Approximation and limit theorems for quantum stochastic models with unbounded coefficients

Luc Bouten; Ramon van Handel; Andrew Silberfarb

doi:10.1016/j.jfa.2008.02.013

Approximation and limit theorems for quantum stochastic models with unbounded coefficients

Luc Bouten, Ramon van Handel, Andrew Silberfarb

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations and singular perturbations are obtained. The results are illustrated in several examples of physical interest.

Original language	English (US)
Pages (from-to)	3123-3147
Number of pages	25
Journal	Journal of Functional Analysis
Volume	254
Issue number	12
DOIs	https://doi.org/10.1016/j.jfa.2008.02.013
State	Published - Jun 15 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Adiabatic elimination
Approximation and limit theorems
Hudson-Parthasarathy equations
Quantum stochastic models
Singular perturbation
Trotter-Kato theorem

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10.1016/j.jfa.2008.02.013

Cite this

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title = "Approximation and limit theorems for quantum stochastic models with unbounded coefficients",

abstract = "We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations and singular perturbations are obtained. The results are illustrated in several examples of physical interest.",

keywords = "Adiabatic elimination, Approximation and limit theorems, Hudson-Parthasarathy equations, Quantum stochastic models, Singular perturbation, Trotter-Kato theorem",

author = "Luc Bouten and {van Handel}, Ramon and Andrew Silberfarb",

year = "2008",

month = jun,

day = "15",

doi = "10.1016/j.jfa.2008.02.013",

language = "English (US)",

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journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

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T1 - Approximation and limit theorems for quantum stochastic models with unbounded coefficients

AU - Bouten, Luc

AU - van Handel, Ramon

AU - Silberfarb, Andrew

PY - 2008/6/15

Y1 - 2008/6/15

N2 - We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations and singular perturbations are obtained. The results are illustrated in several examples of physical interest.

AB - We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations and singular perturbations are obtained. The results are illustrated in several examples of physical interest.

KW - Adiabatic elimination

KW - Approximation and limit theorems

KW - Hudson-Parthasarathy equations

KW - Quantum stochastic models

KW - Singular perturbation

KW - Trotter-Kato theorem

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VL - 254

SP - 3123

EP - 3147

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 12

ER -

Approximation and limit theorems for quantum stochastic models with unbounded coefficients

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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