Quantum dissipation induced noncommutative geometry

Abstract

The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geometry. The noncommutative geometric plane is a consequence of a quantum dissipation induced phase interference which is closely analogous to the Aharanov-Bohm effect.

12 pages, 2 figures

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• Chiral decomposition in the non-commutative Landau problem
• An Introduction to Noncommutative Physics
• Links. Relating different physical systems through the common QFT algebraic structure
• Klein-Gordon theory in noncommutative phase space
• Non-Commutative Geometry and Measurements of Polarized Two Photon Coincidence Counts
• Noncommutative spectral geometry, dissipation and the origin of quantization
• On the molecular dynamics in the hurricane interactions with its environment
• The structure of Green functions in quantum field theory with a general state
• Squeezed coherent states for gravitational well in noncommutative space
• Dynamics of zero-point energy and two-slit phenomena for photons
• Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory