A Langevin Approach to a Classical Brownian Oscillator in an Electromagnetic Field

[摘要] We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli spinor-like) representation, hitherto exploited in classical Lorentz related dynamics. Within this formalism, in a very straight forward and elegant fashion, we compute the exact solution for the resulting generalized Langevin equation, for the case of a constant magnetic field. For the case the source electromagnetic fields satisfy Maxwell's equations, yielding spinor-like Mathieu equations, we compute the solutions within the JWKB approximation. With the solutions at hand we further compute spatial, velocities and crossed time correlations. In particular we study the (kinetically defined) nonequilbrium temperature. Therefore, we can display the system's time evolution towards equilibrium or towards non equilibrium (steady or not) states.

[发布机构] Departamento de Física, IFQC, Universidade Federal de Goiás, Catalão, Goiás; 75704/020, Brazil^1;Instituto de Física Gleb Wataghin, UNICAMP, Campinas; SP; 13083/970, Brazil^2;Departamento de Física, IGCE, UNESP, Rio Claro; SP; 13500/970, Brazil^3

[效力级别] 数学

[关键词] Brownian oscillators;Brownian particles;Constant magnetic fields;Electric and magnetic fields;Generalized Langevin equation;Harmonic potential;Mathieu equation;Time correlations