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Journal of Experimental and Theoretical Physics Letters

Local Quench Within the Keldysh Technique: the Role of Interaction

D. V. Lopatin, A. A. Radovskaya, A. G. Semenov

Published Jul 1, 2026• 0 citations
Publisher

Abstract

This work introduces a novel approach that makes it possible to take interaction into account in the problem of the evolution of a quantum field after an instantaneous local perturbation (quench). Using scalar theory $$g{{\varphi }^{4}}$$ as an example, we demonstrate a method for describing the influence of interaction on the field dynamics after a quench within the semiclassical approximation in the Keldysh technique. The proposed approach is nonperturbative in the coupling constant, valid for arbitrary initial conditions, and well suited for numerical computation. As an illustration, we show how the interaction drives thermalization toward a new stationary state of the system and leads to a loss of coherence, which manifests itself in the destruction of the interference pattern that is characteristic of the noninteracting case.

DOI
10.1134/s002136402660062x

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This work introduces a novel approach that makes it possible to take interaction into account in the problem of the evolution of a quantum field after an instantaneous local perturbation (quench). Using scalar theory gφ4g{{\varphi }^{4}}gφ4 as an example, we demonstrate a method for describing the influence of interaction on the field dynamics after a quench within the semiclassical approximation in the Keldysh technique. The proposed approach is nonperturbative in the coupling constant, valid for arbitrary initial conditions, and well suited for numerical computation. As an illustration, we show how the interaction drives thermalization toward a new stationary state of the system and leads to a loss of coherence, which manifests itself in the destruction of the interference pattern that is characteristic of the noninteracting case.
The problem of quantum scalar field evolution after an instantaneous local perturbation (quench) is considered. A new approach to descriptions of a quench from an arbitrary initial state is developed in the framework of the Keldysh technique. This approach does not require the procedure of the analytical continuation, which can be ambiguous in some cases. The evolution of the energy density after local quench is calculated for a simple case, and its dependence on the interaction region width and the initial conditions is analyzed.
The problem of quantum scalar field evolution after an instantaneous local perturbation (quench) is considered. A new approach to descriptions of a quench from an arbitrary initial state is developed in the framework of the Keldysh technique. This approach does not require the procedure of the analytical continuation, which can be ambiguous in some cases. The evolution of the energy density after local quench is calculated for a simple case, and its dependence on the interaction region width and the initial conditions is analyzed.
Abstract We modify the nonequilibrium Keldysh diagram technique to systematically account for non-Gaussian initial correlations. We represent information about the initial state of the system as an additional term in the Keldysh action, which is expressed in terms of the cumulants of the initial Wigner functional. This additional term leads to the appearance of additional vertices in the diagram technique. We study the role of non-Gaussian initial correlations in the further evolution of correlation functions. In particular, we show that the presence of non-Gaussian correlations of odd order leads to the generation of a mean field. We obtain Dyson equations with partially resummed self-energies and prove that diagrams with a finite number of loops contain a finite number of non-Gaussian cumulants of the initial Wigner functional. We apply the modified diagram technique to the description of the evolution of a scalar field after a quench and show that in the limit of short interaction times this technique leads to exact results.
Determining the role of initial conditions in the late time evolution is a key issue for the theory of nonequilibrium dynamics of isolated quantum systems. Here we extend the theory of quantum quenches to the case in which before the quench the system is in an excited state. In particular, we show perturbatively in the size of the quench (and for arbitrarily strong interactions among the quasiparticles) that persistent oscillations of one-point functions require the presence of a one-quasiparticle contribution to the nonequilibrium state, as originally shown in [J. Phys. A 47 (2014) 402001] for the quenches from the ground state. Also in the present case, we argue that the results generically have nonperturbative implications. Oscillations staying undamped within the accessible time interval, far beyond the perturbative time scale, are nowadays observed in numerical simulations.
In the majority of analytical verifications of the conjecture that the Generalized Gibbs Ensemble (GGE) describes the large time asymptotics of local observables in quantum quench problems, both post- and pre-quench Hamiltonians are essentially noninteracting. We test this conjecture studying field correlations in the more general case of an arbitrary pre-quench Hamiltonian, while keeping the post-quench one noninteracting. We first show that, in the previously studied special case of a noninteracting pre-quench Hamiltonian, the validity of the conjecture is a consequence of Wick's theorem. We then show that this conjecture is more generally valid for an arbitrary interacting pre-quench Hamiltonian, but this time as a consequence of the cluster decomposition property of the initial state, which is a fundamental principle for generic physical states. For arbitrary initial states that do not satisfy the cluster decomposition property, the above conjecture is not generally true. As a byproduct of our investigation we obtain an analytical derivation of earlier numerical results for the large time evolution of correlations after a quantum quench of the interaction in the Lieb–Liniger model from a nonzero value to zero.
In this work, we theoretically investigate the non-equilibrium evolution of the correlation functions of a quantum scalar field following a mass quantum quench in a finite-size system. The self-consistent equation for the Keldysh (statistical) correlation function is solved numerically in the one-loop approximation. A specific spatio-temporal effect is observed: at a point in time approximately equal to half the system size, the effective mass experiences a strong disturbance. It is shown that this effect is driven by the interference of counter-propagating wave fronts of fluctuations that propagate within the light cone and is induced by periodic boundary conditions.