Quantum Probability and Applications III: Proceedings of a Conference Held in Oberwolfach, Frg, January 25-31, 1987

Luigi Accardi, Wilhelm von Waldenfels

Published May 1, 1988• 1 citation

Abstract

A note on Meyer's note.- Stochastic integration.- Quantum stochastic parallel transport on non-commutative vector bundles.- Input and output channels in quantum systems and quantum stochastic differential equations.- Some noncommutative Radon-Nikodym Theorems for von Neumann algebras.- Multidimensional quantum diffusions.- An application of de finetti's theorem.- The quantum Langevin equation from the independent-oscillator model.- Quantum poisson processes: Physical motivations and applications.- A noncommutative generalization of conditionally positive definite functions.- Contraction semigroups in L2 over a von neumann algebra.- Survey on a theory of non-commutative stationary markov processes.- Dynamical entropy for quantum systems.- An integral kernel approach to noise.- A note on shifts and cocycles.- Local measures in fock space stochastic calculus and a generalized ito-tanaka formula.- Representation of a class of quantum martingales II.- Conditional expectation in quantum probability.- Mutual quadratic variation and ito's table in quantum stochastic calculus.- On mixing properties of automorphisms of von neumann algebras related to measure space transformations.- First exit time: A theory of stopping times in quantum processes.- A central limit theorem on the free lie group.- Entropy, observability and the generalised second law of thermodynamics.- Remarks on asymptotic properties of groups of the bogoliubov transformations of car c*-algebras.- Linear and non-linear stochastic processes.- Detailed balance and critical slowing down.- Quantum martingales and stochastic integrals.

Related papers

Quantum Probability and Applications IV: Proceedings of the Year of Quantum Probability, Held at the University of Rome Ii, Italy, 1987

Luigi Accardi, Wilhelm von Waldenfels

Oct 1, 19890 citations

Quantum probability communications : QP-PQ

R. L. Hudson, J. Martin Lindsay, Philippe Biane +1 more

WORLD SCIENTIFIC eBooksJan 1, 19981 citation

Stochastic processes in quantum physics

正雄長沢

Birkhäuser-Verlag eBooksJan 1, 20002 citations

Stochastic analysis and mathematical physics II : 4th International ANESTOC Workshop in Santiago, Chile

Rolando Rebolledo, Anestoc

Birkhäuser-Verlag eBooksJan 1, 20030 citations

Quantum probability & related topics : QP-PQ

Luigi Accardi, A. Frigerio

WORLD SCIENTIFIC eBooksJan 1, 19910 citations

Quantum probability and related topics : proceedings of the 28th conference CIMAT-Guanajuato, Mexico, 2-8 September 2007

Related Topics, J. C. García, Roberto B. Quezada +1 more

WORLD SCIENTIFIC eBooksJan 1, 20080 citations

Quantum Probability and Applications III: Proceedings of a Conference Held in Oberwolfach, Frg, January 25-31, 1987

Luigi Accardi, Wilhelm von Waldenfels

Published May 1, 1988• 1 citation

OpenAlex

Abstract

Related papers

Quantum Probability and Applications IV: Proceedings of the Year of Quantum Probability, Held at the University of Rome Ii, Italy, 1987

