# The level repulsion exponent of localized chaotic eigenstates as a function of the classical transport time scales in the stadium billiard

@inproceedings{Batistic2021TheLR, title={The level repulsion exponent of localized chaotic eigenstates as a function of the classical transport time scales in the stadium billiard}, author={Benjamin Batisti'c and vCrt Lozej and Marko Robnik}, year={2021} }

We study the aspects of quantum localization in the stadium billiard, which is a classically chaotic ergodic system, but in the regime of slightly distorted circle billiard the diffusion in the momentum space is very slow. In quantum systems with discrete energy spectrum the Heisenberg time tH = 2π~/∆E, where ∆E is the mean level spacing (inverse energy level density), is an important time scale. The classical transport time scale tT (diffusion time) in relation to the Heisenberg time scale tH…

## 4 Citations

### Spectral form factors and dynamical localization

- Physics
- 2023

: Quantum dynamical localization occurs when quantum interference stops the diffusion of wave packets in momentum space. The expectation is that dynamical localization will occur when the typical…

### Statistical properties of the localization measure of chaotic eigenstates in the Dicke model.

- PhysicsPhysical review. E
- 2020

The findings extend the previous results in billiards to the quantum many-body system with classical counterpart described by a smooth Hamiltonian, and they indicate that the properties of localized chaotic eigenstates are universal.

### Identification of quantum scars via phase-space localization measures

- PhysicsQuantum
- 2022

There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies…

### Quantum chaos in triangular billiards

- MathematicsPhysical Review Research
- 2022

We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of…

## References

SHOWING 1-10 OF 36 REFERENCES

### Integral geometry and geometric probability

- Mathematics
- 1976

Part I. Integral Geometry in the Plane: 1. Convex sets in the plane 2. Sets of points and Poisson processes in the plane 3. Sets of lines in the plane 4. Pairs of points and pairs of lines 5. Sets of…

### Commun

- Math. Phys. 65, 295
- 1979

### A: Math

- Theor. 46, 315102
- 2013

### Phys

- Rev. E 88, 052913
- 2013

### Quantum Chaos - An Introduction (Cambridge

- 1999

### Lecture Notes in Physics 93

- 334
- 1979

### Proc

- Roy. Soc. Lond. A 400, 229
- 1985

### in Proc

- of the Int. School in Phys. ”Enrico Fermi”, Course CXLIII, Eds. G. Casati and U. Smilansky
- 2000

### Phys

- Rep. 196, 299
- 1990