Lorenzo Sadun

Optimal Quantum Pumps

We study adiabatic quantum pumps on time scales that are short relative to the cycle of the pump. In this regime the pump is characterized by the matrix of energy shift which we introduce as the dual to Wigners time delay. The energy shift determines the charge transport, the dissipation, the noise, and the entropy production. We prove a general lower bound on dissipation in a quantum channel and define optimal pumps as those that saturate the bound. We give a geometric characterization of optimal pumps and show that they are noiseless and transport integral charge in a cycle. Finally we discuss an example of an optimal pump related to the Hall effect.

When shape matters: deformations of tiling spaces

We investigate the dynamics of tiling dynamical systems and their deformations. If two tiling systems have identical combinatorics, then the tiling spaces are homeomorphic, but their dynamical properties may differ. There is a natural map I from the parameter space of possible shapes of tiles to H of a model tiling space, with values in R. Two tiling spaces that have the same image under I are mutually locally derivable (MLD). When the difference of the images is “asymptotically negligible”, then the tiling dynamics are topologically conjugate, but generally not MLD. For substitution tilings, we give a simple test for a cohomology class to be asymptotically negligible, and show that infinitesimal deformations of shape result in topologically conjugate dynamics only when the change in the image of I is asymptotically negligible. Finally, we give criteria for a (deformed) substitution tiling space to be topologically weakly mixing. 1991 Mathematics Subject Classification. 37B50, 52C23, 37A20, 37A25, 52C22.

Chern Numbers, Quaternions, and Berry's Phases in Fermi Systems

Yes, but some parts are reasonably concrete.

Tiling spaces are inverse limits

Let M be an arbitrary Riemannian homogeneous space, and let Ω be a space of tilings of M, with finite local complexity (relative to some symmetry group Γ) and closed in the natural topology. Then Ω is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Γ. This result extends previous results of Anderson and Putnam, of Ormes, Radin, and Sadun, of Bellissard, Benedetti, and Gambaudo, and of Gahler. In particular, the construction in this paper is a natural generalization of Gahler’s.

When size matters: subshifts and their related tiling spaces

We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling space to be weakly mixing, and for the dynamics of two such spaces to be topologically conjugate.

Geometry, statistics, and asymptotics of quantum pumps

We give a pedestrian interpretation of a formula of Buttiker et. al. (BPT) relating the adiabatically pumped current to the S matrix and its (time) derivatives. We relate the charge in BPT to Berrys phase and the corresponding Brouwer pumping formula to curvature. As applications we derive explicit formulas for the joint probability density of pumping and conductance when the S matrix is uniformly distributed; and derive a new formula that describes hard pumping when the S matrix is periodic in the driving parameters.

Trapping and cascading of eigenvalues in the large coupling limit

AbstractWe consider eigenvaluesEλ of the HamiltonianHλ=−Δ+V+λW,W compactly supported, in the λ→∞ limit. ForW≧0 we find monotonic convergence ofEλ to the eigenvalues of a limiting operatorH∞ (associated with an exterior Dirichlet problem), and we estimate the rate of convergence for 1-dimensional systems. In 1-dimensional systems withW≦0, or withW changing sign, we do not find convergence. Instead, we find a cascade phenomenon, in which, as λ→∞, each eigenvalueEλ stays near a Dirichlet eigenvalue for a long interval (of lengthO(

Continuum Regularization of {QCD}

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