Biomedical subjects

H-J Stöckmann

Publications and source records attributed to H-J Stöckmann.

11 recordsLinked to original sources

PubMed2006

Anomalous slow fidelity decay for symmetry-breaking perturbations.

Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on exponentiated linear response will be given. For one representative case the exact solution is obtained from a supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.

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PubMed2006

Fidelity freeze for a random matrix model with off-diagonal perturbation.

The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Znidaric in the linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Znidaric are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely imaginary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.

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PubMed2005

Experimental verification of fidelity decay: from perturbative to fermi golden rule regime.

The scattering matrix was measured for a flat microwave cavity with classically chaotic dynamics. The system can be perturbed by small changes of the geometry. We define the "scattering fidelity" in terms of parametric correlation functions of scattering matrix elements. In chaotic systems and for weak coupling, the scattering fidelity approaches the fidelity of the closed system. Without free parameters, the experimental results agree with random matrix theory in a wide range of perturbation strengths, reaching from the perturbative to the Fermi golden rule regime.

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PubMed2005

Direct processes in chaotic microwave cavities in the presence of absorption.

We quantify the presence of direct processes in the S matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P(S)(S) of the S matrix, i.e., S=sqrt[R]e(itheta), is studied in cavities with time-reversal symmetry for different antenna coupling strengths T(a) or direct processes. The experimental results are compared with random-matrix calculations and with numerical simulations including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with theoretical predictions for all cases.

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PubMed2005

Universal transport properties of open microwave cavities with and without time-reversal symmetry.

We measure the transmission through asymmetric and reflection-symmetric chaotic microwave cavities in dependence on the number of attached waveguides. Ferrite cylinders are placed inside the cavities to break time-reversal symmetry. The phase-breaking properties of the ferrite and its range of applicability are discussed in detail. We use the random matrix theory accounting for absorption effects to calculate the universal distribution of transmission coefficients T and their energy derivatives dT/depsilon. Using the absorption strength as a fitting parameter, we find good agreement between universal transmission fluctuations predicted by the theory and the experimental data.

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PubMed2005

Measurement of long-range wave-function correlations in an open microwave billiard.

We investigate the statistical properties of wave functions in an open chaotic cavity. When the number of channels in the openings of the billiard is increased by varying the frequency, wave functions cross over from real to complex. The distribution of the phase rigidity, which characterizes the degree to which a wave function is complex, and long-range correlations of intensity and current density are studied as a function of the number of channels in the openings. All measured quantities are in perfect agreement with theoretical predictions.

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PubMed2004

Tunable Fano resonances in transport through microwave billiards.

We present a tunable microwave scattering device that allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. Transport in this device is nearly fully coherent. By comparison with quantum calculations, employing the modular recursive Green's-function method, the scattering wave function and the degree of residual decoherence can be determined. The parametric variation of Fano line shapes in terms of interacting resonances is analyzed.

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PubMed2003

Distribution of reflection coefficients in absorbing chaotic microwave cavities.

The distribution of reflection coefficients P(R) for chaotic microwave cavities with time-reversal symmetry is investigated in different absorption and antenna coupling regimes. For all regimes the agreement between experimental distributions and random-matrix theory predictions is very good, provided both the antenna coupling T(a) and the wall absorption strength T(w) are taken into account in an appropriate way. These parameters are determined by independent experimental quantities.

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PubMed2002

Geometry-dependent scattering through quantum billiards: experiment and theory.

We present experimental studies of geometry-specific quantum scattering in microwave billiards of a given shape. We perform full quantum-mechanical scattering calculations and find excellent agreement with experimental results. We also carry out semiclassical calculations where the conductance is given as a sum over all classical trajectories between the leads, each of the trajectories carrying a quantum-mechanical phase. We unambiguously demonstrate that the characteristic frequencies of the oscillations in the transmission and reflection amplitudes t and r are related to the length distribution of the classical trajectories between the leads, whereas the frequencies of the probabilities T=/t/(2) and R=/r/(2) can be understood in terms of the length difference distribution in the pairs of classical trajectories. We also discuss the effect of nonclassical "ghost" trajectories, i.e., trajectories that include classically forbidden reflection off the lead mouths.

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PubMed2002

Transition from Gaussian-orthogonal to Gaussian-unitary ensemble in a microwave billiard with threefold symmetry.

Recently it has been shown that time-reversal invariant systems with discrete symmetries may display, in certain irreducible subspaces, spectral statistics corresponding to the Gaussian-unitary ensemble (GUE) rather than to the expected orthogonal one (GOE). A Kramers-type degeneracy is predicted in such situations. We present results for a microwave billiard with a threefold rotational symmetry and with the option to display or break a reflection symmetry. This allows us to observe the change from GOE to GUE statistics for one subset of levels. Since it was not possible to separate the three subspectra reliably, the number variances for the superimposed spectra were studied. The experimental results are compared with a theoretical and numerical study considering the effects of level splitting and level loss.

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PubMed2002

Effective Hamiltonian for a microwave billiard with attached waveguide.

In a recent work the resonance widths in a microwave billiard with attached waveguide were studied in dependence on the coupling strength [E. Persson et al., Phys. Rev. Lett. 85, 2478 (2000)], and resonance trapping was experimentally found. In the present paper an effective Hamiltonian is derived that depends exclusively on billiard and waveguide geometry. Its eigenvalues give the poles of the scattering matrix provided that the system and environment are defined adequately. Further, we present the results of resonance trapping measurements where, in addition to our previous work, the position of the slit aperture within the waveguide was varied. Numerical simulations with the derived Hamiltonian qualitatively reproduce the experimental data.

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