Quantum Interacting Particle Systems

The dynamics of infinite classical lattice systems has been considered and has led to the study of the properties of ergodicity and convergence to equilibrium of a new class of Markov semigroups. Quantum analogues of these semigroups have also been considered. However, the problem of deriving these Markovian semigroups and, what is much more interesting, the associated stochastic flows, as limits of Hamiltonian systems, rather than postulating their form on a phenomenological basis, is essentially open both in the classical case and in the quantum case.This book presents a conjecture that, by coupling a quantum spin system in finite volume to a quantum field via a suitable interaction, applying the stochastic golden rule and taking the thermodynamic limit, one may obtain a class of quantum flows which, when restricted to an appropriate Abelian subalgebra, gives rise to the classical interacting particle systems studied in classical statistical mechanics.

Product details

• Assisted by: Luigi Accardi (Editor), Accardi Luigi (Editor), Franco Fagnola (Editor), Fagnola Franco (Editor)
• Publisher: Ingram Publishers Services
• Languages: English
• Product format: Hardback
• Released: 22.07.2002
• EAN: 9789812381040
• ISBN: 978-981-238-104-0
• Series: Qp-Pq: Quantum Probability and; Qp-Pq: Quantum Probability and; Qp-pq: Quantum Probability And White Noise Analysis
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; MATHEMATICS / Probability & Statistics / General, SCIENCE / Physics / Quantum Theory, MATHEMATICS / Applied, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Particle & high-energy physics, Probability & statistics, Maths for scientists, Probability and statistics, Particle and high-energy physics, SCIENCE / Physics / Particle