The effective Hamiltonian and propagator of a parabolic confined dissipative electron under a perpendicular magnetic field (original) (raw)

We give a basic explanation for the oscillating properties of some physical quantities of a two-electron quantum dot in the presence of a static magnetic field. This behaviour was discussed in a previous work of ours [AM Maniero, et al. J. Phys. B: At. Mol. Opt. Phys. 53:185001, 2020] and was identified as a manifestation of the de Haas-van Alphen effect, originally observed in the framework of diamagnetism of metals in the 30's. We show that this behaviour is a consequence of different eigenstates of the system assuming, in a certain interval of the magnetic field, the condition of the lowest energy singlet and triplet states.

We use the quantum Langevin equation as a starting point to study the response function, the position–velocity correlation function and the velocity autocorrelation function of a charged quantum Brownian particle in the presence of a magnetic field and linearly coupled to a heat bath via position coordinate. We study two bath models – the Ohmic bath model and the Drude bath model and make a detailed comparison in various time–temperature regimes. For both bath models, there is a competition between the cyclotron frequency and the viscous damping rate giving rise to a transition from an oscillatory to a monotonic behaviour as the damping rate is increased. In the zero point fluctuation dominated low-temperature regime, non-trivial noise correlations lead to some interesting features in this transition. We study the role of the memory time-scale which comes into play in the Drude model and study the effect of this additional time-scale. We discuss the experimental implications of our ...

We use the Quantum Langevin equation as a starting point to study the response function, the position-velocity correlation function and the velocity autocorrelation function of a charged Quantum Brownian particle in a magnetic field coupled to a bath. We study two bath modelsthe Ohmic bath model and the Drude bath model and make a detailed comparison in various timetemperature regimes. For both bath models there is a competition between the cyclotron frequency and the viscous damping rate giving rise to a transition from an oscillatory to a monotonic behaviour as the damping rate is increased. In the zero point fluctuation dominated low temperature regime, non-trivial noise correlations lead to some interesting features in this transition. We study the role of the memory time scale which comes into play in the Drude model and study the effect of this additional time scale. We discuss the experimental implications of our analysis in the context of experiments in cold ions.

The energy spectrum of two interacting electrons confined in a quantum dot in the presence of a magnetic field has been calculated by interpolating between the eigenenergies in the high- and low-field limits.