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

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 (Δr and Δp) 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.

Keywords
Aharanov-Bohm effect; Caldirola-Kanai oscillators; Lane-Endem oscillators; uncertainty; mean energy; 2D parabolic quantum dot