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Convergence of empirical distributions in an interpretation of quantum mechanics
- Source :
- Ann. Appl. Probab. 26, no. 4 (2016), 2540-2555
- Publication Year :
- 2014
-
Abstract
- From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical "worlds." The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman [Physical Review X 4 (2014) 041013] have introduced an explicit many-interacting-worlds harmonic oscillator model to provide support for this approach. In this note we provide a proof of their claim that the particle configuration is asymptotically Gaussian, thus matching the stationary ground-state solution of Schroedinger's equation when the number of worlds goes to infinity. We also construct a Markov chain based on resampling from the particle configuration and show that it converges to an Ornstein-Uhlenbeck process, matching the time-dependent solution as well.
- Subjects :
- Statistics and Probability
Gaussian
media_common.quotation_subject
FOS: Physical sciences
Stein’s method
Mathematics - Statistics Theory
Statistics Theory (math.ST)
01 natural sciences
Article
010104 statistics & probability
symbols.namesake
81Q65
60F05
0103 physical sciences
FOS: Mathematics
Statistical physics
0101 mathematics
010306 general physics
Wave function
Harmonic oscillator
Mathematics
media_common
Quantum Physics
Markov chain
Interacting particle system
Interpretations of quantum mechanics
Infinity
normal approximation
81Q65, 60F05
60F17
symbols
Statistics, Probability and Uncertainty
Quantum Physics (quant-ph)
Schrödinger's cat
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ann. Appl. Probab. 26, no. 4 (2016), 2540-2555
- Accession number :
- edsair.doi.dedup.....0b247e67baa389fd191a7ce474d9179f