Download Open Quantum Systems III: Recent Developments by Walter Aschbacher, Vojkan Jakšić, Yan Pautrat (auth.), PDF

By Walter Aschbacher, Vojkan Jakšić, Yan Pautrat (auth.), Stéphane Attal, Alain Joye, Claude-Alain Pillet (eds.)

Understanding dissipative dynamics of open quantum structures continues to be a problem in mathematical physics. This challenge is appropriate in numerous components of primary and utilized physics. From a mathematical viewpoint, it contains a wide physique of data. major development within the figuring out of such platforms has been made over the past decade. those books found in a self-contained method the mathematical theories thinking about the modeling of such phenomena. They describe bodily correct versions, enhance their mathematical research and derive their actual implications.

In quantity I the Hamiltonian description of quantum open platforms is mentioned. This contains an advent to quantum statistical mechanics and its operator algebraic formula, modular concept, spectral research and their functions to quantum dynamical systems.

Volume II is devoted to the Markovian formalism of classical and quantum open structures. an entire exposition of noise conception, Markov strategies and stochastic differential equations, either within the classical and the quantum context, is supplied. those mathematical instruments are positioned into standpoint with actual motivations and applications.

Volume III is dedicated to contemporary advancements and purposes. the subjects mentioned contain the non-equilibrium houses of open quantum structures, the Fermi Golden Rule and susceptible coupling restrict, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continuous quantum measurements.

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Extra resources for Open Quantum Systems III: Recent Developments

Sample text

Let βeq and µeq be given equilibrium values of the inverse temperature and the chemical potential. The affinities (thermodynamic forces) conjugated to the currents Φj and Jj are Yj = βj µj − βeq µeq . Xj = βeq − βj , Indeed, it follows from the conservations laws (12) and (39) that M Ep(ωλ+ ) = (Xj ωλ+ (Φj ) + Yj ωλ+ (Jj )) . j=1 Since ρβj µj (r) = 1 , 1 + eβeq (r−µeq )−(Xj r+Yj ) we have ∂Xk ρβj µj (r)|X=Y =0 = δkj ρ(r)(1 − ρ(r)) r, ∂Yk ρβj µj (r)|X=Y =0 = δkj ρ(r)(1 − ρ(r)), where ρ ≡ ρβeq µeq .

Assumption (SEBB2) implies that the function G(z) ≡ e+ e− |f (r)|2 dr = −i r−z ∞ g(t) e−itz dt, 0 which is obviously analytic in the lower half-plane C− ≡ {z | Im z < 0}, is con¯ − . We denote by G(r − io) the value of this tinuous and bounded on its closure C function at r ∈ R. Assumption (SEBB3) For j = 1, · · · , M , the generator TRj is the operator of multiplication by a continuous function ρj (r) such that 0 < ρj (r) < 1 for r ∈ (e− , e+ ). Moreover, if ρj (r) sj (r) ≡ log , 1 − ρj (r) we assume that sj (r)fj (r) ∈ L2 ((e− , e+ ), dr).

5 Fermi Golden Rule (FGR) Thermodynamics Let λ ∈ R be a control parameter. We consider an open quantum system with coupling λV and write τλ for τλV , ωλ+ for ω+ , etc. The NESS and thermodynamics of the system can be described, to second order of perturbation theory in λ, using the weak coupling (or van Hove) limit. This approach is much older than the ”microscopic” Hamiltonian approach discussed so far, and has played an important role in the development of the subject. The classical references are [Da1,Da2,Haa,VH1,VH2,VH3].

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