Two interacting particles in a random potential: mapping onto one parameter localization theories without interaction

We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correpondences we demonstrate that both cases can be described in terms familiar from theories of noninteracting particles. In particular, these two cases are shown to be controlled by a single scaling variable, namely the pair conductance $g_2$. For an attractive or repulsive Hubbard interaction and starting from a certain effective Hamiltonian we derive a supersymmetric nonlinear $\sigma$ model. Its action turns out to be closely related to the one found by Efetov for noninteracting electrons in disordered metals. This enables us to describe the diffusive motion of the particle pair on scales exceeding the one-particle localization length $L_1$ and to discuss the corresponding level statistics. For tightly bound pairs in one dimension, on the other hand, we follow early work by Dorokhov and exploit the analogy with the transfer matrix approach to quasi 1d conductors. Extending our study to M particles we obtain a M-particle localization length scaling like the Mth power of the one-particle localization length.Comment: 29 pages, Revtex, no figure

Imaging and manipulating electrons in a 1D quantum dot with Coulomb blockade microscopy

Motivated by the recent experiments by the Westervelt group using a mobile tip to probe the electronic state of quantum dots formed on a segmented nanowire, we study the shifts in Coulomb blockade peak positions as a function of the spatial variation of the tip potential, which can be termed "Coulomb blockade microscopy". We show that if the tip can be brought sufficiently close to the nanowire, one can distinguish a high density electronic liquid state from a Wigner crystal state by microscopy with a weak tip potential. In the opposite limit of a strongly negative tip potential, the potential depletes the electronic density under it and divides the quantum wire into two partitions. There the tip can push individual electrons from one partition to the other, and the Coulomb blockade micrograph can clearly track such transitions. We show that this phenomenon can be used to qualitatively estimate the relative importance of the electron interaction compared to one particle potential and kinetic energies. Finally, we propose that a weak tip Coulomb blockade micrograph focusing on the transition between electron number N=0 and N=1 states may be used to experimentally map the one-particle potential landscape produced by impurities and inhomogeneities.Comment: 4 pages 7 figure

Fine Structure and Fractional Aharonov-Bohm Effect

We find a fine structure in the Aharonov-Bohm effect, characterized by the appearence of a new type of periodic oscillations having smaller fractional period and an amplitude, which may compare with the amplitude of the conventional Aharonov-Bohm effect. Specifically, at low density or strong coupling on a Hubbard ring can coexist along with the conventional Aaronov-Bohm oscillations with the period equal to an integer, measured in units of the elementary flux quantum, two additional oscillations with periods $1/N$ and $M/N$. The integers $N$ and $M$ are the particles number and the number of down-spin particles, respectively. {}From a solution of the Bethe ansatz equations for $N$ electrons located on a ring in a magnetic field we show that the fine structure is due to electron-electron and Zeeman interactions. Our results are valid in the dilute density limit and for an arbitrary value of the Hubbard repulsion $U$Comment: 40 pages (Latex,Revtex) 12 figures by request, in Technical Reports of ISSP , Ser. A, No.2836 (1994

Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model

The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions. In the present study, we determine the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. For this, the sheet structure of the amplitude is determined. To show the precision of the resonance extraction and discuss phenomena such as resonance interference, we discuss the S11 amplitude in greater detail.Comment: 22 pages, 22 figure

Strangeness Production close to Threshold in Proton-Nucleus and Heavy-Ion Collisions

We discuss strangeness production close to threshold in p+A and A+A collision. Comparing the body of available K+, K0, K-, and Lambda data with the IQMD transport code and for some key observables as well with the HSD transport code, we find good agreement for the large majority of the observables. The investigation of the reaction with help of these codes reveals the complicated interaction of the strange particles with hadronic matter which makes strangeness production in heavy-ion collisions very different from that in elementary interactions. We show how different strange particle observables can be used to study the different facets of this interaction (production, rescattering and potential interaction) which finally merge into a comprehensive understanding of these interactions. We identify those observables which allow for studying (almost) exclusively one of these processes to show how future high precision experiments can improve our quantitative understanding. Finally, we discuss how the K+ multiplicity can be used to study the hadronic equation of state.Comment: 134 pages, pdf 3.3MB, version to be published in Physics Report

Anisotropy and scaling corrections in turbulence

We analyze second-order turbulent velocity moments both in r and in p space. Finite size corrections induce dramatic differences between local r- and p-space scaling exponents. As analytically accessible examples we focus on two popular parametrizations: the Batchelor parametrization for the r-space structure function and a common parametrization for the energy spectrum, E(p) [is proportional to] p-5/3exp(-p/pd). The spectral bottleneck energy pileup hidden in the Batchelor parametrization results in an extended r-space scaling range, comparable to experimental ones for the same Taylor-Reynolds number Re lambda . Shear effects are discussed in terms of (global) apparent scaling correction delta zeta app(Re lambda ) to classical scaling, which again depend on whether looked at in r or in p space. The differences can be traced back to the subtleties of the crossovers in the velocity moments. Our observations emphasize the need for more experimental information on crossovers between different subranges

Wege zur inneren Einheit - was trennt die Deutschen nach der Ueberwindung der Mauer?: 94. Bergedorfer Gespraechskreis am 11. und 12. Januar 1992 im Hotel Bellevue, Dresden

Available from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel D 17455 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Festreden anlaesslich der Feier des 75jaehrigen Bestehens am 20. Februar 1989

Available from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel B 251373 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Zukunftsfaehigkeit von Politik, Wirtschaft und Gesellschaft: 102. Bergedorfer Gespraechskreis am 18. und 19. Juni 1994 im Schloss Reinhardsbrunn Friedrichsroda bei Gotha

Available from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel D 17823 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Antikaon-Nukleon-Wechselwirkung im Mesonaustauschbild

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman