Low-energy effective theory of nonthermal fixed points in a multicomponent Bose gas

Abstract

Non-thermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of non-thermal fixed points in a bosonic quantum many-body system by integrating out long-wavelength density fluctuations. The system consists of N distinguishable spatially uniform Bose gases with U(N)symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relativephase excitations. It is similar in character to the non-linear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal non-local coupling function depending, in the large-N limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the non-thermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields N. Numerical results for N = 3 allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.

Understanding the dynamics of field theories far from equilibrium

“…As for the lattice results shown in the left panel, the lowest momenta describe a rather flat distribution, while higher momenta follow a p −κ power law with κ = 4 for the kinetic theory in d = 3 dimensions (see also [33]) and κ 4 − 4.5 for the lattice results. We note that the observed scaling can also be described with a recently developed effective low-energy theory [34].…”

“…Its universal quantities can be reproduced by the Large-N kinetic theory [10,30]. Despite the progress in recent years, some aspects of the IR region are not fully understood yet, as, e.g., when quasiparticles or defects dominate for different N [9,10,34,36,45].…”

Gauge-invariant condensation in the nonequilibrium quark-gluon plasma

“…Accordingly, this corresponds to scaling towards low momentum modes in Fourier space. Asymptotically, the scaling function obeys [42] lim…”

Far-from-equilibrium universality in the two-dimensional Heisenberg model

“…Conclusions.-Our results on self-similar relaxation in the Heisenberg model extend the paradigm of scaling close to non-thermal fixed points to spin models [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. In this regard, we plan to develop in the near future a non-equilibrium renormalization group theory to inspect the nature of the universality class unveiled in this work.…”

“…However, self-similar scaling has recently been shown to occur also in isolated systems where the system acts as its own bath. Prominent examples of dynamical scaling in isolated quantum many-body systems include pre-thermal critical states [5,[13][14][15][16][17][18][19][20][21][22][23] and nonthermal fixed points in scalar and gauge theories [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Research into these phenomena is further fueled by a surge of experimental evidence for universal dynamics in cold atoms [41][42][43][44][45][46][47], and dynamical phase transitions in trapped ions [48] and cavity QED [49].…”