Towards the Web of Quantum Chaos Diagnostics
arXiv:1909.01894 · doi:10.1140/epjc/s10052-022-10035-3
Abstract
We study the connections between three quantities that can be used as diagnostics for quantum chaos, i.e., the out-of-time-order correlator (OTOC), Loschmidt echo (LE), and complexity. We generalize the connection between OTOC and LE for infinite dimensions and extend it for higher-order OTOCs and multi-fold LEs. Novel applications of this intrinsic relation are proposed. We also propose a relationship between a specific circuit complexity and LE by using the inverted oscillator model. These relationships signal a deeper connection between these three probes of quantum chaos.
arXiv comment22 pages, 14 figures, 1 appendix. In this version the presentation has been improved, a few arguments have been strengthened, and three figures have been added
References in corpus (61)
- A bound on chaos
- Comments on the Sachdev-Ye-Kitaev model
- Complexity and Shock Wave Geometries
- Chaos in quantum channels
- Localized shocks
- Dynamics of Loschmidt echoes and fidelity decay
- Quantum Computation as Geometry
- The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
- Decoherence, Chaos, and the Second Law
- Multiple Shocks
- Chaos and complexity by design
- Circuit complexity in quantum field theory
- Towards Complexity for Quantum Field Theory States
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Lieb-Robinson and the butterfly effect
- The Second Law of Quantum Complexity
- Out-of-Time-Order Correlation for Many-Body Localization
- Chaos, Complexity, and Random Matrices
- Circuit Complexity in Fermionic Field Theory
- Circuit complexity for free fermions
- Loschmidt Echo
- A quantum hydrodynamical description for scrambling and many-body chaos
- On The Evolution Of Operator Complexity Beyond Scrambling
- Black hole scrambling from hydrodynamics
- Krylov complexity in conformal field theory
- Circuit complexity in interacting QFTs and RG flows
- Many-body chaos and energy dynamics in holography
- Quantum Complexity and Negative Curvature
- Weak Quantum Chaos
- Information Scrambling and Loschmidt Echo
- The quasiprobability behind the out-of-time-ordered correlator
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Toda chain flow in Krylov space
- Complexity as a novel probe of quantum quenches: universal scalings and purifications
- Time Evolution of Complexity: A Critique of Three Methods
- Quantum chaos: an introduction via chains of interacting spins-1/2
- Black holes, complexity and quantum chaos
- Chaos and Complexity in Quantum Mechanics
- Quantum Complexity of Time Evolution with Chaotic Hamiltonians
- Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
- Renormalized Circuit Complexity
- The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
- Cosmological Complexity
- Scrambling and Complexity in Phase Space
- The Black Hole S-Matrix from Quantum Mechanics
- Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
- Quantum work statistics, Loschmidt echo and information scrambling
- Post-Quench Evolution of Complexity and Entanglement in a Topological System
- Quasinormal Modes and Hawking-Unruh effect in Quantum Hall Systems: Lessons from Black Hole Phenomena
- The Rise of Cosmological Complexity: Saturation of Growth and Chaos
- Decoherence from a Chaotic Environment: An Upside Down "Oscillator" as a Model
- Thermal Emission from Semi-classical Dynamical Systems
- Conditional Mutual Information of Bipartite Unitaries and Scrambling
- Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?
- Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
- Time evolution of the complexity in chaotic systems: concrete examples
- Recovery of Damaged Information and the Out-of-Time-Ordered Correlators
- Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
- Randomness and Chaos in Qubit Models
- Spectral Form Factor as an OTOC Averaged over the Heisenberg Group
- Holographic fluctuations and the principle of minimal complexity