Luis Benet

Efficient quantum transport in disordered interacting many-body networks

The coherent transport of n fermions in disordered networks of l single-particle states connected by k-body interactions is studied. These networks are modeled by embedded Gaussian random matrix ensemble (EGE). The conductance bandwidth and the ensemble-averaged total current attain their maximal values if the system is highly filled n∼l-1 and k∼n/2. For the cases k=1 and k=n the bandwidth is minimal. We show that for all parameters the transport is enhanced significantly whenever centrosymmetric embedded Gaussian ensemble (csEGE) are considered. In this case the transmission shows numerous resonances of perfect transport. Analyzing the transmission by spectral decomposition, we find that centrosymmetry induces strong correlations and enhances the extrema of the distributions. This suppresses destructive interference effects in the system and thus causes backscattering-free transmission resonances that enhance the overall transport. The distribution of the total current for the csEGE has a very large dominating peak for n=l-1, close to the highest observed currents.

Quantum efficiencies in finite disordered networks connected by many‐body interactions

The quantum efficiency in the transfer of an initial excitation in disordered finite networks, modeled by the

Strands and braids in narrow planetary rings: a scattering system approach

k

Spectral domain of large nonsymmetric correlated Wishart matrices

-body embedded Gaussian ensembles of random matrices, is studied for bosons and fermions. The influence of the presence or absence of time-reversal symmetry and centrosymmetry/centrohermiticity are addressed. For bosons and fermions, the best efficiencies of the realizations of the ensemble are dramatically enhanced when centrosymmetry (centrohermiticity) is imposed. For few bosons distributed in two single-particle levels this permits perfect state transfer for almost all realizations when one-particle interactions are considered. For fermionic systems the enhancement is found to be maximal for cases when all but one single particle levels are occupied.

Fidelity decay in interacting two-level boson systems: freezing and revivals.

We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings are shepherded. We consider the problem as Hamiltonian scattering of a large number of non-interacting massless point particles in an effective potential. Using the existence of stable motion in scattering regions in this set up, we describe a mechanism in phase space for the occurrence of narrow rings and some consequences in their structure. We illustrate our approach with three examples. We find eccentric narrow rings displaying sharp edges, variable width and the appearance of distinct ring components (strands) which are spatially organized and entangled (braids). We discuss the relevance of our approach for narrow planetary rings.

Nearest-neighbor distributions and tunneling splittings in interacting many-body two-level boson systems

We study complex eigenvalues of the Wishart model for nonsymmetric correlation matrices. The model is defined for two statistically equivalent but different Gaussian real matrices, as C=AB(t)/T, where B(t) is the transpose of B and both matrices A and B are of dimensions N×T. If A and B are uncorrelated, or equivalently if C vanishes on average, it is known that at large matrix dimension the domain of the eigenvalues of C is a circle centered-at-origin and the eigenvalue density depends only on the radial distances. We consider actual correlation in A and B and derive a result for the contour describing the domain of the bulk of the eigenvalues of C in the limit of large N and T where the ratio N/T is finite. In particular, we show that the eigenvalue domain is sensitive to the correlations. For example, when C is diagonal on average with the same element c≠0, the contour is no longer a circle centered at origin but a shifted ellipse. In this case we explicitly derive a result for the spectral density which again depends only on the radial distances. For more general cases, we show that the contour depends on the symmetric and antisymmetric parts of the correlation matrix resulting from the ensemble-averaged C. If the correlation matrix is normal, then the contour depends only on its spectrum. We also provide numerics to justify our analytics.

Phase-Space Structure for Narrow Planetary Rings

We study the fidelity decay in the k-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the k-body embedded ensemble of random matrices and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time t(H). By selecting specific k-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of t(H), thus relating the period of the revivals with the range of the interaction k of the perturbing terms. Numerical calculations confirm the analytical results.

Multiple components in narrow planetary rings.

We study the nearest-neighbor distributions of the k -body embedded ensembles of random matrices for n bosons distributed over two-degenerate single-particle states. This ensemble, as a function of k , displays a transition from harmonic-oscillator behavior (k=1) to random-matrix-type behavior (k=n) . We show that a large and robust quasidegeneracy is present for a wide interval of values of k when the ensemble is time-reversal invariant. These quasidegenerate levels are Shnirelman doublets which appear due to the integrability and time-reversal invariance of the underlying classical systems. We present results related to the frequency in the spectrum of these degenerate levels in terms of k and discuss the statistical properties of the splittings of these doublets.

Numerical Results on a Simple Model for the Confinement of Saturn’s F Ring

We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non–interacting particles where open motion (escape) takes place, and includes the quasi–periodic perturbations of the shepherd’s Kepler motion with small and zero eccentricity. We concentrate in the phase–space structure and establish connections with properties like the eccentricity, sharp edges and narrowness of the ring. Within our scattering approach, the organizing centers necessary for the occurrence of the rings are stable periodic orbits, or more generally, stable tori. In the case of eccentric motion of the shepherd, the rings are narrower and display a gap which defines different components of the ring.

Narrow Rings: A Scattering Billiard Model

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with 2 degrees of freedom, respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.