Non-equilibrium time evolution in the sine-Gordon model revisited

Abstract

We study the non-equilibrium dynamics of the quantum sine-Gordon model describing a pair of Josephson-coupled one-dimensional bosonic quasi-condensates. Motivated by experimentally accessible quench procedures where the zero mode of the quasi-condensates is weakly coupled to finite momentum modes, we develop a novel Hamiltonian truncation scheme relying on a mini-superspace treatment of the zero mode (MSTHA). We apply this method to simulate the time evolution after both weak and strong quantum quenches, injecting a low or high energy density into the system, and demonstrate that MSTHA accurately captures the dynamics from the hard core boson limit to the experimentally relevant weakly interacting regime for sufficiently mild quenches. In the case of high energy densities, MSTHA breaks down for weak interaction but still extends the range of validity of previous Hamiltonian truncation schemes. We also compare these results to the semiclassical truncated Wigner approximation (TWA) and establish that the dynamics can be well approximated by the semiclassical description in the weakly interacting regime realised in the experiments. In addition, we clarify the importance of the phononic modes depending on the sine-Gordon interaction strength.

14 pages, 3 figures. v2: accepted version

References in corpus (11)

• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms
• Quantum quench in the sine-Gordon model
• Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
• Universal Rephasing Dynamics after a Quantum Quench via Sudden Coupling of Two Initially Independent Condensates
• Experimental Observation of Curved Light-Cones in a Quantum Field Simulator
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Quantum quench in the attractive regime of the sine-Gordon model
• Chirally Factorised Truncated Conformal Space Approach
• Thermodynamics and fractal Drude weights in the sine-Gordon model

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