Stochastic Analysis and Mathematical Physics II: 4th International Anestoc Workshop in Santiago, Chile

ISBN-13: 9783764369972 / Angielski / Twarda / 2002 / 162 str.

R. Rebolledo; Rolando Rebolledo

Opis

The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focussing, in particular, on quantum probability. Key topics covered include novel tools for the qualitative analysis of quantum dynamical semigroups (existence of invariant states, subharmonic projections and faithful normal invariant states, propagation of molecular chaos), and new results on quantum information and quantum large deviations. All articles have been thoroughly refereed and are an outgrowth of the International Workshop in Stochastic Analysis and Mathematical Physics held in Santiago, Chile, in January 2000. The book is addressed to an audience of mathematical physicists, as well as specialists in probability theory, stochastic analysis, and operator algebras. Contributors: L. Accardi, A. Chebotarev, F. Cipriano, H. Comman, M. Corgini, F. Fagnola, C. Fern ndez, J.C. Garc a, A. Gottlieb, S. Kozyrev, K.R. Parthasarathy, H. Prado, R. Quezada, O. Rask, R. Rebolledo

Spis treści

1 Quantum Boltzmann Statistics in Interacting Systems.- 1 Introduction.- 2 Quantum Boltzmann statistics for entangled operators.- 3 References.- 2 Interaction Representation Method for Markov Master Equations in Quantum Optics.- 1 Sufficient conditions for conservativity.- 2 A priori bounds.- 3 Structure of generators of MME in quantum optics.- 4 Examples.- 5 Discussion.- 6 References.- 3 A Stochastic Variational Principle for Burgers Equation and its Symmetries.- 1 Introduction.- 2 Variational problem.- 3 Stochastic first integrals.- 4 An integration by parts formula.- 5 References.- 4 Noncommutative Versions of Prohorov and Varadhan Theorems.- 1 Vague and narrow convergence of positive functionals.- 1.1 Vague and narrow topologies.- 1.2 Tightness.- 1.3 Application to quantum dynamical semigroups.- 2 Noncommutative large deviations.- 2.1 Noncommutative capacities and q-semi-continuity.- 2.2 Large deviation principle for states.- 2.3 General Varadhan-type theorem.- 3 References.- 5 Gaussian Domination and Bose-Einstein Condensation.- 1 Introduction.- 2 Some Historical Remarks.- 2.1 Mean field and related model systems: Some mathematical approaches.- 2.2 Infrared bounds approach.- 3 Model Systems.- 4 Gaussian Domination and its Application to the Study of Bose Systems.- 4.1 Bogolubov’s inner product.- 4.2 Bose-Einstein condensation.- 4.3 Upper and Lower Bounds on $$ \left\langle {{{\hat n}_j}} \right\rangle $$.- 4.4 Gaussian Domination and upper bound on $$ {\left( {a_j^\dag ,} \right)_{{H^L}}} $$.- 4.5 The phase transition.- 5 References.- 6 Quantum Markov Semigroups and their Stationary States.- 1 Introduction.- 1.1 Preliminaries.- 2 Ergodic theorems.- 3 The minimal quantum dynamical semigroup.- 4 The existence of Stationary States.- 4.1 A general result.- 4.2 Conditions on the generator.- 4.3 Applications.- 5 Faithful Stationary States and Irreducibility.- 5.1 Introduction.- 5.2 The support of an invariant state.- 5.3 Subharmonic projections. The case A=B (h).- 5.4 Examples.- 6 The convergence towards the equilibrium.- 6.1 A result due to Frigerio and Verri.- 6.2 Quantum Markovian Cocycles.- 6.3 Main results.- 6.4 Applications.- 7 References.- 7 Exponential Decay for Perturbations of Pure Point Hamiltonians.- 1 Introduction.- 2 Absolutely continuous perburbations of pure point operators.- 3 Sojourn time and Spectral Entropy.- 4 References.- 8 Propagation of Chaos in Classical and Quantum Kinetics.- 1 Overview.- 2 Classical and Quantum Molecular Chaos.- 2.1 Classical molecular chaos.- 2.2 Quantum molecular chaos.- 2.3 Spohn’s quantum mean-field dynamics.- 3 Classical Manifestations of the Propagation of Quantum Molecular Chaos.- 3.1 Measurement of complete observables.- 3.2 Generalized measurements.- 4 Acknowledgements.- 5 References.- 9 Imprimitivity Systems and Quantum Codes.- 1 Introduction.- 2 Imprimitivity systems and quantization of classical codes.- 3 Tensor products of imprimitivity system and quantum codes.- 4 References.- 10 Boson Fock Algebra on the Unit Ball of the d-Dimensional Complex Numbers.- 1 Introduction.- 2 Operators on the algebra A0 (Bd).- 3 Introduction to Boson Fock space.- 4 Boson Fock space on the unit ball.- 5 References.