Separated spectral functions for the quasifree12C(e,e′p)reaction

Abstract

A separation of the longitudinal and transverse 12 C(e,eЈp) cross sections in the quasifree region has been performed in parallel kinematics at Q 2 of 0.64 and 1.8 GeV 2 for initial proton momentum Ͻ80 MeV. The separated transverse and longitudinal spectral functions at Q 2 ϭ0.64 GeV 2 show significant differences for missing energy between 25 and 60 MeV indicating a breakdown in the single nucleon knockout picture. The transverse spectral functions exhibit definite momentum transfer dependence.PACS number͑s͒: 25.30.Fj, 25.30.Rw

Disorder perturbed flat bands. II. Search for criticality

“…As well-known, the standard Anderson transition undergoes a delocalization → localization transition with increasing disorder [19]. Notwithstanding these differences, the complexity parameter formulation predicts an Anderson analog of a weakly disordered flat band and also reveals its connection of to a wide range of other ensembles [27,28,39] of the same global constraint class; the prediction is verified by a numerical analysis discussed later in the paper. Although the theoretical analysis presented here is based on the Gaussian disorder in flat bands but it can also be extended to other type of disorders [18].…”

“…It also reveals an important analogy in the localization to delocalization crossover in finite systems: notwithstanding the difference in the number of critical points as well as equilibrium limits, the statistics of a disordered flat band can be mapped to that of a single parametric Brownian ensemble [20] as well as multi-parametric Anderson ensemble [19] (see section VI). The analogy of these ensembles to other multiparametric ensembles intermediate between Poisson and Wigner-Dyson is already known [18,20,27,39]. In fact it seems a wide range of localization → delocalization transition can be modeled by a single parameter Brownian ensemble appearing between Poisson and GOE (Rosenzweig-Porter ensemble) [28].…”

“…A detailed derivation of eq. (1) is technically complicated and is discussed in [17] for multi parametric Gaussian ensembles (also see [16,27]) and in [18] for multi-parametric non-Gaussian ensembles. As an example, consider the case which can be modelled by the…”

“…The mapping not only implies connections of the flat band statistics with the BE but also with other complex systems under similar global constraints e.g. symmetry conditions and conservation laws [27,28]. Additionally, as discussed in detail in [15], it also leads to a single parametric formulation of the level density and inverse participation ratio of the perturbed flat band.…”

Many-body approach to the properties of interacting atoms

“…Some typical diagrams for the "21 and YFi The HFS terms in the matrix elements are represented in the diagrams by wiggly lines terminating with a triangle. The frequency-dependent energy denominators involved in F," , PA, and p" of Equations (lo), (1 1 ), and (1 2) are seen to be different from those of F;" in Equation (9). To symbolize this difference we used "diamond" shaped diagrams for F t and /I" (and /IR) in Figures 2b and 2c in place of the usual lens-like ones for F f .…”