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On Doob h-transformations for finite-time quantum state reduction.
- Source :
-
Journal of Mathematical Physics . Mar2024, Vol. 65 Issue 3, p1-14. 14p. - Publication Year :
- 2024
-
Abstract
- The paper develops a finite-time quantum state reduction framework via the use of Lévy random bridges (LRBs) that can be understood as Doob h-transformations on Lévy processes. Building upon the non-anticipative semimartingale representation of LRBs, we propose a family of energy-driven stochastic Schrödinger equations that go beyond the purely-continuous Brownian motion setup, and enter the scope of quantum systems involving discontinuities and heavy-tails. In doing so, we allow collapse dynamics to be governed intrinsically by the Markovian statistics of LRBs. The framework can host progressively convoluted stochastic state reduction dynamics in a tractable way and encapsulates jump-diffusion Schrödinger evolutions by use of the Lévy-Itô decomposition. Our construct motivates the usage of more general Markov processes and Doob h-transformations in producing consistent wave function collapse dynamics in finite-time. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 65
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 176343043
- Full Text :
- https://doi.org/10.1063/5.0162658