Two-dimensional chaotic thermostat and behavior of a thermalized charge in a weak magnetic field

Abstract

A two-dimensional (2D) version of a chaotic thermostat is investigated. Its structure follows the concept previously introduced by the author to generate a one-dimensional chaotic thermostat, namely the usual friction force of a deterministic thermostat is supplemented with a self-consistent fluctuating force that depends on the drag coefficient associated with coupling to the heat bath. Azimuthal symmetry requires the thermostat to have two internal degrees of freedom, thus the Martyna-Klein-Tuckerman (MKT) model is chosen for the heat bath. The unmagnetized system exhibits two-dimensional diffusive behavior, achieves symmetric Maxwellian velocity distributions in the absence of an external potential, and satisfies the Einstein relation when an external force is applied. The velocity fluctuations display the characteristic exponential frequency spectrum associated with chaotic systems. The model is used to explore the diffusive motion of a thermalized charge in a weak magnetic field and the associated Hall and Pedersen mobilities. Over a range of magnetic field strengths the charge exhibits absolute negative mobility (ANM).

Correlated noise effect on the structure formation in the phase‐field crystal model

“…14,44 The delta-correlated noise term in the dynamical equation cannot be derived in the context of DDFT through the Brownian particles with thermal noise since the density field (⃗ r, t) is an ensemble-averaged quantity. 34,35,45 But for the set of applications such as charged colloidal particles in an external electromagnetic field, the colored noise correlated in space and time has to be introduced into the Brownian motion. [46][47][48] The statistical ensemble averaging of correlated fluctuations lead to the colored noise term in the flux in the manner of the atomic diffusion flux fluctuations in the spinodal decomposition: [49][50][51]…”

Intermittent fluctuations due to Lorentzian pulses in turbulent thermal convection

“…Recently, the exponential spectrum has been attributed to the presence of uncorrelated Lorentzian pulses in the temporal dynamics. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] This includes the Lorenz model, which describes chaotic dynamics in Rayleigh-Bénard convection. [23][24][25][26][27][28][29][30] In two-dimensional thermal convection, it is well known that the convection rolls in a horizontally periodic domain can give rise to the spontaneous formation of strong mean flows through a tilting instability.…”