Luigi Accardi, Wilhelm von Waldenfels

Cecchini's transition expectations and markov chains.- Central limits of squeezing operators.- On the weak coupling limit problem.- On multi-dimensional markovian cocycles.- Quantum stop times.- Quantum random walks.- Unitary dilation of a nonlinear quantum boltzmann equation.- On isometries of non associative Lp-spaces.- Convolution semigroups in quantum probability and quantum stochastic calculus.- Stochastic couplings for von neumann algebras.- The covering property in a causal logic.- Temperature states of spin-boson models.- Bernoulli fields.- The relations of the non-commutative coefficient algebra of the unitary group.- Orthogonal series and strong laws of large numbers in von neumann algebras.- Limit theorems for repeated measurements and continuous measurement processes.- Quantum diffusions on the algebra of all bounded operators on a hilbert space.- Asymptotic formula for normal operators in non-commutative L2-spaces.- Convergences in W*-algebras - Their strange behaviour and tools for their investigation.- Positive mappings on matrix algebras.- Fluctuations of the dicke maser.- Tangent bimodule and locality for dissipative operators on C*-algebras.- Noncommutative stochastic processes with independent and stationary additive increments.- The atom in the radiation field as a quantum stochastic process.Cecchini's transition expectations and markov chains.- Central limits of squeezing operators.- On the weak coupling limit problem.- On multi-dimensional markovian cocycles.- Quantum stop times.- Quantum random walks.- Unitary dilation of a nonlinear quantum boltzmann equation.- On isometries of non associative Lp-spaces.- Convolution semigroups in quantum probability and quantum stochastic calculus.- Stochastic couplings for von neumann algebras.- The covering property in a causal logic.- Temperature states of spin-boson models.- Bernoulli fields.- The relations of the non-commutative coefficient algebra of the unitary group.- Orthogonal series and strong laws of large numbers in von neumann algebras.- Limit theorems for repeated measurements and continuous measurement processes.- Quantum diffusions on the algebra of all bounded operators on a hilbert space.- Asymptotic formula for normal operators in non-commutative L2-spaces.- Convergences in W*-algebras - Their strange behaviour and tools for their investigation.- Positive mappings on matrix algebras.- Fluctuations of the dicke maser.- Tangent bimodule and locality for dissipative operators on C*-algebras.- Noncommutative stochastic processes with independent and stationary additive increments.- The atom in the radiation field as a quantum stochastic process.

Oct 1, 19890 citations

Quantum probability communications : QP-PQ

R. L. Hudson, J. Martin Lindsay, Philippe Biane +1 more

Extensions of Quantum Stochastic Calculus (S Attal) Quantum Ito Algebras: Axioms, Representations, Decompositions (V Belavkin) Free Probability for Probabilists (P Biane) Conditional Expectations on von Neumann Algebras (C Cecchini) Classical Probability Theory: An Outline of Stochastic Integrals and Diffusions (M Emery) Quantum Stochastic Differential Equations (F Fagnola) Canonical Commutation and Anticommutation Relations (M Fannes) Quantum and Classical Stochastic Calculus (A Holevo) An Introduction to Quantum Stochastic Calculus and Some of Its Applications (R Hudson) Stationary Processes in Quantum Probability (B Kummerer)Extensions of Quantum Stochastic Calculus (S Attal) Quantum Ito Algebras: Axioms, Representations, Decompositions (V Belavkin) Free Probability for Probabilists (P Biane) Conditional Expectations on von Neumann Algebras (C Cecchini) Classical Probability Theory: An Outline of Stochastic Integrals and Diffusions (M Emery) Quantum Stochastic Differential Equations (F Fagnola) Canonical Commutation and Anticommutation Relations (M Fannes) Quantum and Classical Stochastic Calculus (A Holevo) An Introduction to Quantum Stochastic Calculus and Some of Its Applications (R Hudson) Stationary Processes in Quantum Probability (B Kummerer)

