## Fachbereich Physik

### Filtern

#### Dokumenttyp

- Wissenschaftlicher Artikel (41) (entfernen)

#### Schlagworte

- resonances (8)
- Wannier-Stark systems (7)
- lifetimes (7)
- Quantum mechanics (6)
- quantum mechanics (5)
- lifetime statistics (4)
- entropy (3)
- localization (3)
- dynamical systems (2)
- phase-space (2)

We study the statistics of the Wigner delay time and resonance width for a Bloch particle in ac and dc fields in the regime of quantum chaos. It is shown that after appropriate rescaling the distributions of these quantities have universal character predicted by the random matrix theory of chaotic scattering.

We present an entropy concept measuring quantum localization in dynamical systems based on time averaged probability densities. The suggested entropy concept is a generalization of a recently introduced [PRL 75, 326 (1995)] phase-space entropy to any representation chosen according to the system and the physical question under consideration. In this paper we inspect the main characteristics of the entropy and the relation to other measures of localization. In particular the classical correspondence is discussed and the statistical properties are evaluated within the framework of random vector theory. In this way we show that the suggested entropy is a suitable method to detect quantum localization phenomena in dynamical systems.

The Filter-Diagonalization Method is applied to time periodic Hamiltonians and used to find selectively the regular and chaotic quasienergies of a driven 2D rotor. The use of N cross-correlation probability amplitudes enables a selective calculation of the quasienergies from short time propagation to the time T (N). Compared to the propagation time T (1) which is required for resolving the quasienergy spectrum with the same accuracy from auto-correlation calculations, the cross-correlation time T (N) is shorter by the factor N , that is T (1) = N T (N).

The global dynamical properties of a quantum system can be conveniently visualized in phase space by means of a quantum phase space entropy in analogy to a Poincare section in classical dynamics for two-dimensional time independent systems. Numerical results for the Pullen Edmonds systems demonstrate the properties of the method for systems with mixed chaotic and regular dynamics.

The Filter-Diagonalization Method is used to ,nd the broad and even overlapping resonances of a 1D Hamiltonian used before as a test model for new resonance theories and computational methods. It is found that the use of several complex-scaled cross-correlation probability amplitudes from short time propagation enables the calculation of broad overlapping resonances, which can not be resolved from the amplitude of a single complex-scaled autocorrelation calculation.

A formalism is developed for calculating the quasienergy states and spectrum for time-periodic quantum systems when a time-periodic dynamical invariant operator with a nondegenerate spectrum is known. The method, which circumvents the integration of the Schr-odinger equation, is applied to an integrable class of systems, where the global invariant operator is constructed. Furthermore, a local integrable approximation for more general non-integrable systems is developed. Numerical results are presented for the doubleresonance model.

We consider N coupled linear oscillators with time-dependent coecients. An exact complex amplitude - real phase decomposition of the oscillatory motion is constructed. This decomposition is further used to derive N exact constants of motion which generalise the so-called Ermakov-Lewis invariant of a single oscillator. In the Floquet problem of periodic oscillator coecients we discuss the existence of periodic complex amplitude functions in terms of existing Floquet solutions.

Quantum Chaos
(1999)

The study of dynamical quantum systems, which are classically chaotic, and the search for quantum manifestations of classical chaos, require large scale numerical computations. Special numerical techniques developed and applied in such studies are discussed: The numerical solution of the time-dependent Schr-odinger equation, the construction of quantum phase space densities, quantum dynamics in phase space, the use of phase space entropies for characterizing localization phenomena, etc. As an illustration, the dynamics of a driven one-dimensional anharmonic oscillator is studied, both classically and quantum mechanically. In addition, spectral properties and chaotic tunneling are addressed.