Chaos and integrability in triangular billiards
- URL: http://arxiv.org/abs/2407.11114v1
- Date: Mon, 15 Jul 2024 18:00:00 GMT
- Title: Chaos and integrability in triangular billiards
- Authors: Vijay Balasubramanian, Rathindra Nath Das, Johanna Erdmenger, Zhuo-Yu Xian,
- Abstract summary: We characterize quantum dynamics in triangular billiards in terms of five properties.
The billiards we study are classified as integrable, pseudointegrable or non-integrable.
A consistent picture emerges when transitioning from integrable to non-integrable triangles.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We characterize quantum dynamics in triangular billiards in terms of five properties: (1) the level spacing ratio (LSR), (2) spectral complexity (SC), (3) Lanczos coefficient variance, (4) energy eigenstate localisation in the Krylov basis, and (5) dynamical growth of spread complexity. The billiards we study are classified as integrable, pseudointegrable or non-integrable, depending on their internal angles which determine properties of classical trajectories and associated quantum spectral statistics. A consistent picture emerges when transitioning from integrable to non-integrable triangles: (1) LSRs increase; (2) spectral complexity growth slows down; (3) Lanczos coefficient variances decrease; (4) energy eigenstates delocalize in the Krylov basis; and (5) spread complexity increases, displaying a peak prior to a plateau instead of recurrences. Pseudo-integrable triangles deviate by a small amount in these charactertistics from non-integrable ones, which in turn approximate models from the Gaussian Orthogonal Ensemble (GOE). Isosceles pseudointegrable and non-integrable triangles have independent sectors that are symmetric and antisymmetric under a reflection symmetry. These sectors separately reproduce characteristics of the GOE, even though the combined system approximates characteristics expected from integrable theories with Poisson distributed spectra.
Related papers
- Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
arXiv Detail & Related papers (2024-10-21T10:56:49Z) - Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented.
We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
arXiv Detail & Related papers (2024-04-04T14:45:28Z) - Integrability as an attractor of adiabatic flows [0.0]
We consider two generic models of spin chains that are parameterized by two independent couplings.
In one, the integrability breaking is global while, in the other, integrability is broken only at the boundary.
These regions act as attractors of adiabatic flows similar to river basins in nature.
arXiv Detail & Related papers (2023-08-18T18:00:03Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Quantum scars in spin-1/2 isotropic Heisenberg clusters [0.0]
In the presence of uniform field in one direction, the SU(2) symmetry of the system allows that almost whole spectrum consists of a large number of towers with identical level spacing.
Our finding reveals the possibility of quantum information processing that is immune to the thermalization in finite size quantum spin clusters.
arXiv Detail & Related papers (2022-12-23T14:33:41Z) - Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
We introduce a class of quantum optical Hamiltonian characterized by three-body couplings.
We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
arXiv Detail & Related papers (2022-04-07T15:39:21Z) - Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling.
In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures.
By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
arXiv Detail & Related papers (2022-02-14T02:23:16Z) - Interacting bosons in a triple well: Preface of many-body quantum chaos [0.0]
We investigate the onset of quantum chaos in a triple-well model that moves away from integrability as its potential gets tilted.
Even in its deepest chaotic regime, the system presents features reminiscent of integrability.
arXiv Detail & Related papers (2021-11-26T19:00:03Z) - Quantum chaos in triangular billiards [0.0]
We compute two million consecutive eigenvalues for six representative cases of triangular billiards.
We find excellent agreement of short and long range spectral statistics with the Gaussian ensemble of random matrix theory for the most irrational generic triangle.
This result extends the quantum chaos conjecture to systems with dynamical mixing in the absence of hard (Lyapunov) chaos.
arXiv Detail & Related papers (2021-10-08T14:51:39Z) - SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from
Symmetric PEPS [55.41644538483948]
Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS)
Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder.
Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
arXiv Detail & Related papers (2019-12-31T16:30:25Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.