Monitoring approach to open quantum dynamics using scattering theory

It is shown how S-matrix theory and the concept of continuous quantum measurements can be combined to yield Markovian master equations which describe the environmental interaction non-perturbatively. The method is then applied to obtain the master equation for the effects of a gas on the internal dynamics of an immobile complex quantum system, such as a trapped molecule, in terms of the exact multi-channel scattering amplitudes.Comment: 5 pages; published versio

Pointer basis induced by collisional decoherence

We study the emergence and dynamics of pointer states in the motion of a quantum test particle affected by collisional decoherence. These environmentally distinguished states are shown to be exponentially localized solitonic wave functions which evolve according to the classical equations of motion. We explain their formation using the orthogonal unraveling of the master equation, and we demonstrate that the statistical weights of the arising mixture are given by projections of the initial state onto the pointer basis.Comment: 26 pages, 9 figures; v2: minimal corrections, corresponds to published versio

Magnetic edge states

Magnetic edge states are responsible for various phenomena of magneto-transport. Their importance is due to the fact that, unlike the bulk of the eigenstates in a magnetic system, they carry electric current along the boundary of a confined domain. Edge states can exist both as interior (quantum dot) and exterior (anti-dot) states. In the present report we develop a consistent and practical spectral theory for the edge states encountered in magnetic billiards. It provides an objective definition for the notion of edge states, is applicable for interior and exterior problems, facilitates efficient quantization schemes, and forms a convenient starting point for both the semiclassical description and the statistical analysis. After elaborating these topics we use the semiclassical spectral theory to uncover nontrivial spectral correlations between the interior and the exterior edge states. We show that they are the quantum manifestation of a classical duality between the trajectories in an interior and an exterior magnetic billiard.Comment: 170 pages, 48 figures (high quality version available at http://www.klaus-hornberger.de

Testing the limits of quantum mechanical superpositions

Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the linearity of quantum mechanics extends into the macroscopic domain. Scientific progress over the last decades inspires hope that this debate may be decided by table-top experiments.Comment: 16 pages, 4 Figures; published version differs by minor editorial change

Spectral cross correlations of magnetic edge states

We observe strong, non-trivial cross-correlations between the edge states found in the interior and the exterior of magnetic quantum billiards. Our analysis is based on a novel definition of the edge state spectral density which is rigorous, practical and semiclassically accessible.Comment: 4 pages, 3 figures (high quality version available at http://www.klaus-hornberger.de

Relaxation dynamics of a quantum Brownian particle in an ideal gas

We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal gas by means of a translation-covariant master equation. We discuss the type of approximations required to obtain the generalized form of the Caldeira-Leggett master equation, along with their physical justification. Microscopic expressions for the diffusion and relaxation coefficients are obtained by analyzing the limiting form of the equation in both the Schroedinger and the Heisenberg picture.Comment: 15 pages; to appear in Eur. Phys. J. Special Topics (2007