By Howard Carmichael

This quantity includes ten lectures awarded within the sequence ULB Lectures in Nonlinear Optics on the Universite Libre de Bruxelles through the interval October 28 to November four, 1991. a wide a part of the 1st six lectures is taken from fabric ready for a publication of a bit higher scope with a view to be published,by Springer lower than the identify Quantum Statistical equipment in Quantum Optics. The primary reason behind the early ebook of the current quantity issues the cloth inside the final 4 lectures. the following i've got prepare, in a roughly systematic manner, a few rules in regards to the use of stochastic wavefunctions within the conception of open quantum optical structures. those rules have been built with the aid of of my scholars, Murray Wolinsky and Liguang Tian, over a interval of roughly years. they're outfitted on a starting place laid down in a paper written with Surendra Singh, Reeta Vyas, and Perry Rice on waiting-time distributions and wavefunction cave in in resonance fluorescence [Phys. Rev. A, 39, 1200 (1989)]. The ULB lecture notes comprise my first severe atte~pt to provide an entire account of the guidelines and their capability purposes. i'm thankful to Professor Paul Mandel who, via his invitation to provide the lectures, inspired me to prepare anything important out of labor that can, another way, have waited significantly longer to be introduced jointly.

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**Additional info for An open systems approach to quantum optics: lectures presented at the Universite libre de Bruxelles, October 28 to November 4, 1991**

**Sample text**

Fluctuation theorem . . . . . . . . . . . . . . . . . . . . Kubo Formula and Central Limit Theorem . . . . . . . . . . . 69 71 75 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e. with a finite number of degrees of freedom) in contact with one or several large reservoirs. There are several ways to model reservoirs and we will take the point of view that the reservoirs are also Hamiltonian systems themselves.

It is also mathematically 42 Luc Rey-Bellet convenient to assume that the Gibbs measures of the reservoir have very good ergodic properties. e the Gibbs measures are Gaussian measures). Our model of a reservoir will be the classical field theory given by a linear wave equation in Rd ∂t2 ϕt (x) = ∆ϕt (x) . (1) This is a Hamiltonian system for the Hamiltonian (|∇x ϕ(x)|2 + |π(x)|2 ) . H(ϕ, π) = (2) Rd If we consider a single particle in a confining potential with Hamiltonian H(p, q) = p2 + V (q) , 2 (3) we will take as Hamiltonian of the complete system ∇ϕ(x)ρ(x) dx , H(ϕ, π) + H(p, q) + q (4) Rd which corresponds to a dipole coupling approximation (ρ(x) is a given function which models the coupling of the particle with the field).

Fluctuation theorem . . . . . . . . . . . . . . . . . . . . Kubo Formula and Central Limit Theorem . . . . . . . . . . . 69 71 75 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e. with a finite number of degrees of freedom) in contact with one or several large reservoirs. There are several ways to model reservoirs and we will take the point of view that the reservoirs are also Hamiltonian systems themselves. It is a convenient physical and mathematical idealization to separate scales and assume that the reservoirs have infinitely many degrees of freedom.