Biomedical subjects

R Blümel

Publications and source records attributed to R Blümel.

At least 19 recordsLinked to original sources

PubMed2002

Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs.

We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs in the paper. One simple application is the energy levels of a particle in a piecewise constant potential. Since the classical ray trajectories (including ray splitting) in such systems are strongly chaotic, this result provides an explicit quantization of a classically chaotic system.

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PubMed2002

Explicitly solvable cases of one-dimensional quantum chaos.

We identify a set of quantum graphs with unique and precisely defined spectral properties called regular quantum graphs. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact, convergent periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit, and exact.

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PubMed2001

Parametric correlations of the energy levels of ray-splitting billiards.

Parameter-dependent statistical properties of the spectra of ray-splitting billiards are studied experimentally and theoretically. The autocorrelation functions c(x) and c(omega,x) of level velocities as well as the generalized conductance C(0) are calculated for two different classically chaotic ray-splitting billiards. Experimentally a modified Sinai ray-splitting billiard is studied consisting of a thin microwave rectangular cavity with two quarter-circle-shaped Teflon inserts. The length of the cavity serves as the experimentally adjustable parameter. For the theoretical estimates of the parametric correlations we compute the quantum spectrum of a scaling triangular ray-splitting billiard. Our experimental and numerical results are compared with each other and with the predictions of random matrix theory.

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PubMed2001

Exact trace formulas for a class of one-dimensional ray-splitting systems.

Using quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman et al. [Phys. Rev. A 46, 6193 (1992)] is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested.

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PubMed1999

Test of semiclassical amplitudes for quantum ray-splitting systems.

We compute semiclassically and numerically the weights of ray-splitting orbits in the density of states of a rectangular and an annular ray-splitting billiard. The agreement between the semiclassical and the numerical results is very good, confirming the necessity of including reflection and transmission coefficients of non-Newtonian ray-splitting orbits in semiclassical expressions for the density of states of ray-splitting systems.

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PubMed1999

Synchrotron radiation of crystallized beams.

We study the modifications of synchrotron radiation of charges in a storage ring as they are cooled. The pair correlation lengths between the charges are manifest in the synchrotron radiation and coherence effects exist for wavelengths longer than the coherence lengths between the charges. Therefore, the synchrotron radiation can be used as a diagnostic tool to determine the state (gas, liquid, crystal) of the charged plasma in the storage ring. We show also that the total power of the synchrotron radiation is significantly reduced for crystallized beams, both coasting and bunched. This opens the possibility of accelerating particles to ultrarelativistic energies using small-sized cyclic accelerators.

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PubMed1996