Hans Jürgen Korsch

Wannier-Stark Resonances in optical and semiconductor superlattices

Abstract In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally, this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier–Stark problem. We describe a novel approach to the Wannier–Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier–Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier–Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier–Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.

Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer

We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex on-site energy describes an effective decay from one of the modes. Recently a generalized mean-field approximation for this non-Hermitian many-particle system yielding an alternative complex nonlinear Schroedinger equation was introduced. Here we give details of this mean-field approximation and show that the resulting dynamics can be expressed in a generalized canonical form that includes a metric gradient flow. The interplay of nonlinearity and non-Hermiticity introduces a qualitatively new behavior to the mean-field dynamics: The presence of the non-Hermiticity promotes the self-trapping transition, while damping the self-trapping oscillations, and the nonlinearity introduces a strong sensitivity to the initial conditions in the decay of the normalization. Here we present a complete characterization of the mean-field dynamics and the fixed point structure. We also investigate the full many-particle dynamics, which shows a rich variety of breakdown and revival as well as tunneling phenomena on top of the mean-field structure.

On the zeros of the Husimi distribution

The basic features of the zeros of the Husimi phase-space density of a quantum eigenstate are discussed. It is demonstrated that some special properties of the harmonic oscillator related to the number of zeros and their location within the classical energy shell are not valid for anharmonic potentials, as illustrated by numerical examples for the Morse oscillator. Also discussed is the distribution of zeros in quantum Poincare sections for systems with two degrees of freedom.

Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential

The resonance states and the decay dynamics of the nonlinear Schrodinger (or Gross–Pitaevskii) equation are studied for a simple, but flexible, model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two-basis states in terms of a nonlinear, non-Hermitian matrix problem.

Rotational rainbow effects in electron-molecule and atom-molecule scattering

Rotational rainbow structures in atom/electron-molecule scattering are analysed by means of simple dynamical approximations as hard-shell molecules, the infinite order sudden (IOS) approximation and the N-centre spectator model. Typical collision systems described are atom-molecule scattering for collision energies of 10-1 eV and electron-molecule scattering at 102 eV. The IOS and spectator rotational rainbow patterns are compared and special features related to initially excited molecules, m-changing collisions, multiple rainbows, and inversion techniques are discussed. The rotational rainbow patterns for polyatomic molecules (symmetric tops) are discussed as well as vibrational effects in the rotational rainbow structures of diatomics.

BLOCH OSCILLATIONS OF COLD ATOMS IN OPTICAL LATTICES

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.

Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator

The non-Hermitian quadratic oscillator studied by Swanson is one of the popular

Bose-Einstein condensates on tilted lattices: Coherent, chaotic, and subdiffusive dynamics

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Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices

-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phase-space trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets. It is shown that the classical metric and trajectories as well as the quantum wave functions can diverge in finite time even though the

The nonlinear Schröder equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

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