Quantum Poisson processes and dilations of dynamical semigroups

DOI10.1007/BF01845700zbMath0684.60081OpenAlexW1973287149MaRDI QIDQ1825539

Hans Maassen, Alberto Frigerio

Publication date: 1989

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01845700

zbMATH Keywords

quantum mechanicstransition operatorsquantum Poisson processquantum measure space

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items

Limit theorems for dilute quantum systems leading to quantum Poisson processes, Low density limit: Without rotating wave approximation, The low density limit in finite temperature case, The low-density limit in terms of collective squeezed vectors, Unnamed Item, The number process as low density limit of Hamiltonian models, Stochastic integration on the full Fock space with the help of a kernel calculus, Deformations of cocycles, quantum Lévy processes and quantum stochastic flows

Cites Work

• Stochastic dilations of uniformly continuous completely positive semigroups
• Quantum Ito's formula and stochastic evolutions
• Markov dilations and quantum detailed balance
• Fermion Ito's formula and stochastic evolutions
• Covariant Markov dilations of quantum dynamical semigroups
• Markov dilations on \(W^ *\)-algebras
• The essentially commutative dilations of dynamical semigroups on \(M_ n\)
• The Ito-Clifford integral
• Quantum detailed balance and KMS condition
• The low density limit for an N-level system interacting with a free Bose or Fermi gas
• Tomita's theory of modular Hilbert algebras and its applications
• Factorizable representation of current algebra. Non commutative extension of the Levy-Kinchin formula and cohomology of a solvable group with values in a Hilbert space
• Conditional expectations in von Neumann algebras
• Continuous tensor products of hilbert spaces and generalized random fields
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