Quantum stochastic calculus | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-24

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Quantum_stochastic_calculus


00:00:43 1 Heat baths
00:06:24 1.1 White noise formalism
00:12:43 1.2 Quantum Wiener process
00:16:06 2 Quantum stochastic integration
00:16:25 2.1 Quantum Itō integral
00:18:20 2.2 Itō quantum stochastic differential equation
00:21:00 2.3 Quantum Stratonovich integral
00:24:11 2.4 Stratonovich quantum stochastic differential equation
00:26:02 2.5 Relation between Itō and Stratonovich integrals
00:27:45 2.6 Calculus rules
00:29:21 3 Quantum trajectories
00:30:16 3.1 Example unravelings
00:35:39 3.2 Computational considerations



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SUMMARY
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Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum trajectories. Just as the Lindblad master equation provides a quantum generalization to the Fokker-Planck equation, quantum stochastic calculus allows for the derivation of quantum stochastic differential equations (QSDE) that are analogous to classical Langevin equations.
For the remainder of this article stochastic calculus will be referred to as classical stochastic calculus, in order to clearly distinguish it from quantum stochastic calculus.