Krylov complexity and chaos in quantum mechanics
- URL: http://arxiv.org/abs/2305.16669v2
- Date: Fri, 19 Jan 2024 06:38:53 GMT
- Title: Krylov complexity and chaos in quantum mechanics
- Authors: Koji Hashimoto, Keiju Murata, Norihiro Tanahashi, Ryota Watanabe
- Abstract summary: We numerically evaluate Krylov complexity for operators and states.
We find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents.
Our work provides a firm bridge between Krylov complexity and classical/quantum chaos.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Recently, Krylov complexity was proposed as a measure of complexity and
chaoticity of quantum systems. We consider the stadium billiard as a typical
example of the quantum mechanical system obtained by quantizing a classically
chaotic system, and numerically evaluate Krylov complexity for operators and
states. Despite no exponential growth of the Krylov complexity, we find a clear
correlation between variances of Lanczos coefficients and classical Lyapunov
exponents, and also a correlation with the statistical distribution of adjacent
spacings of the quantum energy levels. This shows that the variances of Lanczos
coefficients can be a measure of quantum chaos. The universality of the result
is supported by our similar analysis of Sinai billiards. Our work provides a
firm bridge between Krylov complexity and classical/quantum chaos.
Related papers
- Benchmarking quantum chaos from geometric complexity [0.23436632098950458]
We consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems.
Within some limitations, geometric complexity can indeed be a good indicator of quantum chaos.
arXiv Detail & Related papers (2024-10-24T14:04:58Z) - Attractive-repulsive interaction in coupled quantum oscillators [14.37149160708975]
We find an interesting symmetry-breaking transition from quantum limit cycle oscillation to quantum inhomogeneous steady state.
This transition is contrary to the previously known symmetry-breaking transition from quantum homogeneous to inhomogeneous steady state.
Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analogue in the classical domain.
arXiv Detail & Related papers (2024-08-23T10:45:19Z) - Krylov complexity as an order parameter for quantum chaotic-integrable transitions [0.0]
Krylov complexity has emerged as a new paradigm to characterize quantum chaos in many-body systems.
Recent insights have revealed that in quantum chaotic systems Krylov state complexity exhibits a distinct peak during time evolution.
We propose that this Krylov complexity peak (KCP) is a hallmark of quantum chaotic systems and suggest that its height could serve as an 'order parameter' for quantum chaos.
arXiv Detail & Related papers (2024-07-24T07:32:27Z) - Computational supremacy in quantum simulation [22.596358764113624]
We show that superconducting quantum annealing processors can generate samples in close agreement with solutions of the Schr"odinger equation.
We conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe.
arXiv Detail & Related papers (2024-03-01T19:00:04Z) - Spread complexity in saddle-dominated scrambling [0.0]
We study the spread complexity of the thermofield double state within emphintegrable systems that exhibit saddle-dominated scrambling.
Applying the Lanczos algorithm, our numerical investigation reveals that the spread complexity in these systems exhibits features reminiscent of emphchaotic systems.
arXiv Detail & Related papers (2023-12-19T20:41:14Z) - On the quantum time complexity of divide and conquer [42.7410400783548]
We study the time complexity of quantum divide and conquer algorithms for classical problems.
We apply these theorems to an array of problems involving strings, integers, and geometric objects.
arXiv Detail & Related papers (2023-11-28T01:06:03Z) - Krylov Complexity of Fermionic and Bosonic Gaussian States [9.194828630186072]
This paper focuses on emphKrylov complexity, a specialized form of quantum complexity.
It offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible bases.
arXiv Detail & Related papers (2023-09-19T07:32:04Z) - Krylov complexity in quantum field theory, and beyond [44.99833362998488]
We study Krylov complexity in various models of quantum field theory.
We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
arXiv Detail & Related papers (2022-12-29T19:00:00Z) - Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
Quantization smears the gravitational singularity avoiding its localization in the configuration space.
Results suggest that the generic singularity of general relativity can be avoided at quantum level.
arXiv Detail & Related papers (2022-04-24T13:32:45Z) - Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states.
Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
arXiv Detail & Related papers (2020-07-23T19:05:56Z)
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.