Microscope for Quantum Dynamics with Planck Cell Resolution
arXiv:2101.09971 · doi:10.1103/PhysRevResearch.3.033239
Abstract
We introduce the out-of-time-correlation(OTOC) with the Planck cell resolution. The dependence of this OTOC on the initial state makes it function like a microscope, allowing us to investigate the fine structure of quantum dynamics beyond the thermal state. We find an explicit relation of this OTOC to the spreading of the wave function in the Hilbert space, unifying two branches of the study of quantum chaos: state evolution and operator dynamics. By analyzing it in the vicinity of the classical limit, we clarify the dependence of the OTOC's exponential growth on the classical Lyapunov exponent.
arXiv comment9 pages, 6 figures
References in corpus (32)
- A bound on chaos
- Comments on the Sachdev-Ye-Kitaev model
- Operator Spreading in Random Unitary Circuits
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Out-of-time-order correlators in quantum mechanics
- Scrambling and thermalization in a diffusive quantum many-body system
- Does scrambling equal chaos?
- Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
- Scrambling and entanglement spreading in long-range spin chains
- Power-law out of time order correlation functions in the SYK model
- Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
- Commutability between Semiclassical Limit and Adiabatic Limit
- Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
- Early-Time Exponential Instabilities in Non-Chaotic Quantum Systems
- Out-of-time-order Operators and the Butterfly Effect
- Mean-Field- and Classical Limit of Many-Body Schrödinger Dynamics for Bosons
- Operator Spreading in Quantum Maps
- Operator scrambling and quantum chaos
- Breakdown of correspondence in chaotic systems: Ehrenfest versus localization times
- Entropy for Quantum Pure States and Its Dynamical Relaxation
- Ergodicity and Mixing in Quantum Dynamics
- Ehrenfest breakdown of the mean-field dynamics of Bose gases
- Generalized Wigner-von Neumann entropy and its typicality
- Genuine Quantum Chaos and Physical Distance Between Quantum States
- Quantum phase space with a basis of Wannier functions
- Quantum-classical correspondence in integrable systems
- Wannier basis method for KAM effect in quantum mechanics
- Quantum ergodicity and mixing and their classical limits with quantum kicked rotor
Cited by in corpus (6)
- Analyticity constraints bound the decay of the spectral form factor
- Quantum Dynamical Tunneling Breaks Classical Conserved Quantities
- Uncovering Quantum Many-body Scars with Quantum Machine Learning
- Escaping Local Minima with Quantum Coherent Cooling
- Self-Similarity Among Energy Eigenstates
- Logarithmic quantum time crystal