The dynamics of a (quasi-) one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schrödinger equation. If the static field is varied, the system shows a plethora of dynamical phenomena. In the strong field limit, we demonstrate the existence of (almost) nonspreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so-called quantum carpets). With decreasing field, the dynamics becomes irregular, however, still confined in configuration space. For even weaker fields, we find subdiffusive dynamics with a wave-packet width growing as t 1/4 .

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

In this paper, we examine the effect of introducing a conical disclination on the thermal and optical properties of a two dimensional GaAs quantum dot in the presence of a uniform and constant magnetic field. In particular, our model consists of a single-electron subject to a confining Gaussian potential with a spin-orbit interaction in the Rashba approach. We compute the specific heat and the magnetic susceptibility from the exact solution of the Schrödinger equation via the canonical partition function, and it is shown that the peak structure of the Schottky anomaly is linearly displaced as a function of the topological defect. We found that such defect and the Rashba coupling modify the values of the temperature and magnetic field in which the system behaves as a paramagnetic material. Remarkably, the introduction of a conical disclination in the quantum dot relaxes the selection rules for the electronic transitions when an external electromagnetic field is applied. This creates a new set of allowed transitions causing the emergence of semi-suppressed resonances in the absorption coefficient as well as in the refractive index changes which are blue-shifted with respect to the regular transitions for a quantum dot without the defect.

We theoretically investigate the unexpected occurrence of an extra emission peak that has been experimentally observed in off-resonant studies of cavity QED systems. Our results within the Markovian master equation approach successfully explain why the central peak arises, and how it reveals that the system is suffering a dynamical phase transition induced by the phonon-mediated coupling. Our findings are in perfect agreement with previous reported experimental results and for the first time the fundamental physics behind this quantum phenomenon is understood.