Characterization of states of infinite boson systems. I: On the construction of states of boson systems

DOI10.1007/BF02431883zbMath0723.60052OpenAlexW2092406917MaRDI QIDQ756851

Karl-Heinz Fichtner, Wolfgang Freudenberg

Publication date: 1991

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02431883

zbMATH Keywords

point processsecond quantizationposition measurementsconditional reduced density matrixinfinite boson systemslocal measurements

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Quantum field theory; related classical field theories (81T99) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Stochastic quantization (81S20)

Related Items

Quantum and non-causal stochastic calculus ⋮ Internal Noise Caused by the Memory ⋮ On the relations between Poissonian white noise analysis and harmonic analysis on configuration spaces ⋮ ON A CENTRAL LIMIT THEOREM FOR MONOTONE NOISE ⋮ A characterization of Gibbs states of lattice boson systems ⋮ Holomorphic Bogoliubov functionals for interacting particle systems in continuum ⋮ A canonical ensemble approach to the fermion/boson random point processes and its applications ⋮ Markov evolutions and hierarchical equations in the continuum. II: Multicomponent systems ⋮ On a Quantum Model of Brain Activities — Distribution of the Outcomes of EEG-Measurements and Random Point Fields ⋮ Bernstein theorems and transformations of correlation measures in statistical physics ⋮ The particle structure of the quantum mechanical Bose and Fermi gas ⋮ Characterization of states of infinite boson systems. I: On the construction of states of boson systems ⋮ Characterization of states of infinite boson systems. II: On the existence of the conditional reduced density matrix ⋮ Mean-field interacting boson random point fields in weak harmonic traps ⋮ Nonindependent splittings and Gibbs states ⋮ Large deviation principle for noninteracting boson random point processes ⋮ Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems. ⋮ Teleportation schemes in infinite dimensional Hilbert spaces ⋮ Time Evolution and Invariance of Boson Systems Given by Beam Splittings ⋮ On exchange mechanisms for bosons

Cites Work

• Characterization of states of infinite boson systems. I: On the construction of states of boson systems
• A remark on the integration of Schrödinger equation using quantum Itô's formula
• Canonical Gibbs measures. Some extensions of de Finetti's representation theorem for interacting particle systems
• Point processes and the position distribution of infinite boson systems
• Gibbsian random fields. The general case
• Integral representation of states on a \(C^*\)-algebra
• Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
• Bemerkungen zu einer Arbeit von NGUYEN XUAN XANH und HANS ZESSIN
• On a Probabilistic Model of Infinite Quantum Mechanical Particle Systems
• On the Position Distribution of the Ideal Bose Gas
• A Condition Σcλ for Point Processes
• On conditional intensities of point processes
• The conditional intensity of general point processes and an application to line processes
• The Mathematics of Second Quantization
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Characterization of states of infinite boson systems. I: On the construction of states of boson systems