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#### Keywords

- Wannier-Stark systems (2)
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- Quantum Chaos (1)
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- Fachbereich Physik (5) (remove)

A new method for calculating Stark resonances is presented and applied for illustration to the simple case of a one-particle, one-dimensional model Hamiltonian. The method is applicable for weak and strong dc fields. The only need, also for the case of many particles in multi-dimensional space, are either the short time evolution matrix elements or the eigenvalues and Fourier components of the eigenfunctions of the field-free Hamiltonian.

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 paper studies quantum states of a Bloch particle in presence of external ac and dc fields. Provided the period of the ac field and the Bloch period are commensurate, an effective scattering matrix is introduced, the complex poles of which are the system quasienergy spectrum. The statistics of the resonance width and the Wigner delay time shows a close relation of the problem to random matrix theory of chaotic scattering.

The paper studies metastable states of a Bloch electron in the presence of external ac and dc fields. Provided resonance condition between period of the driving frequency and the Bloch period, the complex quasienergies are numerically calculated for two qualitatively different regimes (quasiregular and chaotic) of the system dynamics. For the chaotic regime an effect of quantum stabilization, which suppresses the classical decay mechanism, is found. This effect is demonstrated to be a kind of quantum interference phenomenon sensitive to the resonance condition.

A novel method is presented which allows a fast computation of complex energy resonance states in Stark systems, i.e. systems in a homogeneous field. The technique is based on the truncation of a shift-operator in momentum space. Numerical results for space periodic and non-periodic systems illustrate the extreme simplicity of the method.