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Laser Physics Letters

Axiomatic quasi-classical quantization of particle motion in the dissipative media

С. В. Сазонов

Published Apr 25, 2024• 0 citations
Publisher

Abstract

Abstract A self-consistent quasi-classical generalization of the axiomatic quantization of the translational motion of a particle in a dissipative medium is proposed, which is modeled by a drag force F d , which depends in a power-law manner on the velocity v : F d ∼ v n , where n is an arbitrary real number. A detailed analysis of the quasi-classical coherent state is carried out. It is shown that under condition n < 3 the dissipative medium suppresses the quantum properties of particle motion, performing the function of a classical measuring device. Otherwise, there is no suppression of quantum properties.

DOI
10.1088/1612-202x/ad3f97

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Abstract A version of the quasi-classical approach is proposed, which makes it possible to describe the straight-line motion of a micro-particle in a bulk dissipative medium. From the side of the medium, the particle is acted upon by the force of viscous friction and the drag force, which are proportional to the velocity and the square of the velocity, respectively. In addition, an external conservative force is applied to the particle. The Green’s function of the particle and the quasi-classical coherent state in the form of a three-dimensional localized wave packet are found. It is shown that the translational motion of the wave packet is accompanied by a monotonic increase in the uncertainties of the particle coordinates up to certain maximum asymptotic values. Due to the drag force, these asymptotic uncertainties contain information about the corresponding initial uncertainties in the coordinates of the micro-particle, about its initial velocity, as well as about the external conservative force.
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.
The quasiclassical one-dimensional motion of a particle in a medium, where the drag force is proportional to the square of the particle velocity, is considered using the Caldirola–Kanai approach. The coherent state of the particle in the presence of a constant conservative force in addition to the drag force is studied. It has been shown that the wave packet undergoes quantum extension to a certain limit, forming a steady propagating profile. Thus, the drag force suppresses the quantum properties of the particle, and the classical features become more pronounced in its motion with time. This property allows one to consider such a medium as a classical instrument continuously measuring the state of the particle. For this reason, the restriction of the spatial extension of the wavefunction can be interpreted as one of the manifestations of the quantum Zeno effect.
Abstract On the basis of the canonical quantization procedure, the motion of a micro-particle in a viscous medium is considered, where the drag force consists of two components proportional to the first and second degrees of velocity, respectively. The wave function of a particle corresponding to its quantum coherent state is found using the quasi-classical approach. It is shown that due to the viscous of the medium, a static localized domain of the probability density is formed at relatively long times. It is shown that the parameters of this domain contain the information about the parameters of the particle on the input to medium.