Abstract
This study proposes the usage of an effective potential to investigate a dissipative quantum system with rotational velocity. After gauge transformation, a Doebner- Goldin equation (DGE) that describes the dissipative quantum system with a Dirac potential is obtained. The DGE is solved based on constraint of vertical relation between the rotational velocity field and density gradient when a harmonic oscillator model is considered. It is observed that the dissipative quantum system is directly equivalent to a monopole system and that the two gauge potentials that are given by Wu and Yang in the north and south hemispheres can be reproduced. Furthermore, a set of gauge-invariant parameters is obtained to discuss the dissipation characteristics of the system.
Highlights
This study proposes the usage of an effective potential to investigate a dissipative quantum system with rotational velocity
The Dirac potential has been introduced by Dirac as part of the discussion related to magnetic monopoles in 19311
The simple three-dimensional Doebner- Goldin equation (DGE) can be solved and a set of gauge-invariant parameters can be obtained when a central potential and a constraint related to the vertical relation between the rotational velocity field and density gradient are suggested
Summary
This study proposes the usage of an effective potential to investigate a dissipative quantum system with rotational velocity. The introduction of a spinor order parameter allows the GPE to become the extended GPE, and the velocity potential is observed to subsequently become equivalent to the Dirac potential This indicates that the Dirac potential can be generated with considerable ease in a different quantum system that can be described using the nonlinear Schrödinger equation (NLSE) containing several nonlinear terms. After the introduction of an effective potential, such as quantum pressure[14,22,23,24], the resulting subfamily of DGE is observed to become similar to the analogous classical fluid equation Based on this analogy, the simple three-dimensional DGE can be solved and a set of gauge-invariant parameters can be obtained when a central potential (such as the harmonic oscillator) and a constraint related to the vertical relation between the rotational velocity field and density gradient are suggested.
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