Bound states and the Bekenstein bound

TL;DR

This paper examines the generalized Bekenstein bound's validity for localized quantum states, highlighting the importance of interactions and finite-size effects in ensuring the bound's applicability.

Contribution

It demonstrates that the Bekenstein bound holds when interactions are included, addressing issues from boundary conditions and finite-size effects.

Findings

Bound is valid with proper interactions.

Finite-size effects influence energy contributions.

Challenges with boundary conditions and negative Casimir energy.

Abstract

We explore the validity of the generalized Bekenstein bound, S <= pi M a. We define the entropy S as the logarithm of the number of states which have energy eigenvalue below M and are localized to a flat space region of width a. If boundary conditions that localize field modes are imposed by fiat, then the bound encounters well-known difficulties with negative Casimir energy and large species number, as well as novel problems arising only in the generalized form. In realistic systems, however, finite-size effects contribute additional energy. We study two different models for estimating such contributions. Our analysis suggests that the bound is both valid and nontrivial if interactions are properly included, so that the entropy S counts the bound states of interacting fields.