. The Hamiltonian thermostat is shown to maintain a fixed kinetic energy and, although this system is nonergodic in the force-free case, leads to a confined system that approaches thermal equilibrium slowly with the same temperature as the thermostat. In addition, we find its displacement has a significant dependence on lambda via the amplitude of the external logarithmic potential. The continuous reduction of the scaling exponent is vital in the quantitative evaluation of all diffusive processes.

Automated summary

Research shows that under a Hamiltonian thermostat, particles controlled by a logarithmic-oscillator thermostat moving in an external logarithmic potential exhibit an inversion in scaling exponents for the mean-squared displacement, with a significant dependence on λ. This continuous reduction of the scaling exponent is crucial in quantitatively evaluating all diffusive processes.