Kinetic theory of nonthermal fixed points in a Bose gas

Abstract

We outline a kinetic theory of non-thermal fixed points for the example of a dilute Bose gas, partially reviewing results obtained earlier, thereby extending, complementing, generalizing and straightening them out. We study universal dynamics after a cooling quench, focusing on situations where the time evolution represents a pure rescaling of spatial correlations, with time defining the scale parameter. The non-equilibrium initial condition set by the quench induces a redistribution of particles in momentum space. Depending on conservation laws, this can take the form of a wave-turbulent flux or of a more general self-similar evolution, signaling the critically slowed approach to a non-thermal fixed point. We identify such fixed points using a non-perturbative kinetic theory of collective scattering between highly occupied long-wavelength modes. In contrast, a wave-turbulent flux, possible in the perturbative Boltzmann regime, builds up in a critically accelerated self-similar manner. A key result is the simple analytical universal scaling form of the non-perturbative many-body scattering matrix, for which we lay out the concrete conditions under which it applies. We derive the scaling exponents for the time evolution as well as for the power-law tail of the momentum distribution function, for a general dynamical critical exponent z and an anomalous scaling dimension η. The approach of the non-thermal fixed point is, in particular, found to involve a rescaling of momenta in time t by t β , with β = 1/z, within our kinetic approach independent of η. We confirm our analytical predictions by numerically evaluating the kinetic scattering integral as well as the non-perturbative many-body coupling function. As a side result we obtain a possible finite-size interpretation of wave-turbulent scaling recently measured by Navon et al.

Highly occupied gauge theories in 2+1 dimensions: A self-similar attractor

“…Nonthermal fixed points have recently also been found experimentally in ultra-cold atom experiments [21,22]. A kinetic theory description of the underlying theory is often a natural way to explain the existence and properties of such fixed points [1,14,[23][24][25][26][27]. These NTFPs appear because the interaction rate of the initial conditions is faster than that of the final equilibrium state.…”

Violation of single-length-scaling dynamics via spin vortices in an isolated spin-1 Bose gas

“…Dissipative coarsening forms a special case of more general spatio-temporal universal dynamical phenomena far from equilibrium which can occur in both, open and isolated (quantum) many-body systems [4,[27][28][29]. Following a quench far out of equilibrium, a system can in general approach a non-thermal fixed point [10,[30][31][32][33][34][35]. Such fixed points have been discussed and experimentally observed with [35][36][37][38][39][40] and without [10,[30][31][32][33][41][42][43] reference to ordering patterns and kinetics as well as topological defects.…”

Spectral, statistical, and vertex functions in scalar quantum field theory far from equilibrium

“…As pointed out in Refs. [4,15,16], the values of these exponents coincide with those of the corresponding non-relativistic scalar model, since infrared momenta below m eff of the relativistic theory behave non-relativistically. Within errors, we also find α = dβ for d = 3 spatial dimensions such that p f (t, |p|) = t α−dβ q f S (|q|) is approximately conserved, reflecting a transport of particles towards lower momenta for the β > 0 observed.…”

“…A calculation of the far-from-equilibrium scaling exponents and function has so far only been done using additional assumptions, such as a quasi-particle ansatz for an effective kinetic description at the non-thermal fixed point in Refs. [4,15,16], or based on classical-statistical field theory approximations in Ref. [4] in the weak-coupling limit.…”