TY - JOUR

T1 - Effective field theory of time-translational symmetry breaking in nonequilibrium open system

AU - Hongo, Masaru

AU - Kim, Suro

AU - Noumi, Toshifumi

AU - Ota, Atsuhisa

N1 - 38 pages, 3 figures

PY - 2019/2/20

Y1 - 2019/2/20

N2 - We develop the effective field theoretical (EFT) approach to time-translational symmetry breaking of nonequilibrium open systems based on the Schwinger-Keldysh formalism. In the Schwinger-Keldysh formalism, all the symmetries of the microscopic Lagrangian are doubled essentially because the dynamical fields are doubled to describe the time-evolution along the closed-time-path. The effective Lagrangian for open systems are then obtained by coarse-graining the microscopic Schwinger-Keldysh Lagrangian. As a consequence of coarse-graining procedure, there appear the noise and dissipation effects, which explicitly break the doubled time-translational symmetries into a diagonal one. We therefore need to incorporate this symmetry structure to construct the EFT for Nambu-Goldstone bosons in symmetry broken phases of open systems. Based on this observation together with the consistency of the Schwinger-Keldysh action, we construct and study the general EFT for time-translational symmetry breaking in particular, having in mind applications to synchronization, time crystal, and cosmic inflation.

AB - We develop the effective field theoretical (EFT) approach to time-translational symmetry breaking of nonequilibrium open systems based on the Schwinger-Keldysh formalism. In the Schwinger-Keldysh formalism, all the symmetries of the microscopic Lagrangian are doubled essentially because the dynamical fields are doubled to describe the time-evolution along the closed-time-path. The effective Lagrangian for open systems are then obtained by coarse-graining the microscopic Schwinger-Keldysh Lagrangian. As a consequence of coarse-graining procedure, there appear the noise and dissipation effects, which explicitly break the doubled time-translational symmetries into a diagonal one. We therefore need to incorporate this symmetry structure to construct the EFT for Nambu-Goldstone bosons in symmetry broken phases of open systems. Based on this observation together with the consistency of the Schwinger-Keldysh action, we construct and study the general EFT for time-translational symmetry breaking in particular, having in mind applications to synchronization, time crystal, and cosmic inflation.

KW - Effective Field Theories

KW - Quantum Dissipative Systems

KW - Space-Time Symmetries

KW - Spontaneous Symmetry Breaking

U2 - 10.1007/JHEP02(2019)131

DO - 10.1007/JHEP02(2019)131

M3 - Article

SN - 1029-8479

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

ER -