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WORLD SCIENTIFIC eBooks

Quantum probability & related topics : QP-PQ

Luigi Accardi, A. Frigerio

Published Jan 1, 1991• 0 citations
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Abstract

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.

Related papers

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)

WORLD SCIENTIFIC eBooks•Jan 1, 1998•1 citation

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

Luigi Accardi, Wilhelm von Waldenfels

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.

•May 1, 1988•1 citation

Quantum probability and infinite dimensional analysis : from foundations to applications : Krupp-Kolleg Greifswald, Germany, 22-28 June, 2003

Michael Schürmann, Uwe Franz

Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.) Generating Function Methods for Orthogonal Polynomials and Jacobi-Szego Parameters (N Asai et al.) Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V Belavkin & C Williams) A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A Belton) Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & M Lindsay) Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Levy Processes (V K Dobrev et al.) On Algebraic and Quantum Random Walks (D Ellinas) Dual Representations for the Schrodinger Algebra (P H Feinsilver & R Schott) A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.) On Quantum Logical Gates on a General Fock Space (W Feudenberg et al.) On an Argument of David Deutsch (R Gill) The Method of Double Product Integrals in Quantization of Lie Bialgebras (R Hudson) Asymptotics of Large Truncated Haar Unitary Matrices (J Reffy) Three Ways to Representations of Ba(E) (M Skeide) On Topological Entropy of Quotients and Extensions (J Zacharias) and other papers.

WORLD SCIENTIFIC eBooks•Jan 1, 2005•1 citation

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.

•Oct 1, 1989•0 citations

Proceedings of the second International Workshop, Stochastic Analysis and Mathematical Physics, ANESTOC '96 : Viña del Mar, Chile, 16-20 December 1996

Rolando Rebolledo

Feynman functional integrals and the stochastic limit, L. Accardi dynamical programming, filtering and control of quantum Markov processes, V.P. Belavkin quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrodinger equation, A.M. Chebotarev on phase transitions, M. Corgini existence of attractors for dissipative Schrodinger equation in R, M.A. Astaburuaga and V.H. Cortes reduction of noise by squeezed vacuum, F. Fagnola et al outgoing states and resonant behaviour, C. Fernandez stochastic Dyson series and the solution to associated stochastic evolution equations, G.W. Johnson and G. Kallianpur norm estimates for a class of semigroups of Schrodinger type, H. Prado on the recurrence of quantum dynamical semigroups, R. Rebolledo collective interactions in CQED, C. Saavedra T-product and Wiener Measure, D.P. Sankovich from Feynman-Kac formulae to Feynman-Kac semigroups, J.A. van Casteren completely positive quantum stochastic flows with infinite degrees of freedom, J. Lindsay and S.J. Wills characterization of continuous operators on infinite dimension distribution spaces, S.-L. Luo and J.-A. Yan a special time-dependent quantum invariant and a general theorem on quantum symmetries, J.-G. Zambrini.

WORLD SCIENTIFIC eBooks•Jan 1, 1998•1 citation

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.

Birkhäuser-Verlag eBooks•Jan 1, 2003•0 citations
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.
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)
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.
Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.) Generating Function Methods for Orthogonal Polynomials and Jacobi-Szego Parameters (N Asai et al.) Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V Belavkin & C Williams) A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A Belton) Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & M Lindsay) Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Levy Processes (V K Dobrev et al.) On Algebraic and Quantum Random Walks (D Ellinas) Dual Representations for the Schrodinger Algebra (P H Feinsilver & R Schott) A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.) On Quantum Logical Gates on a General Fock Space (W Feudenberg et al.) On an Argument of David Deutsch (R Gill) The Method of Double Product Integrals in Quantization of Lie Bialgebras (R Hudson) Asymptotics of Large Truncated Haar Unitary Matrices (J Reffy) Three Ways to Representations of Ba(E) (M Skeide) On Topological Entropy of Quotients and Extensions (J Zacharias) and other papers.
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.
Feynman functional integrals and the stochastic limit, L. Accardi dynamical programming, filtering and control of quantum Markov processes, V.P. Belavkin quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrodinger equation, A.M. Chebotarev on phase transitions, M. Corgini existence of attractors for dissipative Schrodinger equation in R, M.A. Astaburuaga and V.H. Cortes reduction of noise by squeezed vacuum, F. Fagnola et al outgoing states and resonant behaviour, C. Fernandez stochastic Dyson series and the solution to associated stochastic evolution equations, G.W. Johnson and G. Kallianpur norm estimates for a class of semigroups of Schrodinger type, H. Prado on the recurrence of quantum dynamical semigroups, R. Rebolledo collective interactions in CQED, C. Saavedra T-product and Wiener Measure, D.P. Sankovich from Feynman-Kac formulae to Feynman-Kac semigroups, J.A. van Casteren completely positive quantum stochastic flows with infinite degrees of freedom, J. Lindsay and S.J. Wills characterization of continuous operators on infinite dimension distribution spaces, S.-L. Luo and J.-A. Yan a special time-dependent quantum invariant and a general theorem on quantum symmetries, J.-G. Zambrini.
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 ⟨n^j⟩ \left\langle {{{\hat n}_j}} \right\rangle ⟨n^j​⟩.- 4.4 Gaussian Domination and upper bound on (aj†,aj)HL {\left( {a_j^\dag ,{a_j}} \right)_{{H^L}}} (aj†​,aj​)HL​.- 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.