The kinetic-equation approach to particle production in strong, time-dependent external fields is revisited and three limiting cases are discussed for different field patterns: the Sauter pulse, a harmonic pulse with a Gaussian envelope, and a Poisson-distributed stochastic field. It is shown that for transient subcritical electric fields E ( t ) a finite residual particle number density n ( ∞ ) would be absent if the field-dependence of the dynamical phase in the Schwinger source term would be neglected. In this case the distribution function of created particles follows the law f ( t ) ∼ E 2 ( t ) . Two lessons for particle production in heavy-ion collisions are derived from this exercise. First: the shorter the (Sauter-type) pulse, the higher the residual density of produced particles. Second: although the Schwinger process in a string-type field produces a non-thermal particle spectrum, a Poissonian distribution of the (fluctuating) strings produces a thermal spectrum with an apparent temperature that coincides with the Hawking–Unruh temperature for the mean value of the string tension.
Soft Particle Production, Flow and Correlations in Heavy Ion Collisions at the LHC
