Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation

Abstract

We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover the truncated Wigner approximation, where the evolution is still classical but the initial conditions are distributed according to the Wigner transform of the initial density matrix. Further corrections can be characterized as quantum scattering events, which appear in the form of a nonlinear response of the observable to an infinitesimal displacement of the field along its classical evolution. At the end of the paper we give a few numerical examples to test the formalism.

published version

References in corpus (3)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Evolution of the macroscopically entangled states in optical lattices

Cited by in corpus (52)

• Quantum fluids of light
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Finite Temperature Models of Bose-Einstein Condensation
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Quantum turbulence and correlations in Bose-Einstein condensate collisions
• Quantum versus classical statistical dynamics of an ultracold Bose gas
• Decay of a superfluid currents in a moving system of strongly interacting bosons
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices
• The Quantum de Laval Nozzle: stability and quantum dynamics of sonic horizons in a toroidally trapped Bose gas containing a superflow
• A quantum Langevin model for non-equilibrium condensation
• Functional Wigner representation of BEC quantum dynamics
• Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
• Dynamical instabilities of Bose-Einstein condensates at the band-edge in one-dimensional optical lattices
• Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems
• Many-body physics in the classical-field description of a degenerate Bose gas
• Chaos in the three-site Bose-Hubbard model -- classical vs quantum
• Quench from Mott Insulator to Superfluid
• Ultracold gases far from equilibrium
• Importance of realistic phase space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions
• Bridging the gap between classical and quantum many-body information dynamics
• False vacuum decay in the 1+1 dimensional ${\phi }^4$ theory
• Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations
• Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice
• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
• Mass Renormalization in Lattice Simulations of False Vacuum Decay
• Eigenstate thermalization scaling in approaching the classical limit
• User-friendly TWA for dissipative spin dynamics
• Quantum fluctuations approach to the nonequilibrium $GW$ approximation
• Self-organized cavity bosons beyond the adiabatic elimination approximation
• Theory for dissipative time crystals in coupled parametric oscillators
• Vortex formation and dynamics in two-dimensional driven-dissipative condensates
• Decoherence Limits the Cost to Simulate an Anharmonic Oscillator
• Path-Integral Formulation of Truncated Wigner Approximation for Bosonic Markovian Open Quantum Systems
• Non-equilibrium time evolution in the sine-Gordon model revisited
• A convenient Keldysh contour for thermodynamically consistent perturbative and semiclassical expansions
• Hyper-entangling mesoscopic bound states
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model
• How to exploit driving and dissipation to stabilize and manipulate quantum many-body states
• Nonequilibrium Transport in a Superfluid Josephson Junction Chain: Is There Negative Differential Conductivity?
• Semiclassical dynamics of a dark soliton in a one-dimensional bosonic superfluid in an optical lattice
• Emergent equilibrium and quantum criticality in a two-photon dissipative oscillator
• Inversion of coherent backscattering with interacting Bose-Einstein condensates in two-dimensional disorder : a Truncated Wigner approach
• Chaos and anomalous transport in a semiclassical Bose-Hubbard chain
• Computing Quantum Mean Values in the Deep Chaotic Regime
• Dynamics of quantum vortices at finite temperature
• Perturbation theory under the truncated Wigner approximation reveals how system-environment entanglement formation drives quantum decoherence
• The Dynamics of the Hubbard Model through Stochastic Calculus and Girsanov Transformation
• Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation
• Path-Integral Formulation of Bosonic Markovian Open Quantum Dynamics with Monte Carlo stochastic trajectories using the Glauber-Sudarshan P, Wigner, and Husimi Q Functions and Hybrids
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics