How complex is the quantum motion?
arXiv:0808.3243 · doi:10.1103/PhysRevE.79.025201
Abstract
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. Here we introduce a notion of complexity for a quantum system and relate it to its stability and reversibility properties.
4 pages, 3 figures, new figure added
References in corpus (10)
- Dynamics of Loschmidt echoes and fidelity decay
- Sensitivity of Quantum Motion for Classically Chaotic Systems
- Chaos and Complexity of quantum motion
- Chaos and Lyapunov exponents in classical and quantal distribution dynamics
- On the stability of classical chaotic motion under system's perturbations
- Complexity of Quantum States and Reversibility of Quantum Motion
- Wigner--Dyson statistics for a class of integrable models
- Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions
- Phase-space characterization of complexity in quantum many-body dynamics
- Quantum dephasing and decay of classical correlation functions in chaotic systems
Cited by in corpus (28)
- Emergent irreversibility and entanglement spectrum statistics
- Information geometric methods for complexity
- Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
- Isospectral twirling and quantum chaos
- Random Matrix Theory of the Isospectral twirling
- The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models
- Quantifying The Complexity Of Geodesic Paths On Curved Statistical Manifolds Through Information Geometric Entropies and Jacobi Fields
- Experimental observation of time singularity in classical-to-quantum chaos transition
- Quantum chaos and operator fidelity metric
- Complexity of quantum motion and quantum-classical correspondence: A phase-space approach
- Statistical and dynamical properties of the quantum triangle map
- Information Geometric Modeling of Scattering Induced Quantum Entanglement
- Information Geometry of Quantum Entangled Gaussian Wave-Packets
- Phase-space characterization of complexity in quantum many-body dynamics
- Wigner separability entropy and complexity of quantum dynamics
- Complexity and non-separability of classical Liouvillian dynamics
- Relation between irreversibility and entanglement in classically chaotic quantum kicked rotors
- On The Complexity Of Statistical Models Admitting Correlations
- Complexity and instability of quantum motion near a quantum phase transition
- Time-reversal Characteristics of Quantum Normal Diffusion
- The transition to chaos of coupled oscillators: An operator fidelity susceptibility study
- Quantum Dynamics Against a Noisy Background
- Entanglement dynamics and classical complexity
- Quantum mechanics in phase space: First order comparison between the Wigner and the Fermi function
- Measuring lifetime of correspondence with classical decay of correlation in quantum chaos
- Quantum Entropies and Decoherence for the Multiparticle Quantum Arnol'd Cat
- Softening the Complexity of Entropic Motion on Curved Statistical Manifolds
- Reexamination of an Information Geometric Construction of Entropic Indicators of Complexity