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Why are there only three quantum noises?
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  • Published: November 2000

Why are there only three quantum noises?

  • Agnès Coquio1 

Probability Theory and Related Fields volume 118, pages 349–364 (2000)Cite this article

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  • 7 Citations

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Abstract.

In quantum stochastic calculus on the symmetric Fock space over L 2(ℝ+), adapted processes of operators are integrated with respect to creation, annihilation and number processes. The main property which allows this integration is that the increments of integrators between s and t act only on Fock space over L 2([s, t]). In this article, we prove that there are no other process of closable operators on coherent vectors with this property. Thus the only possible integrators in quantum stochastic calculus are the creation, annihilation and number processes.

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Authors and Affiliations

  1. Université de Grenoble I, Institut Fourier, Laboratoire de Mathématiques, UMR 5582 CNRS-UJF, B.P. 74, 38402 St Martin D'hères Cedex, France. e-mail: Agnes.Coquio@ujf-grenoble.fr, , , , , , FR

    Agnès Coquio

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  1. Agnès Coquio
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Received: 7 June 1999 / Revised version: 27 December 1999 / Published online: 12 October 2000

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Coquio, A. Why are there only three quantum noises?. Probab Theory Relat Fields 118, 349–364 (2000). https://doi.org/10.1007/PL00008746

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  • Issue Date: November 2000

  • DOI: https://doi.org/10.1007/PL00008746

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Keywords

  • Main Property
  • Closable Operator
  • Quantum Noise
  • Number Process
  • Stochastic Calculus
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