Full counting statistics after quantum quenches as hydrodynamic fluctuations
arXiv:2411.14406 · doi:10.1103/gds2-l18d
Abstract
The statistics of fluctuations on large regions of space encodes universal properties of many-body systems. At equilibrium, it is described by thermodynamics. However, away from equilibrium such as after quantum quenches, the fundamental principles are more nebulous. In particular, although exact results have been conjectured in integrable models, a correct understanding of the physics is largely missing. In this letter, we explain these principles, taking the example of the number of particles lying on a large interval in one-dimensional interacting systems. These are based on simple hydrodynamic arguments from the theory of ballistically transported fluctuations, and in particular the Euler-scale transport of long-range correlations. Using these principles, we obtain the full counting statistics in terms of thermodynamic and hydrodynamic quantities, whose validity depends on the structure of hydrodynamic modes and on the fluctuations in the initial state. In fermionic-statistics interacting integrable models with a continuum of hydrodynamic modes, such as the Lieb-Liniger model for cold atomic gases, the formula reproduces previous conjectures, but is in fact not exact: it gives the correct cumulants up to, including, order 5, while long-range correlations modify higher cumulants. In integrable and non-integrable models with two or less hydrodynamic modes, the formula is expected to give all cumulants.
15+4 pages, 3 figures
References in corpus (49)
- Nonequilibrium dynamics of closed interacting quantum systems
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Quantum Quench in the Transverse Field Ising Chain
- Generalized Gibbs ensemble in integrable lattice models
- Macroscopic fluctuation theory
- Experimental Observation of a Generalized Gibbs Ensemble
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Time evolution of local observables after quenching to an integrable model
- Entanglement and thermodynamics after a quantum quench in integrable systems
- Macroscopic fluctuation theory for stationary non equilibrium states
- Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
- Solution for an interaction quench in the Lieb-Liniger Bose gas
- The Quench Action
- Conformal field theory out of equilibrium: a review
- What is an integrable quench?
- Lecture notes on Generalised Hydrodynamics
- Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
- Analytic results for a quantum quench from free to hard-core one dimensional bosons
- Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas
- Hydrodynamic long-time tails after a quantum quench
- From Interacting Particles to Equilibrium Statistical Ensembles
- Quench action and Renyi entropies in integrable systems
- Exact large-scale correlations in integrable systems out of equilibrium
- Entanglement evolution and generalised hydrodynamics: interacting integrable systems
- String-charge duality in integrable lattice models
- Fluctuations in ballistic transport from Euler hydrodynamics
- Transport fluctuations in integrable models out of equilibrium
- Mean values of local operators in highly excited Bethe states
- Exact anomalous current fluctuations in a deterministic interacting model
- Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
- Relaxation dynamics of local observables in integrable systems
- Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
- Ballistic macroscopic fluctuation theory
- Absence of Normal Fluctuations in an Integrable Magnet
- Dynamics of charge fluctuations from asymmetric initial states
- Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
- Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
- Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
- Quench action and large deviations: work statistics in the one-dimensional Bose gas
- Universal anomalous fluctuations in charged single-file systems
- Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
- Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
- Non-Gaussian diffusive fluctuations in Dirac fluids
- Full Counting Statistics of Charge in Quenched Quantum Gases
- Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
- Ballistic Modes as a Source of Anomalous Charge Noise
- Almost everywhere ergodicity in quantum lattice models