2005/08/31 by Thomas F. Jordan · 2 citations
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.73.022101
published as Phys. Rev. A 73, 022101 (2006) · 10 pages. Added references. Improved discussion of equations of motion for mean values. Expanded Introduction
arxiv created 2006/01/26 · openalex publication_date 2006/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proven very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schr"odinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.