Nonlocal looking equations can make nonlinear quantum dynamics local

Abstract

A general method for extending a non-dissipative nonlinear Schrödinger and Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles is described. It is shown at a general level that the dynamics so obtained is completely separable, which is the strongest condition one can impose on dynamics of composite systems. It requires that for all initial states (entangled or not) a subsystem not only cannot be influenced by any action undertaken by an observer in a separated system (strong separability), but additionally that the self-consistency condition $T{r}_2\circ {\varphi }_{1+2}^t={\varphi }_1^t\circ T{r}_2$ is fulfilled. It is shown that a correct extension to $N$ particles involves integro-differential equations which, in spite of their nonlocal appearance, make the theory fully local. As a consequence a much larger class of nonlinearities satisfying the complete separability condition is allowed than has been assumed so far. In particular all nonlinearities of the form $F(|\psi (x)|)$ are acceptable. This shows that the locality condition does not single out logarithmic or 1-homeogeneous nonlinearities.

revtex, final version, accepted in Phys.Rev.A (June 1998)

References in corpus (1)

• Density matrix interpretation of solutions of Lie-Nambu equations

Cited by in corpus (23)

• Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences
• The no-signaling condition and quantum dynamics
• A nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution
• Quantum feedback with weak measurements
• Nonlinear quantum evolution with maximal entropy production
• Darboux-integrable nonlinear Liouville-von Neumann equation
• Correlation experiments in nonlinear quantum mechanics
• Complete positivity of nonlinear evolution: A case study
• Nonlinear evolution and signaling
• Vacuum Cherenkov effect in logarithmic nonlinear quantum theory
• Microscopic Foundation of Nonextensive Statistics
• Signaling, Entanglement, and Quantum Evolution Beyond Cauchy Horizons
• Informal Resource Letter - Nonlinear quantum mechanics on arXiv up to August 2004
• Detecting a logarithmic nonlinearity in the Schrödinger equation using Bose-Einstein condensates
• Loss-of-entanglement prediction of a controlled-PHASE gate in the framework of steepest-entropy-ascent quantum thermodynamics
• Nonlinearity and constrained quantum motion
• Jensen-Shannon Divergence and Non-linear Quantum Dynamics
• Lie-Nambu and beyond
• Probing the limits of quantum theory with quantum information at subnuclear scales
• Causality Violation and Nonlinear Quantum Mechanics
• Beyond the Projection Postulate and Back: Quantum Theories with Generalised State-Update Rules
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
• Torsion-Driven Nonlinearity in Spinless Quantum Mechanics