Scale invariant distribution functions in quantum systems with few degrees of freedom
arXiv:1709.01942 · doi:10.21468/SciPostPhys.5.3.023
Abstract
Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.
8+10 pages. Scipost Submission
References in corpus (23)
- Matter-wave interferometry in a double well on an atom chip
- Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
- Quantum Quench in the Transverse Field Ising Chain
- Generalized Gibbs ensemble in integrable lattice models
- The Luttinger model following a sudden interaction switch-on
- Dephasing and the steady state in quantum many-particle systems
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Generalized Thermalization in an Integrable Lattice System
- Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
- Coherent Oscillations in an Exciton-Polariton Josephson Junction
- Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
- Anomalous thermalization in ergodic systems
- Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
- Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
- The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise
- Quantum quench dynamics of the sine-Gordon model in some solvable limits
- Relaxation to a Phase-locked Equilibrium State in a One-dimensional Bosonic Josephson Junction
- Using a quantum work meter to test non-equilibrium fluctuation theorems
- Universal Rephasing Dynamics after a Quantum Quench via Sudden Coupling of Two Initially Independent Condensates
- Semiclassical analysis of Bose-Hubbard dynamics
- Many-particle dephasing after a quench
- Many-particle interference in a two-component bosonic Josephson junction: an all-optical simulation
- Entanglement and entropy production in coupled single-mode Bose-Einstein condensates