Quantum Instability
arXiv:2208.03371 · doi:10.1103/PhysRevA.107.062204
Abstract
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a unitary quantum description. Using the example of three-wave interactions, we describe how a time-independent, finite-dimensional quantum system, which is Hermitian with all real eigenvalues, can give rise to a linear instability corresponding to that in the classical system. We show that the instability is realized in the quantum theory as a cascade of the wave function in the space of occupation number states, and an unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system. The conditions for quantum instability are described.
References in corpus (22)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- A bound on chaos
- Complex Extension of Quantum Mechanics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Remarks on the notion of quantum integrability
- Does scrambling equal chaos?
- Scrambling and entanglement spreading in long-range spin chains
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Krylov complexity in saddle-dominated scrambling
- Reversible quantum information spreading in many-body systems near criticality
- On applications of quantum computing to plasma simulations
- Mechanical squeezing via unstable dynamics in a microcavity
- Semiclassical roots of universality in many-body quantum chaos
- PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability
- Kelvin-Helmholtz instability is the result of parity-time symmetry breaking
- Simulating nonnative cubic interactions on noisy quantum machines
- Quadratic Quantum Hamiltonians: General Canonical Transformation to a Normal Form
- Plasma physics in strong-field regimes: theories and simulations
- Three-wave scattering in magnetized plasmas: from cold fluid to quantized Lagrangian
- Spontaneous and explicit parity-time-symmetry breaking in drift wave instabilities
- False signals of chaos from quantum probes