The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

relevance for quantum field theory discussed providing validity criteria. To appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.69.045003

We study the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 1+1 spacetime dimensions. At thermal equilibrium we exploit the equivalence between the classical canonical averages and transfer matrix quantum traces of the anharmonic oscillator to obtain exact results for the temperature dependence of several observables, which provide a set of criteria for thermalization. We find that the Hartree approximation is remarkably accurate in equilibrium. The non-equilibrium dynamics is studied by numerically solving the equations of motion in light-cone coordinates for a broad range of initial conditions and energy densities.The time evolution is described by several stages with a cascade of energy towards the ultraviolet. After a transient stage, the spatio-temporal gradient terms become larger than the nonlinear term and a stage of universal cascade emerges.This cascade starts at a time scale t_0 independent of the initial conditions (except for very low energy density). Here the power spectra feature universal scaling behavior and the front of the cascade k(t) grows as a power law k(t) sim t^alpha with alpha lesssim 0.25. The wake behind the cascade is described as a state of Local Thermodynamic Equilibrium (LTE) with all correlations being determined by the equilibrium functional form with an effective time dependent temperatureTeff(t) which slowly decreases as sim t^{-alpha}.Two well separated time scales emerge while Teff(t) varies slowly, the wavectors in the wake with k < k(t) attain LTE on much shorter time scales.This universal scaling stage ends when the front of the cascade reaches the cutoff at a time t_1 sim a^{-1/alpha}. Virialization starts to set much earlier than LTE. We find that strict thermalization is achieved only for an infinite time scale.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-26648

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.