arXiv subjects

R. Blümel

Publications and source records attributed to R. Blümel.

22 records · Page 2Linked to original sources

arXiv2001

A fresh look at 3D microwave ionization curves of hydrogen Rydberg atoms

Analytical arguments and numerical simulations suggest that the shapes of 3D microwave ionization curves measured by Koch and collaborators (see P. M. Koch and K. A. H. van Leeuwen, Phys. Rep. {\bf 255}, 289 (1995)) depend only weakly on the angular momentum of the atoms in the initial microcanonical ensemble, but strongly on the principal quantum number and the magnetic quantum number. Based on this insight, coupled with the computational power of a high-end 60-node Beowulf PC cluster, we present the first 3D quantum calculations of microwave ionization curves in the experimentally relevant parameter regime.

quant-ph↗

arXiv2001

Combinatorial identities for binary necklaces from exact ray-splitting trace formulae

Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (Pólya necklaces).

math-ph↗

arXiv2001

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

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

quant-ph↗

arXiv2001

Explicitly solvable cases of one-dimensional quantum chaos

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it 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 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.

quant-ph↗