WORLD SCIENTIFIC eBooksJan 1, 19981 citation

Stochastic processes in quantum physics

正雄長沢

I Markov Processes.- 1.1 Classical Mechanics.- 1.2 Movement of a Particle with Noise.- 1.3 Transition Probability and the Markov Property.- 1.4 Diffusion Equations.- 1.5 Brownian Motions.- 1.6 The Ito formula.- Appendix. Monotone Lemmas.- II Time Reversal and Duality.- 2.1 Time Reversal of Markov Processes and Duality.- 2.2 Space-Time Markov Processes and Space-Time Duality.- 2.3 Time Reversal and Schroedinger's Representation.- III Non-Relativistic Quantum Theory.- 3.1 Non-Relativistic Equation of Motion.- 3.2 Stationary States and Eigenvalue Problem.- 3.3 Time Reversal of Diffusion Processes.- 3.4 Duality Relation of Diffusion Processes.- 3.5 Equation of Motion in General Cases.- 3.6 Principle of Superposition of Markov Processes.- 3.7 Non-Relativistic Schroedinger Equation.- 3.8 State Preparations and Measurements.- 3.9 Diffusion or Schroedinger Equations ?.- 3.10 The First Technical Convention.- IV Stationary Schroedinger Processes.- 4.1 Stationary States.- 4.2 One-Dimensional Harmonic Oscillator.- 4.3 An Example in Two-Dimension.- 4.4 Superposition of Eigenfunctions.- 4.5 Further Excited States.- 4.6 Hydrogen Atom.- V Construction of the Schroedinger Processes.- 5.1 The Feynman-Kac Formula.- 5.2 Solving the Equation of Motion.- 5.3 Transformation by Multiplicative Functionals.- 5.4 Renormalization.- 5.5 A Variational Method.- 5.6 The Maruyama-Girsanov Formula.- 5.7 A Lagrangian Formulation.- 5.8 The Second Technical Convention.- VI Markov Processes with Jumps.- 6.1 Poisson and Compound Poisson Processes.- 6.2 Poisson Random measures and Point Processes.- 6.3 Stochastic Integrals with Poisson Point Processes.- 6.4 Levy Processes.- 6.5 Stable Processes.- 6.6 Bochner's Subordination.- 6.7 Duality of Subordinate Semi-Groups.- 6.8 Harmonic Transformation of Subordinate Semi-Groups.- 6.9 Duality of Fractional Powers of Time-Dependent Operators.- VII Relativistic Quantum Particles.- 7.1 A Relativistic Schroedinger Equation for a Spinless Paticle.- 7.2 Equation of Motion for Relativistic Quantum Particles.- 7.3 Stationary States of the Relativistic Schroedinger Equation.- 7.4 Stochastic Processes for Relativistic Spinless Particles.- 7.5 Non-Relativistic Limit.- 7.6 A Diffusion Approximation.- VIII Stochastic Differential Equations of Pure-Jumps.- 8.1 Markov Processes with the Generators of Fractional Power.- 8.2 Stochastic Differential Equations of Pure-Jumps.- 8.3 The Case with no Potential Term.- 8.4 To Solve the Stochastic Differential Equations of Pure-Jumps.- 8.5 To Construct Pure-Jump Markov Processes.- 8.6 A Remark on the Integrability Condition.- IX Variational Principle for Relativistic Quantum Particles.- 9.1 Absolute Continuity.- 9.2 Pure-Jump Markov Processes.- 9.3 A Multiplicative Functional.- 9.4 Renormalization and Variational Principle.- X Time Dependent Subordination and Markov Processes with Jumps.- 10.1 Time-Inhomogeneous Subordination.- 10.2 Lemmas.- 10.3 Stochastic Differential Equation with Jumps.- 10.4 A Formula of Feynman-Kac Type.- 10.5 Markov Processes with Jumps.- Appendix. Integration by Parts Formulae.- XI Concave Majorants of Levy Processes and the Light Cone.- 14.1 The Vertex Process of a Levy Process.- 14.2 Propositions on Random walks.- 14.3 Proof of Propositions on Random Walks.- 14.4 Proof of the main Theorems.- 14.5 Examples.- 14.6 The light Cone.- XII The Locality in Quantum Physics.- 12.1 Historical Overview.- 12.2 Hidden-Variable Theories.- 12.3 Locality of Hidden-Variable Theories.- 12.4 Spin-Correlation of Three Particles.- 12.5 Gudder's Hidden-Variable Theory.- 12.6 Spin-Correlations in Gudder's Theory.- 12.7 Some Remarks.- XIII Micro Statistical Theory.- 13.1 The Source of the Noise.- 13.2 Large Deviations of the Renormalized Processes.- 13.3 The Propagation of Chaos.- 13.4 Micro Statistical Mechanics.- 13.5 Propagation of Chaos of Pure-Jump Processes.- 13.6 Superposition of Movements.- 12.7 A Remark on the Gibbs Distribution.- XIV Processes on Open Time Intervals.- 14.1 Diffusion Processes on Open Time Intervals.- 14.2 Time-Reversed Schroedinger Processes.- 14.3 A Theorem of Jeulin-Yor.- 14.4 Reflecting Brownian Motion.- 14.5 Two-Sided Skorokhod Type Problem.- 14.6 Skorokhod Problem with Singular Drift.- 14.7 The Minimum and Maximum Solutions.- 14.8 The Uniqueness and Non-Uniqueness of Solutions.- 14.9 An Application: The Origin of Universes.- XV Creation and Killing of Particles.- 15.1 Non-Linear Differential Equations.- 15.2 Branching Markov Processes.- 15.3 The Expected Number of Particles.- 15.4 Killing.- XVI The lto Calculus.- 16.1 The Ito Integral.- 16.2 Martingales.- 16.3 The Ito Integral with Local Martingales.- 16.4 Ito's formula.- 16.5 Stochastic Differential Equations.