On The Problem of Particle Production in c=1 Matrix Model

TL;DR

This paper investigates particle production in the c=1 matrix model with a draining Fermi sea, introducing a new computational method, analyzing the stress-tensor evolution, and confirming space-time decay through energy radiation.

Contribution

It presents an alternative method for calculating Bogolubov coefficients and extends the analysis of stress-tensor evolution beyond previous approximations.

Findings

Bogolubov coefficients are approximately correct for small deformation.

Stress-tensor regularization reveals a singular term canceled by counterterms.

Energy density decays exponentially, indicating space-time decay.

Abstract

We reconsider and analyze in detail the problem of particle production in the time dependent background of $c=1$ matrix model where the Fermi sea drains away at late time. In addition to the moving mirror method, which has already been discussed in hep-th/0403169 and hep-th/0403275, we describe yet another method of computing the Bogolubov coefficients which gives the same result. We emphasize that these Bogolubov coefficients are approximately correct for small value of the deformation parameter. We also study the time evolution of the collective field theory stress-tensor with a special point-splitting regularization. Our computations go beyond the approximation of the previous treatments and are valid at large coordinate distances from the boundary at a finite time and up-to a finite coordinate distance from the boundary at late time. In this region of validity our regularization produces a certain singular term that is precisely canceled by the collective field theory counter term in the present background. The energy and momentum densities fall off exponentially at large distance from the boundary to the values corresponding to the static background. This clearly shows that the radiated energy reaches the asymptotic region signaling the space-time decay.