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

arXiv:gr-qc/0409063 · International Journal of Theoretical Physics

Noncommutative Dynamics of Random Operators

Michael C. Heller, Leszek Pysiak, Wiesław Sasin

Published Jun 1, 2005• 21 citations
arXivHTMLPDF
DOI
10.1007/s10773-005-3992-7

Related papers

State vector reduction as a shadow of a noncommutative dynamics

Michael C. Heller, Wiesław Sasin, Zdzisław Odrzygóźdź

A model, based on a noncommutative geometry, unifying general relativity and quantum mechanics, is developed. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators, and that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum mechanical approximation gives the standard unitary evolution of observables, and in the “space–time limit” it leads to the state vector reduction. The cases of the spin and position operators are discussed.

arXiv:hep-th/9906132•Journal of Mathematical Physics•Aug 1, 2000•10 citations

Noncommutative Quantum Dynamics

Michael C. Heller, Wiesław Sasin, Zdzisław Odrzygóźdź

GrCo•Jun 1, 2001•0 citations

Noncommutative optimal control and quantum networks

Masahiro Yanagisawa

Optimal control is formulated based on a noncommutative calculus of operator derivatives. The use of optimal control methods in the design of quantum systems relies on the differentiation of an operator-valued function with respect to the relevant operator. Noncommutativity between the operator and its derivative leads to a generalization of the conventional method of control for classical systems. This formulation is applied to quantum networks of both spin and bosonic particles for the purpose of quantum state control via quantum random walks.

Physical Review A•Feb 24, 2006•5 citations

Noncommutative Dynamics

Jakub Rembieliński

Springer eBooks•Jan 1, 1993•1 citation

A System of Stochastic Differential Equations within NETFD : Can Quantumness be an Origin of Dissipation? (Trends in Infinite Dimensional Analysis and Quantum Probability)

Toshihco Arimitsu

Most of the mathematical approaches for quantum Langevin equation are based on the noncommutativity of the random force operators.Non-commutative random force operators are introduced in order to guarantee that the equal-time commutation relation for the stochastic anlihilation and creation operators preserves in time.If it is true, it means that the origin of dissipation is of quantum mechanical.However, physically, it is hard to believe it.By making use of the unified canonical operator formalism for the system of the quantum stochastic differential equations within Non-Equilibri um Thermo Field Dynamics, it is shown that it is not true in general.

数理解析研究所講究録•Aug 1, 2002•0 citations

Two-dimensional noncommutative quantum dynamics

Won-Sang Chung

International Journal of Theoretical Physics•Sep 1, 1997•0 citations
A model, based on a noncommutative geometry, unifying general relativity and quantum mechanics, is developed. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators, and that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum mechanical approximation gives the standard unitary evolution of observables, and in the “space–time limit” it leads to the state vector reduction. The cases of the spin and position operators are discussed.
Optimal control is formulated based on a noncommutative calculus of operator derivatives. The use of optimal control methods in the design of quantum systems relies on the differentiation of an operator-valued function with respect to the relevant operator. Noncommutativity between the operator and its derivative leads to a generalization of the conventional method of control for classical systems. This formulation is applied to quantum networks of both spin and bosonic particles for the purpose of quantum state control via quantum random walks.
Most of the mathematical approaches for quantum Langevin equation are based on the noncommutativity of the random force operators.Non-commutative random force operators are introduced in order to guarantee that the equal-time commutation relation for the stochastic anlihilation and creation operators preserves in time.If it is true, it means that the origin of dissipation is of quantum mechanical.However, physically, it is hard to believe it.By making use of the unified canonical operator formalism for the system of the quantum stochastic differential equations within Non-Equilibri um Thermo Field Dynamics, it is shown that it is not true in general.