Dissipative Dynamics and Uncertainty Measures of a Charged Oscillator in the Presence of the Aharonov-Bohm Effect

Abstract

We analyze the effects of dissipation in a charged oscillator in the presence of the Aharonov-Bohm effect by using time-dependent mass (m(t)) Hamiltonians. We consider two different models for the dissipative Hamiltonian and analyze the uncertainties (∆r and ∆p) and the quantum mechanical expectation value of energy ( E ) in terms of time (t), damping parameters and flux parameter (v). For the Caldirola-Kanai model, we observe that the flux parameter v decreases the energy dissipation in a quantum dot for a certain range of t.

Equivalence of Dissipative and Dissipationless Dynamics of Interacting Quantum Systems With Its Application to the Unitary Fermi Gas

“…U denotes an interaction or an external potential, and c is the dissipation rate (see Equation 26 for the Schrödinger equation and the Hamiltonian for the Caldirola-Kanai model). Taking advantage of its simplicity, the Caldirola-Kanai model has been applied to various dissipative quantum phenomena, including damping of electromagnetic fields in a plasma medium [14], dissipative quantum tunneling in low-energy nuclear fusion reactions [15], dynamics of a damped charged oscillator in the presence of the Aharanov-Bohm effect [16], and so on. While the Caldirola-Kanai model has usually been applied to a singleparticle motion regarding U as an external potential as in the original setting [12,13], we can also consider the dynamics of interacting quantum particles under the dissipation regarding U as inter-particle interactions.…”

Equivalence of dissipative and dissipationless dynamics of interacting quantum systems with its application to the unitary Fermi gas

“…(26) for the Schrödinger equation and the Hamiltonian for the Caldirola-Kanai model). Taking advantage of its simplicity, the Caldirola-Kanai model has been applied to various dissipative quantum phenomena, including damping of electromagnetic fields in a plasma medium [14], dissipative quantum tunneling in low-energy nuclear fusion reactions [15], dynamics of a damped charged oscillator in the presence of the Aharanov-Bohm effect [16], and so on. While the Caldirola-Kanai model has usually been applied to a single-particle motion regarding U as an external potential as in the original setting [12,13], we can also consider the dynamics of interacting quantum particles under the dissipation regarding U as inter-particle interactions.…”