Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

数理解析研究所講究録

General Properties between Canonical Correlation and the Independent-Oscillator Model on a Partial $\ast$-Algebra(Quantum Stochastic Analysis and Related Fields)

Masao Hirokawa

Published Aug 1, 1996• 0 citations
OpenAlex

Related papers

General Properties between Canonical Correlation and the Independent-Oscillator Model on a Partial $\ast$-Algebra(Quantum Stochastic Analysis and Related Fields)

Masao Hirokawa

•Aug 1, 1996•0 citations

General Properties between Canonical Correlation and the Independent-Oscillator Model on a Partial 〓-Algebra (第4回『非平衡系の統計物理』シンポジウム)

真男 広川

物性研究•Oct 1, 1997•0 citations

General properties between the canonical correlation and the independent-oscillator model on a partial *-algebra

Masao Hirokawa

We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial *-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of Ford et al. [ G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.

Journal of Mathematical Physics•Jan 1, 1996•1 citation

On some aspects of general quantum correlations

Ajoy Sen

•Jan 1, 2015•0 citations

On properties of correlations in quantum mechanics and generalized probabilistic theories

Waldemar Kłobus

•Jul 9, 2014•0 citations

A Class of Representations of the *-Algebra of the Canonical Commutation Relations over a Hilbert Space and Instability of Embedded Eigenvalues in Quantum Field Models

Asao Arai

In models of a quantum harmonic oscillator coupled to a quantum field with a quadratic interaction, embedded eigenvalues of the unperturbed system may be unstable under the perturbation given by the interaction of the oscillator with the quantum field.A general mathematical structure underlying this phenomenon is clarified in terms of a class of Fock space representations of the * -algebra of the canonical commutation relations over a Hilbert space.It is also shown that each of the representations is given as a composition of a proper Bogolyubov (canonical) transformation and a partial isometry on the Fock space of the representation.

Journal of Nonlinear Mathematical Physics•Jan 1, 1997•5 citations
General Properties between Canonical Correlation and the Independent-Oscillator Model on a Partial ∗\ast∗-Algebra(Quantum Stochastic Analysis and Related Fields)
General Properties between Canonical Correlation and the Independent-Oscillator Model on a Partial ∗\ast∗-Algebra(Quantum Stochastic Analysis and Related Fields)
We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial *-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of Ford et al. [ G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.
In models of a quantum harmonic oscillator coupled to a quantum field with a quadratic interaction, embedded eigenvalues of the unperturbed system may be unstable under the perturbation given by the interaction of the oscillator with the quantum field.A general mathematical structure underlying this phenomenon is clarified in terms of a class of Fock space representations of the * -algebra of the canonical commutation relations over a Hilbert space.It is also shown that each of the representations is given as a composition of a proper Bogolyubov (canonical) transformation and a partial isometry on the Fock space of the representation.