- 16.6 Stochastic Differential Calculus.- References.I Markov Processes.- 1.1 Classical Mechanics.- 1.2 Movement of a Particle with Noise.- 1.3 Transition Probability and the Markov Property.- 1.4 Diffusion Equations.- 1.5 Brownian Motions.- 1.6 The Ito formula.- Appendix. Monotone Lemmas.- II Time Reversal and Duality.- 2.1 Time Reversal of Markov Processes and Duality.- 2.2 Space-Time Markov Processes and Space-Time Duality.- 2.3 Time Reversal and Schroedinger's Representation.- III Non-Relativistic Quantum Theory.- 3.1 Non-Relativistic Equation of Motion.- 3.2 Stationary States and Eigenvalue Problem.- 3.3 Time Reversal of Diffusion Processes.- 3.4 Duality Relation of Diffusion Processes.- 3.5 Equation of Motion in General Cases.- 3.6 Principle of Superposition of Markov Processes.- 3.7 Non-Relativistic Schroedinger Equation.- 3.8 State Preparations and Measurements.- 3.9 Diffusion or Schroedinger Equations ?.- 3.10 The First Technical Convention.- IV Stationary Schroedinger Processes.- 4.1 Stationary States.- 4.2 One-Dimensional Harmonic Oscillator.- 4.3 An Example in Two-Dimension.- 4.4 Superposition of Eigenfunctions.- 4.5 Further Excited States.- 4.6 Hydrogen Atom.- V Construction of the Schroedinger Processes.- 5.1 The Feynman-Kac Formula.- 5.2 Solving the Equation of Motion.- 5.3 Transformation by Multiplicative Functionals.- 5.4 Renormalization.- 5.5 A Variational Method.- 5.6 The Maruyama-Girsanov Formula.- 5.7 A Lagrangian Formulation.- 5.8 The Second Technical Convention.- VI Markov Processes with Jumps.- 6.1 Poisson and Compound Poisson Processes.- 6.2 Poisson Random measures and Point Processes.- 6.3 Stochastic Integrals with Poisson Point Processes.- 6.4 Levy Processes.- 6.5 Stable Processes.- 6.6 Bochner's Subordination.- 6.7 Duality of Subordinate Semi-Groups.- 6.8 Harmonic Transformation of Subordinate Semi-Groups.- 6.9 Duality of Fractional Powers of Time-Dependent Operators.- VII Relativistic Quantum Particles.- 7.1 A Relativistic Schroedinger Equation for a Spinless Paticle.- 7.2 Equation of Motion for Relativistic Quantum Particles.- 7.3 Stationary States of the Relativistic Schroedinger Equation.- 7.4 Stochastic Processes for Relativistic Spinless Particles.- 7.5 Non-Relativistic Limit.- 7.6 A Diffusion Approximation.- VIII Stochastic Differential Equations of Pure-Jumps.- 8.1 Markov Processes with the Generators of Fractional Power.- 8.2 Stochastic Differential Equations of Pure-Jumps.- 8.3 The Case with no Potential Term.- 8.4 To Solve the Stochastic Differential Equations of Pure-Jumps.- 8.5 To Construct Pure-Jump Markov Processes.- 8.6 A Remark on the Integrability Condition.- IX Variational Principle for Relativistic Quantum Particles.- 9.1 Absolute Continuity.- 9.2 Pure-Jump Markov Processes.- 9.3 A Multiplicative Functional.- 9.4 Renormalization and Variational Principle.- X Time Dependent Subordination and Markov Processes with Jumps.- 10.1 Time-Inhomogeneous Subordination.- 10.2 Lemmas.- 10.3 Stochastic Differential Equation with Jumps.- 10.4 A Formula of Feynman-Kac Type.- 10.5 Markov Processes with Jumps.- Appendix. Integration by Parts Formulae.- XI Concave Majorants of Levy Processes and the Light Cone.- 14.1 The Vertex Process of a Levy Process.- 14.2 Propositions on Random walks.- 14.3 Proof of Propositions on Random Walks.- 14.4 Proof of the main Theorems.- 14.5 Examples.- 14.6 The light Cone.- XII The Locality in Quantum Physics.- 12.1 Historical Overview.- 12.2 Hidden-Variable Theories.- 12.3 Locality of Hidden-Variable Theories.- 12.4 Spin-Correlation of Three Particles.- 12.5 Gudder's Hidden-Variable Theory.- 12.6 Spin-Correlations in Gudder's Theory.- 12.7 Some Remarks.- XIII Micro Statistical Theory.- 13.1 The Source of the Noise.- 13.2 Large Deviations of the Renormalized Processes.- 13.3 The Propagation of Chaos.- 13.4 Micro Statistical Mechanics.- 13.5 Propagation of Chaos of Pure-Jump Processes.- 13.6 Superposition of Movements.- 12.7 A Remark on the Gibbs Distribution.- XIV Processes on Open Time Intervals.- 14.1 Diffusion Processes on Open Time Intervals.- 14.2 Time-Reversed Schroedinger Processes.- 14.3 A Theorem of Jeulin-Yor.- 14.4 Reflecting Brownian Motion.- 14.5 Two-Sided Skorokhod Type Problem.- 14.6 Skorokhod Problem with Singular Drift.- 14.7 The Minimum and Maximum Solutions.- 14.8 The Uniqueness and Non-Uniqueness of Solutions.- 14.9 An Application: The Origin of Universes.- XV Creation and Killing of Particles.- 15.1 Non-Linear Differential Equations.- 15.2 Branching Markov Processes.- 15.3 The Expected Number of Particles.- 15.4 Killing.- XVI The lto Calculus.- 16.1 The Ito Integral.- 16.2 Martingales.- 16.3 The Ito Integral with Local Martingales.- 16.4 Ito's formula.- 16.5 Stochastic Differential Equations.- 16.6 Stochastic Differential Calculus.- References.

