82 citations · 386 across the 15 of their papers we have counts for
16 papers
Semiclassical approximation for barrier billiards
Eugene Bogomolny
Barrier billiards are simple examples of pseudo-integrable models which form an appealing but poorly investigated subclass of dynamical systems. The paper examines the semiclassica…
Positive-Energy Dirac Particles and Dark Matter
Eugene Bogomolny
The relativistic positive-energy wave equation proposed by P. Dirac in 1971 is an old but largely forgotten subject. The purpose of this note is to speculate that particles describ…
Intermediate spectral statistics of rational triangular quantum billiards
Črt Lozej, Eugene Bogomolny
Triangular billiards whose angles are rational multiples of are one of the simplest examples of pseudo-integrable models with intriguing classical and quantum properties. We pe…
Spectral Properties and Dynamical Tunneling in Constant-Width Billiards
B. Dietz, T. Guhr, B. Gutkin +2
We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave res…
Dielectric Square Resonator Investigated with Microwave Experiments
S. Bittner, E. Bogomolny, B. Dietz +2
We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the…
Calculation of mean spectral density for statistically uniform tree-like random models
E. Bogomolny, O. Giraud
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in th…
Experimental Observation of Localized Modes in a Dielectric Square Resonator
S. Bittner, E. Bogomolny, B. Dietz +2
We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the exp…
Trace formula for dielectric cavities III: TE modes
E. Bogomolny, R. Dubertrand
The construction of the semiclassical trace formula for the resonances with the transverse electric (TE) polarization for two-dimensional dielectric cavities is discussed. Special…
Multifractality of eigenfunctions in spin chains
Yasar Yilmaz Atas, Eugene Bogomolny
We investigate different one-dimensional quantum spin-1/2 chain models and by combining analytical and numerical calculations prove that their ground state wave functions in the na…
Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime
E. Bogomolny, O. Giraud
We construct perturbation series for the q-th moment of eigenfunctions of various critical random matrix ensembles in the strong multifractality regime close to localization. Contr…
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
E. Bogomolny, O. Giraud
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both…
Eigenfunction entropy and spectral compressibility for critical random matrix ensembles
E. Bogomolny, O. Giraud
Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D_1 and the spectral c…
SLE description of the nodal lines of random wave functions
E. Bogomolny, R. Dubertrand, C. Schmit
The nodal lines of random wave functions are investigated. We demonstrate numerically that they are well approximated by the so-called SLE_6 curves which describe the continuum lim…
Short-range plasma model for intermediate spectral statistics
E. Bogomolny, U. Gerland, C. Schmit
We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson st…
Spectral statistics of chaotic systems with a point-like scatterer
E. Bogomolny, P. Leboeuf, C. Schmit
The statistical properties of a Hamiltonian perturbed by a localized scatterer are considered. We prove that when describes a bounded chaotic motion, the universal part…
Diffractive corrections in the trace formula for polygonal billiards
E. Bogomolny, N. Pavloff, C. Schmit
We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional polygonal billiards. In polygons, diffraction…