Dissipative dynamics of a parabolic confined particle in the presence of magnetic field

Quantum mechanical properties of a parabolic confined electron in a small quantum dot system with the presence of magnetic field and dissipation were studied. Considering the dissipation as being due to the coupling of the system with a phonon bath at low temperature, we ignore the Brownian motion according to the Yu et al. approach [Phys. Rev. A 49 (1994) 592]. Such an approximation is valid for small quantum dots due to the apparent very strong energy quantization. Therefore assuming that the effective (C–K) Hamiltonian of the charged oscillator in an electromagnetic field describes the dissipative quantum-dot system, the exact evolution operator and wave function through the Wei–Norman ordering method are obtained. Analytical forms of the energy and Hamilton operator expectation values as well as of Δx1,2 and Δp1,2 variances are also presented. As our analysis indicates for low temperature, dissipation in a small quantum dot system results in the production of squeezed coherent states, whose energy increases with the reduction of the dot effective confinement length and with the increase of the magnetic field.