Birkhäuser-Verlag eBooksJan 1, 20002 citations

Stochastic analysis and mathematical physics II : 4th International ANESTOC Workshop in Santiago, Chile

Rolando Rebolledo, Anestoc

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.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.

Birkhäuser-Verlag eBooksJan 1, 20030 citations

Quantum probability & related topics : QP-PQ

Luigi Accardi, A. Frigerio

On the stochastic limit of quantum chromodynamics, L. Accardi et al flows and imprimitivity systems, L. Accardi and A. Mohari fermion stochastic flows on quantum algebras, D. Applebaum examples of unbounded generators leading to nonconservative minimal semigroups, R.B.V. Bhat and K.B. Sinha on the structure of quantum Markov processes, C. Cecchini diffusion processes in fock space, F. Fagnola on the isomorphism of Poisson space and symmetric fock space, V. Liebscher non-linear master equation and non-crossing cumulants, P. Neu and R. Speicher a general central limit theorem and invariance principle, R. Speicher and W. von Waldenfels.On the stochastic limit of quantum chromodynamics, L. Accardi et al flows and imprimitivity systems, L. Accardi and A. Mohari fermion stochastic flows on quantum algebras, D. Applebaum examples of unbounded generators leading to nonconservative minimal semigroups, R.B.V. Bhat and K.B. Sinha on the structure of quantum Markov processes, C. Cecchini diffusion processes in fock space, F. Fagnola on the isomorphism of Poisson space and symmetric fock space, V. Liebscher non-linear master equation and non-crossing cumulants, P. Neu and R. Speicher a general central limit theorem and invariance principle, R. Speicher and W. von Waldenfels.

