Genuine Quantum Chaos and Physical Distance Between Quantum States
arXiv:2007.06244 · doi:10.1103/PhysRevE.103.042209
Abstract
We show that there is genuine quantum chaos despite that quantum dynamics is linear. This is revealed by introducing a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for example, the Fubini-Study distance, the physical distance between two mutually orthogonal quantum states can be very small. As a result, two quantum states, which are initially very close by physical distance, can diverge from each other during the ensuing quantum dynamical evolution. We are able to use physical distance to define quantum Lyaponov exponent and quantum chaos measure. The latter leads to quantum analogue of the classical Poincaré section, which maps out the regions where quantum dynamics is regular and the regions where quantum dynamics is chaotic. Three different systems, kicked rotor, three-site Bose-Hubbard model, and spin-1/2 XXZ model, are used to illustrate our results.
arXiv comment13 pages, 12 figures
References in corpus (19)
- Environment-independent decoherence rate in classically chaotic systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Trace-distance measure of coherence
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Quantum chaos: an introduction via chains of interacting spins-1/2
- Lyapunov exponent in quantum mechanics. A phase-space approach
- Monge Metric on the Sphere and Geometry of Quantum States
- Monge Distance between Quantum States
- An efficient linear programming method for Optimal Transportation
- 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
- Measuring the distance between quantum many-body wave functions
- Quantum Chaos on Complexity Geometry
- Quantum-classical correspondence in integrable systems
- Quantum phase space with a basis of Wannier functions
- Distances between quantum states in the tomographic-probability representation
- Wannier basis method for KAM effect in quantum mechanics
Cited by in corpus (7)
- Quantum Monge-Kantorovich problem and transport distance between density matrices
- Chaos in the three-site Bose-Hubbard model -- classical vs quantum
- Microscope for Quantum Dynamics with Planck Cell Resolution
- Statistical and dynamical aspects of quantum chaos in a kicked Bose-Hubbard dimer
- Uncovering Quantum Many-body Scars with Quantum Machine Learning
- Self-Similarity Among Energy Eigenstates
- Nonlinear dynamics of superpostion of wavepackets