71 research outputs found
Nonlinear Sigma Model for Normal and Superconducting Systems: A Pedestrian Approach
The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to
(interacting) electrons in disordered media. These lectures are aimed at the
audience who might have vaguely heard about its existence but know very little
of what is that, even less so of why it should be used and next to nothing of
how it can be applied. These what, why and mainly how are the subject of the
present lectures. In the first part, after a short description of why to be
bothered, the NLSM is derived from scratch in a relatively simple (but still
rather mathematical) way for non-interacting electrons in the presence of
disorder, and some illustration of its perturbative usage is given. In the
second part it is generalised, not without some leap of faith, to include the
Coulomb repulsion and superconducting pairing.Comment: 21 pages, 5 eps figures. To appear in "Proceedings of the
International School of Physics "Enrico Fermi" Course CLI, edited by B.
Altshuler and V. Tognetti, IOS Press, Amsterdam 200
One-Dimensional Transport of Ultracold Bosons
Advances in cooling and trapping of atoms have enabled unprecedented
experimental control of many-body quantum systems. This led to the observation
of numerous quantum phenomena, important for fundamental science, indispensable
for high-precision simulations of condensed-matter systems and promising for
technological applications. However, transport measurements in neutral quantum
gases are still in their infancy in contrast to the central role they play in
electronics. In these lectures, after reviewing nascent experiments on quantum
fermionic transport, I will focus on our theoretical prediction sand the
possibility of experimental observations of qualitatively new phenomena in
transport of ultracold bosons which do not have a direct counterpart in quantum
electronic transport in condensed matter systems. The description of this
transport is based on the Luttinger liquid (LL) theory. So in the first part of
the lectures I will introduce main concepts of the LL based on the functional
bosonisation approach.Comment: Lecture notes for 13th International School on Theoretical Physics
"Symmetry and Structural Properties of Condensed Matter", Sep 2018,
Rzesz\'ow, Polan
Low temperature decoherence and relaxation in charge Josephson-junction qubits
In this lectures, we have described some essential features of loss of
coherence by a qubit coupled to the environment. We have first presented well
known semiclassical arguments that relate both decoherence and relaxation to
the environmental noise. Then we have shown that models with pure decoherence
(but no relaxation in qubit states) can be exactly solvable. As an example, we
have treated in detail the model of fluctuating background charges which is
believed to describe one of the most important channels for decoherence for the
charge Josephson junction qubit. We have shown that the decoherence rate
saturates at `high' temperatures while becoming linear in T at low temperatures
and showing in all regimes a non-monotonic behaviour as a function of the
coupling of the qubit to the fluctuating background charges. We have also
considered, albeit only perturbatively, the qubit relaxation by the background
charges and demonstrated that a quasi-linear behaviour of the spectral density
of noise deduced from the measurements of the relaxation rate can be
qualitatively explained.Comment: Lecture notes for International workshop on mesoscopic and nanoscopic
systems, Kolkata, India, February 2006, to be published by Springe
Low-Temperature Decoherence of Qubit Coupled to Background Charges
We have found an exact expression for the decoherence rate of a Josephson
charge qubit coupled to fluctuating background charges. At low temperatures
the decoherence rate is linear in while at high temperatures it
saturates in agreement with a known classical solution which, however, reached
at surprisingly high . In contrast to the classical picture, impurity states
spread in a wide interval of energies () may essentially contribute to
.Comment: Both figures are changed to illustrate a more generic case of
impurity states spread in wide interval of energies. Some changes have been
made to the abstract and the introductio
Local impurity in a multichannel Luttinger liquid
We investigate the stability of conducting and insulating phases in multichannel Luttinger liquids with respect to embedding a single impurity. We devise a general approach for finding critical exponents of the conductance in the limits of both weak and strong scattering. In contrast to the one-channel Luttinger liquid, the system state in certain parametric regions depends on the scattering strength which results in the emergence of a bistability. Focusing on the two-channel liquid, the method developed here enables us to provide a generic analysis of phase boundaries governed by the most relevant (i.e., not necessarily single-particle) scattering mechanism. The present approach is applicable to channels of different nature as in fermion-boson mixtures, or to identical ones as on the opposite edges of a topological insulator. We show that interaction per se cannot provide protection in the particular case of topological insulators realized in narrow Hall bars
Impurity Scattering in Luttinger Liquid with Electron-Phonon Coupling
We study the influence of electron-phonon coupling on electron transport
through a Luttinger liquid with an embedded weak scatterer or weak link. We
derive the renormalization group (RG) equations which indicate that the
directions of RG flows can change upon varying either the relative strength of
the electron-electron and electron-phonon coupling or the ratio of Fermi to
sound velocities. This results in the rich phase diagram with up to three fixed
points: an unstable one with a finite value of conductance and two stable ones,
corresponding to an ideal metal or insulator.Comment: 4 pages, 2 figure
SPECTRAL CORRELATIONS IN DISORDERED ELECTRONIC SYSTEMS: CROSSOVER FROM METAL TO INSULATOR REGIME
We use the semiclassical approach combined with the scaling results for the
diffusion coefficient to consider the two-level correlation function
for a disordered electron system in the crossover region,
characterized by the appearance of a macroscopic correlation or localization
length, , that diverges at the metal-insulator transition. We show new
critical statistics, characterized by a nontrivial asymptotic behavior of
, to emerge on both sides of the transition at higher energies,
and to expand to all energies larger than mean level spacing when exceeds
the system size.Comment: 4 pages,1 figure, in self-ectracting uuencoded gz-compressed file to
be published in Phys. Rev. Letters; REVTeX source file is available upon
reques
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