WORLD SCIENTIFIC eBooksJan 1, 19910 citations

Quantum probability and related topics : proceedings of the 28th conference CIMAT-Guanajuato, Mexico, 2-8 September 2007

Related Topics, J. C. García, Roberto B. Quezada +1 more

Linear Independence of the Renormalized Higher Powers of White Noise (L Accardi & A Boukas) Brownian Dynamics Simulation for Protein Holding and Binding (T Ando) Quantum Fokker-Planck Models: the Lindblad and the Wigner Approaches (A Arnold et al.) Free Martingale Polynomials for Stationary Jacobi Processes (N Demni) Accardi Complementarity for -1/2 < A < 0 and Related Results (L A Echavarria et al.) Quantum Models of Brain Activity I. Recognition of Signals (K H Fichtner & L Fichtner) Central Decompositions of Endomorphisms of von Neumann Algebras (R Floricel) Schrodinger Equation, Lp-Duality and the Geometry of Wigner-Yanase-Dyson Information (P Gibilisco et al.) Multiplicative Renormalization Method for Orthogonal Polynomials (H H Kuo) Quantum Lp and Orlicz Spaces (L E Labuschagne & W Majewski) Vicious Random Walkers and Truncated Haar Unitaries (J I Novak) Incoherent Quantum Control (A Pechen & H Rabitz) Compromising Non-demolition and Information Gaining for Qubit State Estimation (L Rupper et al.) Positivity of Free Convolution Semigroups (M Schurman & S VoA ) Quasi-Free Stochastic Integrals and Martingale Representation (W J Spring) A Method of Recovering the Moments of a Probability Measure from Commutators (A I Stan & J J Whitaker) Description of Decoherence by Means of Translation Covariant Master Equation and Levy Processes (B Vachinni) and other papersLinear Independence of the Renormalized Higher Powers of White Noise (L Accardi & A Boukas) Brownian Dynamics Simulation for Protein Holding and Binding (T Ando) Quantum Fokker-Planck Models: the Lindblad and the Wigner Approaches (A Arnold et al.) Free Martingale Polynomials for Stationary Jacobi Processes (N Demni) Accardi Complementarity for -1/2 < A < 0 and Related Results (L A Echavarria et al.) Quantum Models of Brain Activity I. Recognition of Signals (K H Fichtner & L Fichtner) Central Decompositions of Endomorphisms of von Neumann Algebras (R Floricel) Schrodinger Equation, Lp-Duality and the Geometry of Wigner-Yanase-Dyson Information (P Gibilisco et al.) Multiplicative Renormalization Method for Orthogonal Polynomials (H H Kuo) Quantum Lp and Orlicz Spaces (L E Labuschagne & W Majewski) Vicious Random Walkers and Truncated Haar Unitaries (J I Novak) Incoherent Quantum Control (A Pechen & H Rabitz) Compromising Non-demolition and Information Gaining for Qubit State Estimation (L Rupper et al.) Positivity of Free Convolution Semigroups (M Schurman & S VoA ) Quasi-Free Stochastic Integrals and Martingale Representation (W J Spring) A Method of Recovering the Moments of a Probability Measure from Commutators (A I Stan & J J Whitaker) Description of Decoherence by Means of Translation Covariant Master Equation and Levy Processes (B Vachinni) and other papers

WORLD SCIENTIFIC eBooksJan 1, 20080 citations

\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.