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TMF, 1997, Volume 111, Number 2, Pages 218–233 (Mi tmf1002)  

This article is cited in 12 scientific papers (total in 12 papers)

Causal structure of quantum stochastic integrators

J. Gough

St. Patrick's College

Abstract: A class of concrete representations of a non-commutative Stratonovich calculus is defined and its relationship with the quantum Ito calculus of Hudson and Parthasarathy is made explicit. Given a quantum field interacting with a quantum mechanical system, it is possible to extract a quantum noise description for the field using a suitable scaling limit (here the weak coupling limit). The motivation for our construction is to discuss the relationship between the micro-causality of a quantum field and the notion of macro-causality of the quantum noise which replaces it. We derive the Stratonovich quantum stochastic differential equation for the limit evolution operator and show that it agrees with the quantum stochastic limit theory of Accardi, Frigerio and Lu when we convert to the Ito form. The Stratonovich approach, being inherently closer to the physical microscopic equations, leads to an overwhelmingly simplified derivation of the quantum stochastic limit equations of motion. The unification of the two quantum stochastic calculi is given and their physical origins explained.


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English version:
Theoretical and Mathematical Physics, 1997, 111:2, 563–575

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Received: 06.01.1997

Citation: J. Gough, “Causal structure of quantum stochastic integrators”, TMF, 111:2 (1997), 218–233; Theoret. and Math. Phys., 111:2 (1997), 563–575

Citation in format AMSBIB
\by J.~Gough
\paper Causal structure of quantum stochastic integrators
\jour TMF
\yr 1997
\vol 111
\issue 2
\pages 218--233
\jour Theoret. and Math. Phys.
\yr 1997
\vol 111
\issue 2
\pages 563--575

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    This publication is cited in the following articles:
    1. J. Gough, “Non-commutative Ito and Stratonovich noise and stochastic evolutions”, Theoret. and Math. Phys., 113:2 (1997), 1431–1437  mathnet  crossref  crossref  mathscinet  isi
    2. Gough, J, “A new approach to non-commutative white noise analysis”, Comptes Rendus de l Academie Des Sciences Serie i-Mathematique, 326:8 (1998), 981  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Gough, J, “Asymptotic stochastic transformations for nonlinear quantum dynamical systems”, Reports on Mathematical Physics, 44:3 (1999), 313  crossref  mathscinet  zmath  adsnasa  isi
    4. Gough, J, “The Stratonovich interpretation of quantum stochastic approximations”, Potential Analysis, 11:3 (1999), 213  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Gough, J, “Dissipative canonical flows in classical and quantum mechanics”, Journal of Mathematical Physics, 40:6 (1999), 2805  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. J. Gough, “Bosonic and fermionic white noises and the reflection process”, Theoret. and Math. Phys., 124:1 (2000), 887–896  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Gough, J, “Noncommutative Markov approximations”, Doklady Mathematics, 64:1 (2001), 112  mathscinet  zmath  isi
    8. Gough, J, “Quantum white noises and the master equation for Gaussian reference states”, Russian Journal of Mathematical Physics, 10:2 (2003), 142  mathscinet  zmath  isi
    9. Von Waldenfels, W, “Symmetric differentiation and Hamiltonian of a quantum stochastic”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 8:1 (2005), 73  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Von Waldenfels W., “The Hamiltonian of a simple pure number process”, Quantum Probability and Infinite Dimensional Analysis, Qp-Pq Quantum Probability and White Noise Analysis, 18, 2005, 518–524  mathscinet  isi
    11. von Waldenfels W., “The Singular Coupling Limit for a Simple Pure Number Process”, Stochastics, 84:2-3, SI (2012), 417–423  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    12. Gough J.E., “Symplectic Noise and the Classical Analog of the Lindblad Generator”, J. Stat. Phys., 160:6 (2015), 1709–1720  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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