Quantum probability and related topics: Proceedings Guanajuato, 2007 28th Conference

Description

This volume contains recent results in quantum probability and related topics. The contributions include peer-reviewed papers on interacting Fock space and orthogonal polynomials, quantum Markov semigroups, infinitely divisible processes, free probability, white noise, quantum filtering and control, quantum information, dilations, applications of quantum probability in physics, and quantum and classical models in biology. This diversity reflects the strong and constructive relations between quantum probability and different sectors of mathematics, physics, and other sciences and technologies.  Read more... Abstract: Contains results in quantum probability and related topics. This book contains papers on interacting Fock space and orthogonal polynomials, quantum Markov semigroups, infinitely divisible processes, free probability, white noise, quantum filtering and control, quantum information, dilations, and applications of quantum probability in physics.  Read more... Content: Preface CONTENTS Linear Independence of the Renormalized Higher Powers of White Noise L. Accardi & A. Boukas 1. Introduction: Renormalized Higher Powers of White Noise 2. Linear independence of the RHPWN generators References Brownian Dynamics Simulation for Protein Folding and Binding T. Ando 1. Introduction 2. Methods and Models 2.1. Brownian dynamics simulation algorithm 2.2. Force field 2.3. Umbrella sampling 2.4. Models 2.5. Analysis 2.5.1. Native contacts 2.5.2. Cluster analysis 3. Results and Discussion 3.1. Computational time. 3.2. Folding simulations of [alpha]-helical and [beta]-hairpin peptides3.2.1. Folding trajectories 3.2.2. Energy components 3.2.3. Cluster analysis 3.3. Binding a.nity calculation 4. Conclusion Acknowledgments References Quantum Fokker-Planck Models: The Lindblad and Wigner Approaches A. Arnold, F. Fagnola & L. Neumann 1. Quantum Fokker-Planck model 2. Passage from the Wigner equation to the master equation 3. Key inequalities for the existence of a steady state 4. Domain problems 5. Construction of the minimal quantum dynamical semigroup 6. Markovianity of the Quantum Dynamical Semigroup. 7. Stationary state8. Irreducibility and large time behavior 9. The limiting case = 0 Acknowledgement: References Hilbert Space of Analytic Functions Associated with a Rotation Invariant Measure N. Asai 1. Preliminaries. 2. Hilbert space of analytic L2-functions with respect to a rotation invariant measure. 3. Remark on c1,2 &lt 0 and Table of Examples for c1.2 ≥ 0. Appendix A. 4. Connections with Lie algebras. Acknowledgments. References Quantum Continuous Measurements: The Spectrum of the Output A. Barchielli & M. Gregoratti 1. Quantum continuous measurements. 1.1. Hudson Parthasarathy equation1.2. The reduced dynamics of the system 1.3. The field observables 1.4. Characteristic operator, probabilities and moments 2. The spectrum of the output 2.1. The spectrum of a stationary process 2.2. The spectrum of the output in a finite time horizon 2.3. Properties of the spectrum and the Heisenberg uncertainty relations 3. Squeezing of the .uorescence light of a two-level atom References Characterization Theorems in Gegenbauer White Noise Theory A. Barhoumi, A. Riahi & H. Ouerdiane 1. Introduction 2. Gegenbauer White Noise Space. 3. Gegenbauer Test and Generalized Functions4. Characterization Theorems for Test and Generalized Functions 4.1. The S[beta].transform 4.2. Characterization of test and generalized functions References A Problem of Powers and the Product of Spatial Product Systems B.V.R. Bhat, V. Liebscher & M. Skeide 1. Introduction 2. Product systems, CP-semigroups, E0-semigroups and dilations 2.1. Product systems 2.2. Units 2.3. The product system of a CP-semigroup 2.4. The product system of an E0-semigroup on Ba(E) 2.5. Dilation and minimal dilation 2.6. Spatial product systems.