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#### Keywords

- quasienergy (2)
- Filter-Diagonalization (1)
- Wannier-Stark systems (1)
- chaos (1)
- complex energ (1)
- cross-correlation (1)
- initial value representation (1)
- qauntum mechanis (1)
- quantum mechanics (1)
- resonances (1)

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.

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.

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).

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.