Stochastic Analysis and Mathematical Physics II

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.- 2 Noncommutative large deviations.- 3 References.- 5 Gaussian Domination and Bose-Einstein Condensation.- 1 Introduction.- 2 Some Historical Remarks.- 3 Model Systems.- 4 Gaussian Domination and its Application to the Study of Bose Systems.- 5 References.- 6 Quantum Markov Semigroups and their Stationary States.- 1 Introduction.- 2 Ergodic theorems.- 3 The minimal quantum dynamical semigroup.- 4 The existence of Stationary States.- 5 Faithful Stationary States and Irreducibility.- 6 The convergence towards the equilibrium.- 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.- 3 Classical Manifestations of the Propagation of Quantum Molecular Chaos.- 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.