Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall

TL;DR

This paper develops an effective field theory for fluctuating domain walls in open systems, revealing a diffusive Nambu-Goldstone mode and analyzing stability and nonlinear effects in various regimes.

Contribution

It introduces a symmetry-based effective Lagrangian for open systems with broken translational symmetry, highlighting the diffusive NG mode and novel instability terms.

Findings

Diffusive NG mode identified in dissipative Josephson junctions

General effective theory constructed using Schwinger-Keldysh formalism

Potential instability and nonlinear effects in thick and thin wall regimes

Abstract

We investigate macroscopic behaviors of fluctuating domain walls in nonequilibrium open systems with the help of the effective field theory based on symmetry. Since the domain wall in open systems breaks the translational symmetry, there appears a gapless excitation identified as the Nambu-Goldstone (NG) mode, which shows the non-propagating diffusive behavior in contrast to those in closed systems. After demonstrating the presence of the diffusive NG mode in the $(2+1)$-dimensional dissipative Josephson junction, we provide a symmetry-based general analysis for open systems breaking the one-dimensional translational symmetry. A general effective Lagrangian is constructed based on the Schwinger-Keldysh formalism, which supports the presence of the gapless diffusion mode in the fluctuation spectrum in the thin wall regime. Besides, we also identify a term peculiar to the open system, which possibly leads to the instability in the thick-wall regime or the nonlinear Kardar-Parisi-Zhang coupling in the thin-wall regime although it is absent in the Josephson junction.