arXiv subjects

Jakub Zakrzewski

Publications and source records attributed to Jakub Zakrzewski.

173 records · Page 10Linked to original sources

arXiv1998

Resonant dynamics of the H atom in an elliptically polarized microwave field

The dynamics of Rydberg states of atomic hydrogen driven by elliptically polarized microwaves of frequency fulfilling 2:1 classical resonance condition is investigated both semiclassically and quantum mechanically in a simplified two-dimensional model of an atom. Semiclassical results for quasienergies of the system are shown to be in a good agreement with exact quantum data. The structures of the quantum states are found to reflect the underlying classical dynamics; especially we show the existence of nonspreading wavepackets propagating on elliptical trajectories.

chao-dyn↗

arXiv1998

H atom in elliptically polarized microwaves: Semiclassical versus quantum resonant dynamics

The dynamics of Rydberg states of atomic hydrogen illuminated by resonant elliptically polarized microwaves is investigated both semiclassically and quantum mechanically in a simplified two-dimensional model of an atom. Semiclassical predictions for quasienergies of the system are found to be in a very good agreement with exact quantum data enabling a classification of possible types of motion and their dynamics with the change of the ellipticity of the microwaves. Particular attention is paid to the dynamics of the nonspreading wave packet states which are found to exist for an arbitrary microwave polarization.

chao-dyn↗

arXiv1998

Quantum scattering in the strip: from ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined.

cond-mat.mes-hall↗

arXiv1998

Spontaneous emission of non-dispersive Rydberg wave packets

Non dispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states and show that the elastic incoherent component (occuring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single photon emissions and the associated rates in the "harmonic approximation", i.e. when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum mechanical calculations, which validates the analytical approach.

quant-ph↗

arXiv1997

Random matrix approach to `nonuniversal' conductance

Recent experiments on the conductance of high quality quantum wires have revealed an unexpected feature: the quantization step of the conductance is apparently system dependent. We provide the understanding of this behaviour using the appropriately extended random matrix approach. A single additional parameter governs the size of the conductance quantization steps. In effect the behaviour seems to remain `universal', generic for the conductance of a class of mesoscopic systems.

cond-mat.mes-hall↗

arXiv1997

Ionization via Chaos Assisted Tunneling

A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) which may tunnel into a chaotic sea and further escape to infinity via chaotic diffusion. The specific system is realistic : it is the hydrogen atom exposed to either linearly or circularly polarized microwaves. We show that the combination of tunneling followed by chaotic diffusion leads to peculiar statistical fluctuation properties of the energy and the ionization rate, especially to enhanced fluctuations compared to the purely chaotic case. An appropriate random matrix model, whose predictions are analytically derived, describes accurately these statistical properties.

chao-dyn↗

arXiv1996

Nonuniversality in level dynamics

Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime between three universality classes. It is shown that the statistical properties of level dynamics are in general non-universal and strongly depend on the way in which the parametric dynamics is introduced.

chao-dyn↗

arXiv1996

Statistical properties of random scattering matrices

We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are obtained both theoretically and numerically. A simple formula describing the velocity distribution (and hence the distribution of the Wigner time delay) is derived, which is capable to explain the algebraic tail of the time delay distribution observed recently in microwave experiments. A dependence of the eigenphases on other external parameters is also discussed. We show that in the semiclassical limit (large number of channels) the curvature distribution of $S$--matrix eigenphases is the same as that corresponding to the curvature distribution of the underlying Hamiltonian and is given by the generalized Cauchy distribution.

chao-dyn↗

arXiv1995

2D Quantum Hydrogen Atom in Circularly Polarized Microwaves

The ionization of hydrogen Rydberg atoms by circularly polarized microwaves is studied quantum mechanically in a model two dimensional atom. We apply a combination of a transformation to the coordinate frame rotating with the field, with complex rotation approach and representation of atomic subspace in Sturmian-type basis. The diagonalization of resulting matrices allows us to treat exactly the ionization of atoms initially prepared in highly excited Rydberg states of principal quantum number $n_0\approx 60$. Similarities and differences between ionization by circularly and linearly polarized microwaves are discussed with a particular emphasis on the localization phenomenon. The dependence of the ionization character on the type of the initial state (circular, elliptical or low angular momentum state) as well as on the helicity of the polarization is discussed in detail.

chao-dyn↗

arXiv1995

Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.

chao-dyn↗

arXiv1995

On "Universal" Correlations in Disordered and Chaotic Systems

Numerical study of the parametric motion of energy levels in a model system built on Random Matrix Theory is presented. The correlation function of levels' slopes (the so called velocity correlation function) is determined numerically and compared with its limiting analytic form when available. A simple analytic form of the velocity correlation function is proposed which very well reproduces numerical data. The results should be directly applicable in studies of chaotic or mesoscopic systems.

chao-dyn↗