Riassunto
The seminar on Stochastic Analysis and Mathematical Physics of the Ca tholic University of Chile, started in Santiago in 1984, has being followed and enlarged since 1995 by a series of international workshops aimed at pro moting a wide-spectrum dialogue between experts on the fields of classical and quantum stochastic analysis, mathematical physics, and physics. This volume collects most of the contributions to the Fourth Interna tional Workshop on Stochastic Analysis and Mathematical Physics (whose Spanish abbreviation is "ANESTOC"; in English, "STAMP"), held in San tiago, Chile, from January 5 to 11, 2000. The workshop style stimulated a vivid exchange of ideas which finally led to a number of written con tributions which I am glad to introduce here. However, we are currently submitted to a sort of invasion of proceedings books, and we do not want to increase our own shelves with a new one of the like. On the other hand, the editors of conference proceedings have to use different exhausting and com pulsive strategies to persuade authors to write and provide texts in time, a task which terrifies us. As a result, this volume is aimed at smoothly start ing a new kind of publication. What we would like to have is a collection of books organized like our seminar.
Contenuti
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 $$ {\left( {a_j^\dag ,{a_j}} \right)_{{H^L}}} $$.- 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.
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