Non-stationary quasi-classical states of a charged particle in a strong magnetic field under conditions of the dissipative medium

Abstract

Based on the quasi-classical approximation, a general approach is proposed for constructing non-stationary quantum states of a charged particle in a magnetic field, when the dissipative forces of viscous friction and drag, proportional to the velocity and the square of the velocity, respectively, are also significant. The corresponding quasi-classical Green’s function is found, with the help of which the squeezed and coherent states of the particle are studied. It is shown that the dissipation and a magnetic field suppress the quantum properties of the particle. This is especially true for the transverse motion with respect to the magnetic field. Over time, the coherent and squeezed states transform into the same static state, which is characterized by a zero uncertainty of the transverse coordinates and an uncertainty of the longitudinal coordinate, which contains information about the initial velocity of the particle.

Quasi-classical dynamics of a charged particle under conditions of ionization losses in a weak magnetic field

“…The case of a weak magnetic field studied in this work leads, in particular, to the conclusion that the uncertainty of the particle coordinates increases isotropically in all directions up to a certain maximum value (42). In [36], the opposite case was studied, corresponding to a strong magnetic field in the presence of dissipative forces proportional to the velocity and the square of the particle velocity. It was shown in [36] that the uncertainty of the coordinate along the magnetic field also increases over time to a certain maximum value.…”

“…In [36], the opposite case was studied, corresponding to a strong magnetic field in the presence of dissipative forces proportional to the velocity and the square of the particle velocity. It was shown in [36] that the uncertainty of the coordinate along the magnetic field also increases over time to a certain maximum value. However, the uncertainty of the coordinate across the magnetic field decreases to zero.…”

“…where l 0 is the initial uncertainty of the particle coordinates. Substituting (39) into (36) with accounting for relation (37), we will have…”

Quasi-classical theory of cyclotron resonance with accounting for dissipation

“…Summarizing the results of works [17,18,30,31], we write the Hamiltonian corresponding to the set of equations ( 3), ( 6) and ( 7):…”

“…One of the canonical approaches is the Caldirola-Kanai approach [14,15]. Apparently, the greatest success here can be achieved using the quasi-classical approximation [28,29], which has proven itself in the quantization of dissipative systems, including the motion of particles in a magnetic field [30,31].…”