Unitary evolution to a state with a fixed mean number of particles

TL;DR

This paper demonstrates that in finite-dimensional Fock space models, it is possible for unitary evolution to lead to states with a fixed mean particle number, supporting the unitarity of black hole evaporation.

Contribution

It shows the existence of large subspaces of initial states evolving unitarily to states with a fixed mean particle number, including blackbody distributions.

Findings

Existence of subspaces with fixed mean particle number

Blackbody distribution does not contradict unitarity

Supports unitarity in black hole evaporation

Abstract

In the framework of finite-dimensional Fock space models, for a predefined fixed mean number of particles $\bar{n}_{k}$, it is shown that there is a ``large'' multi-dimensional subspace $s_{\bar{n}_{k}}$ of initial pure states, in the space $S$ of all pure states, unitarily evolving to a subspace $S_{\bar{n}_{k}}$ of final pure states which yield $\bar{n}_{k}$. As an example, in particular it follows that the blackbody form of the mean number of particles $\bar{n}_{k}$ does not by itself contradict unitarity of black hole evaporation.