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Laser Physics Letters

Coherent states of the free quantum particle in a viscous medium

С. В. Сазонов

Published Jul 17, 2023• 7 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ace525

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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.
Abstract Based on the formalism of quasi-classical canonical quantization, the translational motion of a particle in a viscous medium is studied. The case is considered when, in addition to the resistance forces, an external conservative force acts on the particle. It is shown that due to the forces of viscous resistance of the medium, the initial coherent state of the particle does not decay. This behavior of the wave function is accompanied by a partial suppression of the quantum properties of the particle. In this case, a viscous medium should be considered as a classical device that continuously measures the state of a particle. Therefore, the stability of the coherent state of a particle can be interpreted as a manifestation of the quantum Zeno effect.
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 A quasi-classical approach is proposed for describing the motion of a charged particle in a magnetic field, taking into account irreversible losses due to the macroscopic viscosity of the medium. The wave function of a charged particle corresponding to its quasi-classical coherent state is found. It is shown that viscosity leads to an irreversible collapse of the wave function in directions perpendicular to the magnetic field. At the same time along the magnetic field the wave function experiences irreversible spreading up to a certain static limit. Thus, in the transverse directions a viscous medium and a magnetic field behave like a classical measuring device. In the longitudinal directions the signs of the quantum Zeno effect are visible. As a result of such anisotropic quantum dynamics the wave packet of the probability density takes the form of a thin filament wound around a magnetic field. The length of the filament is determined by the limiting value of the uncertainty of the longitudinal coordinate of the particle. In turn, this asymptotic uncertainty contains the information about its initial value, about the mass of the particle, and about the properties of the viscous medium.
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.