Exact large-scale fluctuations of the phase field in the sine-Gordon model

Abstract

We present the first exact theory and analytical formulas for the large-scale phase fluctuations in the sine-Gordon model, valid in all regimes of the field theory, for arbitrary temperatures and interaction strengths. Our result is based on the Ballistic Fluctuation Theory combined with Generalized Hydrodynamics, and can be seen as an exact ``dressing" of the phenomenological soliton-gas picture first introduced by Sachdev and Young [S. Sachdev and A. P. Young, PRL 78, 2220 (1997)], to the modes of Generalised Hydrodynamics. The resulting physics of phase fluctuations in the sine-Gordon model is qualitatively different, as the stable quasi-particles of integrability give coherent ballistic propagation instead of diffusive spreading. We provide extensive numerical checks of our analytical predictions within the classical regime of the field theory by using Monte Carlo methods. We discuss how our results are of ready applicability to experiments on tunnel-coupled quasicondensates.

8+14 pages; 4+2 Figures

References in corpus (27)

• The density-matrix renormalization group in the age of matrix product states
• Matter-wave interferometry in a double well on an atom chip
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Finite-temperature transport in one-dimensional quantum lattice models
• Lecture notes on Generalised Hydrodynamics
• Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms
• Generalized TBA and generalized Gibbs
• Diffusive hydrodynamics from integrability breaking
• Correlation functions and transport coefficients in generalised hydrodynamics
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Universal relaxational dynamics of gapped one dimensional models in the quantum sine-Gordon universality class
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• The quantum sine-Gordon model with quantum circuits
• Multimode dynamics and emergence of a characteristic length-scale in a one-dimensional quantum system
• Full counting statistics in the spin-1/2 Heisenberg XXZ chain
• Finite-Temperature Form Factors: a Review
• Experimental Observation of Curved Light-Cones in a Quantum Field Simulator
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Preparing and Analyzing Solitons in the sine-Gordon Model with Quantum Gas Microscopes
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
• Relaxation in an Extended Bosonic Josephson Junction
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• Finite temperature dynamics in gapped 1D models in the sine-Gordon family
• Simulating a quantum commensurate-incommensurate phase transition using two Raman coupled one dimensional condensates

Cited by in corpus (9)

• Generalized hydrodynamics: a perspective
• The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
• Anomalous current fluctuations from Euler hydrodynamics
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Dynamics of quantum discommensurations in the Frenkel-Kontorova chain
• Sine-Gordon dynamics in spin transport
• Quantum fluctuating theory for one-dimensional shock waves
• Anomalous charge transport in the sine-Gordon model