where φ0 is real-valued. We are interested in the semiclassical limit ε → 0. The nonlinear Schrödinger equation (1) appears, for instance, in optics, and also as a model for Bose-Einstein condensates, with f(ρ) = ρ − 1, and the equation is termed Gross-Pitaevskii equation, or also with f(ρ) = ρ2 (see [13]). Some more complicated nonlinearities are also used especially in low dimensions, see [12...

In the context of statin monotherapy, the frequency of myopathy is ~1/1,000, and the frequency of rhabdomyolysis is ~1/100,000. The frequency increases with dose [7,8]. Clinicians often measure serum CK levels, as parameter of severity, but the correlation between symptoms and CK level is incomplete. Therefore, the clinical interpretation of CK level is complex. Elevations less than three-fold ...

We consider a two-level system, S2, coupled to a general n level system, Sn, via a random matrix. We derive an integral representation for the mean reduced density matrix ρ(t) of S2 in the limit n → ∞, and we identify a model of Sn which possesses some of the properties expected for macroscopic thermal reservoirs. In particular, it yields the Gibbs form for ρ(∞). We also consider an analog of t...

We consider a two level system, S2, coupled to a general n level system, Sn, via a random matrix. We derive an integral representation for the mean reduced density matrix ρ(t) of S2 in the limit n → ∞, and we identify a model of Sn which possesses some of the properties expected for macroscopic thermal reservoirs. In particular, it yields the Gibbs form for ρ(∞). We consider also an analog of t...