Quantum Schroedinger bridges

Details Quantum Schroedinger bridges Quantum Schroedinger bridges

2003-06-06

arxiv.org/abs/quant-ph/0306052v1

in Directions in Mathematical Systems Theory and Optimization, A. Rantzer and C. I. Byrnes Eds., Springer-Verlag, 2002, 227-23

Physics

Quantum Physics

15 pages, dedicated to Anders Lindquist on the occasion of his 60th birthday

Scientific paper

Elaborating on M. Pavon, J.Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechanics that produces the von Neumann wave packet reduction after a position measurement. This stochastic control problem parallels, with a different kinematics, the problem of the Schroedinger bridge. This gives a profound meaning to what was observed by Schroedinger in 1931 concerning Schroedinger bridges: "Merkwuerdige Analogien zur Quantenmechanik, die mir sehr des Hindenkens wert erscheinen".

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