Continuum shell model: From Ericson to conductance fluctuations

Abstract

We discuss an approach for studying the properties of mesoscopic systems, where discrete and continuum parts of the spectrum are equally important. The approach can be applied (i) to stable heavy nuclei and complex atoms near the continuum threshold, (ii) to nuclei far from the region of nuclear stability, both of the regions being of great current interest, and (iii) to mesoscopic devices with interacting electrons. The goal is to develop a new consistent version of the continuum shell model that simultaneously takes into account strong interaction between fermions and coupling to the continuum. Main attention is paid to the formation of compound resonances, their statistical properties, and correlations of the cross sections. We study the Ericson fluctuations of overlapping resonances and show that the continuum shell model nicely describes universal properties of the conductance fluctuations.Comment: 10 pages, 6 figures, corrected style and figure

Internal chaos in an open quantum system: From Ericson to conductance fluctuations

“…Correspondingly, the distribution of poles of the scattering matrix undergoes a transition from one to two "clouds" of poles in the complex plane of resonance energies [24]; the number of broad states coincides with the number M of open channels (the rank of the matrix W ). For the model (1), the statistical properties of resonances as a function of the interaction between particles and the coupling to continuum have been thoroughly studied in earlier papers [18,25]. Our main interest is in the dependence of fluctuation and correlation properties of scattering on the degree of internal chaos and strength of continuum coupling.…”

Open system of interacting fermions: Statistical properties of cross sections and fluctuations

“…In the present work, using the same framework as in [29], we study the interplay between the intrinsic dynamics and statistical properties of cross sections comparing the results with those of conventional approaches, namely Hauser-Feshbach average cross sections and Ericson fluctuations and correlations. In particular, we show that the assumption that fluctuations of the resonance widths are negligible for a large number of channels is not correct.…”

“…The energy interval subject to statistical analysis should be also at a distance of at least several widths away from the edges. A rough estimate [29] goes as follows: for M equivalent channels, Γ/D ∝ M , and the distance from the center to the edges is N D/2, then N D/2 ≫ Γ/D that implies M/N ≪ 1/2. This shows that the ratio of the number of channels to that of resonances must be small in order for the results to be model independent.…”

“…The width distribution reveals the separation of the "cloud" of superradiant states far from the real energy axis, while the trapped states are clearly accumulated near the real axis. Some features of the picture are however sensitive to the character and strength of intrinsic interactions as we have demonstrated recently [29]. The analysis included the two-body random ensemble of variable interaction strength in a Fermi system of shell-model type and the GOE as an extreme limit of many-body random interaction.…”

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

“…In the majority of scattering experiments, particularly in quantum physics, the phase is not accessible. In mesoscopic quantum dots [26] the electron transport, that is, the conductance is measured instead, of which the fluctuations are well understood [13,14,27,28]. In a scattering experiment involving quantum particles, i.e., atoms [29][30][31][32], molecules [33,34] or nuclei [35], only the incoming and outgoing particle current can be measured.…”