2003/10/01 by V. P. Belavkin · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Langevin equation #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum probability #Quantum process #Statistical physics #Stochastic differential equation #math-ph #math.MP
paper · pdf · doi:10.1023/b:ijtp.0000005969.92111.b5
published in International Journal of Theoretical Physics 42(10), 2461-2485 (Springer Science+Business Media) · 21 pages. See also relevant publications at http://www.maths.nott.ac.uk/personal/vpb/publications.html
openalex publication_date 2003/10/01 · arxiv created 2005/11/04 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the quantum stochastic unitary dynamics Langevin model for continuous in time measurements provides an exact formulation of the Heisenberg uncertainty error-disturbance principle. Moreover, as it was shown in the 80's, this Markov model induces all stochastic linear and non-linear equations of the phenomenological "quantum trajectories" such as quantum state diffusion and spontaneous localization by a simple quantum filtering method. Here we prove that the quantum Langevin equation is equivalent to a Dirac type boundary-value problem for the second-quantized input "offer waves from future" in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the "trajectories of the output particles". This result supports the wave-particle duality in the form of the thesis of Eventum Mechanics that everything in the future is constituted by quantized waves, everything in the past by trajectories of the recorded particles. We demonstrate how this time arrow can be derived from the principle of quantum causality for nondemolition continuous in time measurements.