## Fachbereich Physik

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#### Year of publication

- 1998 (7) (remove)

#### Keywords

- Electron states in low-dimensional structures (1)
- Quantum mechanics (1)
- Tunneling (1)
- Wannier-Bloch resonance states (1)
- Wannier-Stark systems (1)
- chaos (1)
- initial value representation (1)
- lifetime statistics (1)
- lifetimes (1)
- quantum chaos (1)

- Chaotic Wannier-Bloch resonance states (1998)
- The Wannier-Bloch resonance states are metastable states of a quantum particle in a space-periodic potential plus a homogeneous field. Here we analyze the states of quantum particle in space- and time-periodic potential. In this case the dynamics of the classical counterpart of the quantum system is either quasiregular or chaotic depending on the driving frequency. It is shown that both the quasiregular and the chaotic motion can also support quantum resonances. The relevance of the obtained result to the problem a of crystal electron under simultaneous influence of d.c. and a.c. electric fields is briefly discussed. PACS: 73.20Dx, 73.40Gk, 05.45.+b

- Lifetime statistics for a Bloch particle in ac and dc fields (1998)
- 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.

- Global and local dynamical invariants and quasienergy states of time-periodic Hamiltonians (1998)
- 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.

- The 'Ermakov-Lewis' invariants for Coupled Linear Oscillators (1998)
- 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.

- Calculation of Wannier-Bloch and Wannier-Stark states (1998)
- The paper discusses the metastable states of a quantum particle in a periodic potential under a constant force (the model of a crystal electron in a homogeneous electric ,eld), which are known as the Wannier-Stark ladder of resonances. An ecient procedure to ,nd the positions and widths of resonances is suggested and illustrated by numerical calculation for a cosine potential.

- Semiclassical Quantization of a System with Mixed Regular/Chaotic Dynamics (1998)
- The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time dependent systems. For an anharmonic oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings.