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Журнал Экспериментальной и Теоретической Физики

SAMOSOGLASOVANNYY KVAZIKLASSIChESKIY PODKhOD K OPISANIYu DVIZhENIYa ChASTITsY V DISSIPATIVNOY SREDE

С. В. Сазонов

Published Aug 13, 2024• 0 citations
Publisher

Abstract

An approximate self-consistent approach is proposed that allows describing the quasi-classical translational dynamics of a non-relativistic particle in a dissipative medium with arbitrary dependence of the corresponding dissipative forces on velocity. It is shown that dissipation suppresses the quantum properties of the particle. This leads to the necessity of interpreting propagation in a dissipative medium as a continuous process of measuring the particle state. As examples, non-stationary coherent states of the particle are considered at three stages of its deceleration in the medium due to ionization losses. These stages correspond to high-energy losses, losses in the vicinity of the Bragg peak, and low-energy losses at the final stage of propagation.

DOI
10.31857/s0044451024080017

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An approximate self-consistent approach is proposed that allows describing the quasi-classical translational dynamics of a non-relativistic particle in a dissipative medium with arbitrary dependence of the corresponding dissipative forces on velocity. It is shown that dissipation suppresses the quantum properties of the particle. This leads to the necessity of interpreting propagation in a dissipative medium as a continuous process of measuring the particle state. As examples, non-stationary coherent states of the particle are considered at three stages of its deceleration in the medium due to ionization losses. These stages correspond to high-energy losses, losses in the vicinity of the Bragg peak, and low-energy losses at the final stage of propagation.
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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.
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