2017/07/31 by Luke M. Butcher · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Curvature #Entropy (arrow of time) #Geometry #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Subspace topology #Theoretical physics #gr-qc #quant-ph
paper · pdf · doi:10.1016/j.physleta.2018.06.013
published in Physics Letters A 382(36), 2555-2560 (Elsevier BV) · 7 pages, 1 figure; published version with appendix
openalex publication_date 2018/06/14 · arxiv created 2018/07/10 · arxiv updated 2019/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
I obtain the quantum correction ΔVeff= (ℏ2/8m) [(1- 4ξ(d+1)/(d))(S')2 + 2(1-4ξ)S"] that appears in the effective potential whenever a compact d-dimensional subspace (of volume ∝ exp[S(x)]) is discarded from the configuration space of a nonrelativistic particle of mass m and curvature coupling parameter ξ. This correction gives rise to a force -⟨ΔVeff'⟩ that pushes the expectation value ⟨ x⟩ off its classical trajectory. Because ΔVeff does not depend on the details of the discarded subspace, these results constitute a generic model of the quantum effect of discarded variables with maximum entropy/information capacity S(x).