Density and correlation functions of vortex and saddle points in open billiard systems.
@article{Hhmann2009DensityAC, title={Density and correlation functions of vortex and saddle points in open billiard systems.}, author={Ruven H{\"o}hmann and Ulrich Kuhl and Hans-J{\"u}rgen St{\"o}ckmann and Juan Diego Urbina and Mark R. Dennis}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2009}, volume={79 1 Pt 2}, pages={ 016203 } }
We present microwave measurements for the density and spatial correlation of current critical points in an open billiard system and compare them with new and previous predictions of the random-wave model (RWM). In particular, due to an improvement of the experimental setup, we determine experimentally the spatial correlation of saddle points of the current field. An asymptotic expression for the vortex-saddle and saddle-saddle correlation functions based on the RWM is derived, with experiment…
13 Citations
Wave functions, nodal domains, flow, and vortices in open microwave systems
- Physics
- 2007
Abstract.The signatures of wave functions in open cylindrical microwave billiards are investigated. The wave functions are obtained by means of a transmission measurement from an attached lead to a…
Geometry and scaling of tangled vortex lines in three-dimensional random wave fields
- Physics
- 2014
The short- and long-scale behaviour of tangled wave vortices (nodal lines) in random three-dimensional wave fields is studied via computer experiment. The zero lines are tracked in numerical…
A random wave model for the Aharonov-Bohm effect
- Physics
- 2016
We study an ensemble of random waves subject to the Aharonov–Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a family of…
Poynting singularities in the transverse flow-field of random vector waves.
- PhysicsOptics letters
- 2020
It is shown that a random field confined to a 2D plane has a divergence-free flow- field and exhibits a liquid-like correlation, whereas its freely propagating counterpart has no clear correlation and features a transverse flow-field with the full range of possible 2D topologies around its singularities.
Critical point correlations in random gaussian fields
- Mathematics, Physics
- 2011
We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation…
Effective pair-interaction of phase singularities in random waves.
- MathematicsOptics letters
- 2021
This study initiates a new, to the best of the knowledge, approach for the treatment of singularities in random waves and can be generalized to topological defects in any system.
Modern finite-size criticality: Dirichlet and Neumann boundary conditions
- MathematicsThe European Physical Journal Plus
- 2019
Abstract.Finite-size critical systems defined on a parallel-plate geometry of finite extent along one single (z) direction with Dirichlet and Neumann boundary conditions at z = 0, L are analyzed in…
Geometry and Scaling of Vortex Lines
- Physics
- 2017
Many geometrical properties can be be used to characterise space curves, and for random filaments such as the vortices in wave chaos may take particular statistical values. In this Chapter we…
Nodal portraits of quantum billiards: Domains, lines, and statistics
- Physics
- 2017
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to…
References
SHOWING 1-10 OF 89 REFERENCES
Critical-point screening in random wave fields
- Physics
- 1998
Screening of vortices and other critical points in a two-dimensional random Gaussian field is studied by using large-scale computer simulations and analytic theory. It is shown that the topological…
Wave functions, nodal domains, flow, and vortices in open microwave systems
- Physics
- 2007
Abstract.The signatures of wave functions in open cylindrical microwave billiards are investigated. The wave functions are obtained by means of a transmission measurement from an attached lead to a…
LETTER TO THE EDITOR: Phase critical point densities in planar isotropic random waves
- Physics
- 2001
The densities of critical points of phase (extrema and saddles), which play an important role in the theory of phase singularities (wave dislocations) in two dimensions, are calculated in isotropic…
Curved boundary corrections to nodal line statistics in chaotic billiards
- Mathematics
- 2005
A Gaussian random wavefunction that satisfies Dirichlet and Neumann conditions locally on a convex circular boundary is introduced. The average of the square of the wavefunction and its derivatives…
Nodal-line densities of chaotic quantum billiard modes satisfying mixed boundary conditions
- Physics
- 2005
Statistics of nodal lines for eigenmodes u in the stadium are computed, and compared with previously derived formulae for monochromatic boundary-adapted Gaussian random waves in the plane. These…
Current and Vorticity Auto Correlation Functions in Open Microwave Billiards
- Physics
- 2003
Using the equivalence between the quantum-mechanical probability density in a quantum billiard and the Poynting vector in the corresponding microwave system, current distributions were studied in a…
Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory.
- PhysicsPhysical review letters
- 2008
New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients, and the fluctuation scale is significantly enhanced for Neumann boundary conditions as compared to Dirichlet.
Current and vortex statistics in microwave billiards.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002
Using the one-to-one correspondence between the Poynting vector in a microwave billiard and the probability current density in the corresponding quantum system, probability densities and currents…
Semiclassical construction of random wave functions for confined systems.
- Physics, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004
We develop a statistical description of chaotic wave functions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation…
Distribution of nearest distances between nodal points for the Berry function in two dimensions.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001
Using the property that both the real and imaginary parts of the wave function are random Gaussian fields, the correlation function and densities of the nodal points are analyzed and the distribution of nearest neighbor separations is derived.