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Markovian semigroups, time translation operator and a new development of Hida product between Hida distributions on sharp time fields(Micro-Macro Duality in Quantum Analysis)

Sergio A Albeverio, Minoru W. Yoshida

Published Jul 1, 2007• 0 citations
OpenAlex

Abstract

A new definition of product between the elements of Hida distributions de- fined on the sharp time free field is given.By this procedure the space of Hida distributions has the structure of ring.This newly defined product is different to the well known Stransform.It is much more complicated, but might have more fruitful strucrures than Stransform..

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WORLD SCIENTIFIC eBooks•Jan 1, 2007•1 citation
A new definition of product between the elements of Hida distributions de- fined on the sharp time free field is given.By this procedure the space of Hida distributions has the structure of ring.This newly defined product is different to the well known Stransform.It is much more complicated, but might have more fruitful strucrures than Stransform..
Entangled Markov chains, which can be recognized as quantum Markov chains in the sense of [1∣[1|[1∣ , were inti∨oducedinti^{\vee}oducedinti∨oduced by Accardi and Fidaleo in order to extend the notion of classical random walk to quaritum systems.In [3], using our entanglement criterion for pure states [16] which is based on the notion of the quantum mutual information, we proved that the vector states defining the EMC's on infinite tensor products of matrix algebra ∣∣genericallyI†||generically^{I\dagger}∣∣genericallyI† are entangled.On the other hand we showed that this entanglement condition for pure state is sufficient condition for entanglement in the case of mixtures [4].This fact was then applied to prove that EMC with unitarily im- plementable transition operator induce a mixture entangled state on any local algebra.Interestingly it was also shown that all these local states provide a new class of examples (in any dimension) of entangled states which nevertheless satisfy the PPT condition [4].In this article we report the above results.
A Combinatorial Identity and Its Application to Gaussian Measure (L Accardi, H-H Kuo & A I Stan) Integral Representation of Positive Operator on Infinite Dimensional Space of Entire Functions (W Ayed & H Ouerdiane) Comparison of Some Methods of Quantum State Estimation (D Petz et al.) Entropic Bounds and Continual Measurements (A Barchielli & G Lupieri) Covariant Quantum Stochastic Flows and Their Dilation (V Belavkin & L Gregory) Alicki-Fannes and Hudson-Parthasarathy Evolution Equations (A C R Belton) Functional Integrals Over Smolyanov Surface Measures for Evolution Equations in a Riemannian Manifold (Ya A Butko) Quantum Probabilistic Model for the Financial Market (O Choustova) Note on the Time Operator (T Hida) An Analytic Double Product Integral (R L Hudson) To Quantum Mechanics Through Gaussian Integration and the Taylor Expansion of Functionals of Classical Fields (A Yu Khrennikov) A Theorem on Liftings of Statistical Operators (J Kupsch) Thermodynamical Formalism for Quasi-Local C*-Systems and Fermion Grading Symmetry (H Moriya) Micro-Macro Duality and an Attempt Towards Measurement Scheme of Quantum Fields (I Ojima) The Levy Laplacian Acting on Some Class of Levy Functionals (K Saito & A H Tsoi) On the General Form of the Integral-Sigma Lemma in Symmetric Fock Space (K Schubert) Spatial E0-Semigroups are Restrictions of Inner Automorphism Groups (M Skeide) A Characterization of Poisson Noise (Si Si) On Two Conjectures in Segal-Bargmann Analysis (S B Sontz) Note on Quantum Mutual Type Entropies and Capacity (N Watanabe) and other papers.