Non-Relativistic Quantum Dynamics

Emergence of anomalous dynamics from the underlying singular continuous spectrum in interacting many-body systems

“…Let us introduce the Ruelle-Amrein-Georgescu-Enss (RAGE) theorem [44,46,47], which relates the time average of the mean of a compact operator to the presence of a continuous part. Given a compact operatorÂ, we define the time average of its expectation value at time t as…”

Long-Running-Time (T=0.45 K) Germanium Bolometer for Far Infrared Spectroscopy

“…If κ < 1, take κ 0 = 1 2 [κ + min(1, κ)] and β = 1 2 (1 − κ )(1 − κ 0 ) −1 . Then β ∈ ( 1 2 , 1], κ 0 ∈ (κ , min(1, κ)) and 1 2 − β + βκ 0 = κ 2 . (iii) It remains to carry out similar estimates for P θ(Q)U t g 3 j =1 P j θ(Q)U t g .…”

“…[1,2]). This formula expresses the probability of finding the scattered particles in the far future in a given cone in terms of the scattering operator S. As mentioned in [3], the relevance of such arguments relies on the assumption that the probability of finding a scattered particle at large times in some cone is identical with the scattered flux, integrated over time, across a distant surface subtending this cone.…”

Reducing Subspaces

“…L The question ''is H Raj a reducing subspace?'' appeared in [1,4] and was the original motivation for the present work. Corollary 2.1 also follows from Lyons's characterization of the Rajchman measures as those which give zero weight to all Weyl sets [5].…”