Coulomb interactions in mesoscopic systems介观系统中库仑相互作用.ppt

The disorder-interaction problem Reinhold Egger Institut für Theoretische Physik Universit?t Düsseldorf S. Chen, A. De Martino, M. Thorwart, R. Graham, A.O. Gogolin Overview Introduction: Noninteracting systems Theoretical concepts Wigner-Dyson spectral statistics Correlated disordered systems Bosons in one dimension Interference in interacting clean 1D Bose gas Disordered strongly interacting Bose gas: Bose-Fermi mapping to noninteracting fermions (Anderson insulator) Replica Field Theory (sigma models) Local density of states in disordered multichannel wires Disorder in noninteracting systems Quantum coherent systems Some manifestations of phase coherence in mesoscopic structures: Universal conductance fluctuations (UCF), absence of self-averaging Weak localization: Enhanced return probability Spectral fluctuations, level statistics Why can interactions often be neglected? Fermi liquid theory In normal metals, interactions lead to formation of Landau quasiparticles (Fermi liquid) Weakly interacting Fermions, stable at low energies Quasiparticle relaxation rate due to interactions In disordered systems more dangerous: Standard picture in mesoscopics, usually neglect of interactions protected by Fermi liquid principle But: Breakdown of Fermi liquid possible New physical effects New methods required Methods for noninteracting systems Semiclassical techniques Restricted to essentially clean (chaotic) systems Diagrammatic perturbation theory Breaks down in nonperturbative regime Random matrix theory Wigner-Dyson ensembles and generalization (d=0) 1D multimode wires: Transfer matrix ensembles (DMPK) Field theories (nonlinear sigma model) Supersymmetric formulation (Efetov) Replica/Keldysh field theory (Wegner, Finkel‘stein) Special techniques Berezinskii diagram technique in 1D Fisher RG scheme for disordered spin chains Time and energy scales Ballistic particle motion up to mean free time Diffusion for E Thouless energy Ergodic regime