Field theory for the dynamics of the open $O(N)$ model

Abstract

A field theory approach for the nonequilibrium relaxation dynamics in open systems at late times is developed. In the absence of conservation laws, all excitations are subject to dissipation. Nevertheless, ordered stationary states satisfy Goldstone's theorem. It implies a vanishing damping rate at small momenta, which in turn allows for competition between environment-induced dissipation and thermalization due to collisions. We derive the dynamic theory in the symmetry-broken phase of an $O(N)$-symmetric field theory based on an expansion of the two-particle irreducible (2PI) effective action to next-to-leading order in $1/N$ and highlight the analogies and differences to the corresponding theory for closed systems. A central result of this approach is the systematic derivation of an \emph{open-system Boltzmann equation}, which takes a very different form from its closed-system counterpart due to the absence of well-defined quasiparticles. As a consequence of the general structure of its derivation, it applies to open, gapless field theories that satisfy certain testable conditions, which we identify here. Specifically for the $O(N)$ model, we use scaling analysis and numerical simulations to show that interactions are screened efficiently at small momenta and, therefore, the late-time evolution is effectively collisionless. This implies that fluctuations induced by a quench dissipate into the environment before they thermalize. Goldstone's theorem also constrains the dynamics far from equilibrium, which is used to show that the order parameter equilibrates more quickly for quenches preserving the $O(N)$ symmetry than those breaking it explicitly.

arXiv comment24 pages, 15 figures, v2: published version

References in corpus (46)

• Nonequilibrium dynamical mean-field theory and its applications
• Ultrafast switching to a stable hidden topologically protected quantum state in an electronic crystal
• Non-reciprocal phase transitions
• Keldysh Field Theory for Driven Open Quantum Systems
• Thermodynamics of the BCS-BEC crossover
• Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium
• Light-Induced Charge Density Wave in LaTe${}_3$
• Turbulent Thermalization
• Emergence of a Turbulent Cascade in a Quantum Gas
• Observation of universal dynamics in a spinor Bose gas far from equilibrium
• Coherent dynamics of macroscopic electronic order through a symmetry-breaking transition
• Observation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium
• Disentangling amplitude and phase dynamics of a charge density wave in a photo-induced phase transition
• Visibility of the Amplitude (Higgs) Mode in Condensed Matter
• Landau Theory of Stripe Phases in Cuprates and Nickelates
• Parametric resonance in quantum field theory
• Classical aspects of quantum fields far from equilibrium
• Phase-ordering of charge density waves traced by ultrafast low-energy electron diffraction
• Cooperative photoinduced metastable phase control in strained manganite films
• Universal Prethermal Dynamics of Bose Gases Quenched to Unitarity
• Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points
• Phase Fluctuations and the Absence of Topological Defects in Photo-excited Charge Ordered Nickelate
• Ultrafast transient response and electron-phonon coupling in the iron-pnictide superconductor Ba(Fe(1-x)Co(x))2As2
• Watching the birth of a charge density wave order: diffraction study on nanometer-and picosecond-scales
• Anomalous fluctuations in phases with a broken continuous symmetry
• Strong versus weak wave-turbulence in relativistic field theory
• Exact Conservation Laws of the Gradient Expanded Kadanoff-Baym Equations
• The G1--G2 Scheme: Dramatic Acceleration of Nonequilibrium Green Functions Simulations Within the Hartree--Fock-GKBA
• Nonequilibrium Charge-Density-Wave Order Beyond the Thermal Limit
• Range of validity of transport equations
• Real-time manifestation of strongly coupled spin and charge order parameters in stripe-ordered nickelates via time-resolved resonant x-ray diffraction
• Transient trapping into metastable states in systems with competing orders
• Low rank compression in the numerical solution of the nonequilibrium Dyson equation
• Self-similar dynamics of order parameter fluctuations in pump-probe experiments
• Nonequilibrium Quantum Fields: From Cold Atoms to Cosmology
• Quantum Boltzmann equation for strongly correlated systems: comparison to dynamical mean field theory
• Amplitude dynamics of charge density wave in LaTe${}_3$: theoretical description of pump-probe experiments
• Transient and stationary behavior of the Olami-Feder-Christensen earthquake model
• Signatures of ultrafast reversal of excitonic order in Ta${}_2$NiSe${}_5$
• A quantum Boltzmann equation for strongly correlated electrons
• Ultrafast nematic-orbital excitation in FeSe
• The Universal Time-Dependent Ginzburg-Landau theory
• Fluctuation control of non-thermal orbital order
• Time-Dependent Charge-Order and Spin-Order Recovery in Striped Systems
• Decoupling of static and dynamic criticality in a driven Mott insulator
• Coherent topological defect dynamics and collective modes in superconductors and electronic crystals

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