Brownian Motion and the Stochastic Theory of Quantum Mechanics

1972 ◽  
pp. 457-470 ◽  
Author(s):  
E. Santos
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Stochastic Theory

Quantum Mechanics as a Stochastic Theory

1996 ◽  
pp. 33-66
Author(s):  
Luis de la Peña ◽  
Ana María Cetto
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Theory

scholarly journals SUPERSYMMETRY AND BROWNIAN MOTION ON SUPERMANIFOLDS

2003 ◽  
Vol 06 (supp01) ◽  
pp. 83-102 ◽  
Author(s):  
ALICE ROGERS
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Morse Theory ◽  
Index Theorem ◽  
Supersymmetric Quantum Mechanics ◽  
Supersymmetric Model ◽  
Itô Formula ◽  
Ito Formula ◽  
And Brownian Motion

An anticommuting analogue of Brownian motion, corresponding to fermionic quantum mechanics, is developed, and combined with classical Brownian motion to give a generalised Feynman-Kac-Itô formula for paths in geometric supermanifolds. This formula is applied to give a rigorous version of the proofs of the Atiyah-Singer index theorem based on supersymmetric quantum mechanics. After a discussion of the BFV approach to the quantization of theories with symmetry, it is shown how the quantization of the topological particle leads to the supersymmetric model introduced by Witten in his study of Morse theory.

scholarly journals Brownian Motion and Quantum Mechanics

2019 ◽  
Vol 19 (02) ◽  
pp. 2050017
Author(s):  
Roumen Tsekov
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Turbulent Velocity ◽  
Simultaneous Action ◽  
Quantum Brownian Motion ◽  
Velocity Fluctuations ◽  
Diffusive Behavior ◽  
Stochastic Sources ◽  
Quantum Noises

A theoretical parallel between the classical Brownian motion and quantum mechanics is explored via two stochastic sources. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive behavior. In the case of simultaneous action of the thermal and quantum noises, the quantum Brownian motion is described as well.

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