Current statistics for wave transmission through an open Sinai billiard: Effects of net currents

Sadreev, Almas F.; Berggren, Karl‐Fredrik

doi:10.1103/physreve.70.026201

Cited by 13 publications

(7 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Simulations for open chaotic 2D systems have shown, for example, that there is an abundance of chaotic states that obey generalized wave function distributions that depend on the degree of openness [6,7]. There are universal distributions and correlation functions for nodal points and vortices [8,9,10,11] and the closely related universal distributions [6,12] and correlation functions for the probability current density [13,14].…”

Section: Introductionmentioning

confidence: 99%

Quantum stress in chaotic billiards

et al. 2008

Self Cite

View full text Add to dashboard Cite

This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T ␣␤ ͑x , y͒ for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as = u + iv. With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T ␣␤ . The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T ␣␤ ͑x , y͒ is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantum stress in chaotic billiards

et al. 2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…The theory is valid for isotropic flow, i.e., the current is not biased towards any direction. This is a reasonable assumption as long as the net flow is weak [39]. Consequently the distributions for the current components j x and j y are also isotropic.…”

Section: Current Distributionsmentioning

confidence: 99%

Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

2014

View full text Add to dashboard Cite

A basic quantum-mechanical model for wave functions and current flow in open quantum dots or billiards is investigated. The model involves non-Hertmitian quantum mechanics, parity-time (PT ) symmetry, and PT -symmetry breaking. Attached leads are represented by positive and negative imaginary potentials. Thus probability densities, currents flows, etc., for open quantum dots or billiards may be simulated in this way by solving the Schrödinger equation with a complex potential. Here we consider a nominally open ballistic quantum dot emulated by a planar microwave billiard. Results for probability distributions for densities, currents (Poynting vector), and stress tensor components are presented and compared with predictions based on Gaussian random wave theory. The results are also discussed in view of the corresponding measurements for the analogous microwave cavity. The model is of conceptual as well as of practical and educational interest.

show abstract

“…For such an ensemble, the eigenvector elements acquire correlations between the elements of the same eigenvector 10,22 and between different eigenvectors 23 . For individual systems, such a crossover may be observed already in a billiard with only two attached waveguides 24 . The wave functions in the cross-over regime show long-range correlations 11 like the eigenvectors of the Hamiltonian H(α).…”

Section: Introductionmentioning

confidence: 97%

Phase rigidity and avoided level crossings in the complex energy plane

2006

Self Cite

View full text Add to dashboard Cite

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions phi(lambda), and define the value r(lambda)=(phi(lambda)|phi(lambda))/ that characterizes the phase rigidity of the eigenfunctions phi(lambda). In the scenario with avoided level crossings, r(lambda) varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of r(lambda) is an internal property of an open quantum system. In the literature, the phase rigidity rho of the scattering wave function Psi(C)(E) is considered. Since Psi(C)(E) can be represented in the interior of the system by the phi(lambda), the phase rigidity rho of the Psi(C)(E) is related to the r(lambda) and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity rho to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity rho and transmission numerically for small open cavities.

show abstract

Current statistics for wave transmission through an open Sinai billiard: Effects of net currents

Cited by 13 publications

References 25 publications

Quantum stress in chaotic billiards

Quantum stress in chaotic billiards

Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

Phase rigidity and avoided level crossings in the complex energy plane

Contact Info

Product

Resources

About