Quantum interest in two dimensions

Abstract

The quantum interest conjecture of Ford and Roman asserts that any negative-energy pulse must necessarily be followed by an over-compensating positive-energy one within a certain maximum time delay. Furthermore, the minimum amount of over-compensation increases with the separation between the pulses. In this paper, we first study the case of a negative-energy square pulse followed by a positive-energy one for a minimally coupled, massless scalar field in two-dimensional Minkowski space. We obtain explicit expressions for the maximum time delay and the amount of over-compensation needed, using a previously developed eigenvalue approach. These results are then used to give a proof of the quantum interest conjecture for massless scalar fields in two dimensions, valid for general energy distributions.

17 pages, 4 figures; final version to appear in PRD

References in corpus (6)

• The warp drive: hyper-fast travel within general relativity
• A general worldline quantum inequality
• A Quantum Weak Energy Inequality for Dirac fields in curved spacetime
• Quantum Inequalities for the Electromagnetic Field
• Quantum Inequalities in Curved Two Dimensional Spacetimes
• Quantum inequalities and `quantum interest' as eigenvalue problems

Cited by in corpus (5)

• Energy conditions in general relativity and quantum field theory
• Classical and quantum flux energy conditions for quantum vacuum states
• Lectures on quantum energy inequalities
• Quantum inequalities in two dimensional curved spacetimes
• Quantum Interest in (3+1) dimensional Minkowski space