288 research outputs found
Keldysh technique and non-linear sigma-model: basic principles and applications
The purpose of this review is to provide a comprehensive pedagogical
introduction into Keldysh technique for interacting out-of-equilibrium
fermionic and bosonic systems. The emphasis is placed on a functional integral
representation of underlying microscopic models. A large part of the review is
devoted to derivation and applications of the non-linear sigma-model for
disordered metals and superconductors. We discuss such topics as transport
properties, mesoscopic effects, counting statistics, interaction corrections,
kinetic equation, etc. The sections devoted to disordered superconductors
include Usadel equation, fluctuation corrections, time-dependent
Ginzburg-Landau theory, proximity and Josephson effects, etc. (This review is a
substantial extension of arXiv:cond-mat/0412296.)Comment: Review: 103 pages, 19 figure
Random Matrix Theory and Chiral Symmetry in QCD
Random matrix theory is a powerful way to describe universal correlations of
eigenvalues of complex systems. It also may serve as a schematic model for
disorder in quantum systems. In this review, we discuss both types of
applications of chiral random matrix theory to the QCD partition function. We
show that constraints imposed by chiral symmetry and its spontaneous breaking
determine the structure of low-energy effective partition functions for the
Dirac spectrum. We thus derive exact results for the low-lying eigenvalues of
the QCD Dirac operator. We argue that the statistical properties of these
eigenvalues are universal and can be described by a random matrix theory with
the global symmetries of the QCD partition function. The total number of such
eigenvalues increases with the square root of the Euclidean four-volume. The
spectral density for larger eigenvalues (but still well below a typical
hadronic mass scale) also follows from the same low-energy effective partition
function. The validity of the random matrix approach has been confirmed by many
lattice QCD simulations in a wide parameter range. Stimulated by the success of
the chiral random matrix theory in the description of universal properties of
the Dirac eigenvalues, the random matrix model is extended to nonzero
temperature and chemical potential. In this way we obtain qualitative results
for the QCD phase diagram and the spectrum of the QCD Dirac operator. We
discuss the nature of the quenched approximation and analyze quenched Dirac
spectra at nonzero baryon density in terms of an effective partition function.
Relations with other fields are also discussed.Comment: invited review article for Ann. Rev. Nucl. Part. Sci., 61 pages, 11
figures, uses ar.sty (included); references added and typos correcte
Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions
In these lectures, given at the NATO ASI at Windsor (2001), applications of
the replicas nonlinear sigma model to disordered systems are reviewed. A
particular attention is given to two sets of issues. First, obtaining
non-perturbative results in the replica limit is discussed, using as examples
(i) an oscillatory behaviour of the two-level correlation function and (ii)
long-tail asymptotes of different mesoscopic distributions. Second, a new
variant of the sigma model for interacting electrons in disordered normal and
superconducting systems is presented, with demonstrating how to reduce it,
under certain controlled approximations, to known ``phase-only'' actions,
including that of the ``dirty bosons'' model.Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly
Correlated Fermions and Bosons in Low - Dimensional Disordered Systems",
Windsor, August, 2001; to be published by Kluwe
Finite temperature phase transition for disordered weakly interacting bosons in one dimension
It is commonly accepted that there are no phase transitions in
one-dimensional (1D) systems at a finite temperature, because long-range
correlations are destroyed by thermal fluctuations. Here we demonstrate that
the 1D gas of short-range interacting bosons in the presence of disorder can
undergo a finite temperature phase transition between two distinct states:
fluid and insulator. None of these states has long-range spatial correlations,
but this is a true albeit non-conventional phase transition because transport
properties are singular at the transition point. In the fluid phase the mass
transport is possible, whereas in the insulator phase it is completely blocked
even at finite temperatures. We thus reveal how the interaction between
disordered bosons influences their Anderson localization. This key question,
first raised for electrons in solids, is now crucial for the studies of atomic
bosons where recent experiments have demonstrated Anderson localization in
expanding very dilute quasi-1D clouds.Comment: 8 pages, 5 figure
Pseudogap in a thin film of a conventional superconductor
A superconducting state is characterized by the gap in the electronic density
of states which vanishes at the superconducting transition temperature Tc. It
was discovered that in high temperature superconductors a noticeable depression
in the density of states still remains even at temperatures above Tc; this
feature being called pseudogap. Here we show that a pseudogap exists in a
conventional superconductor: ultrathin titanium nitride films over a wide range
of temperatures above Tc. Our study reveals that this pseudogap state is
induced by superconducting fluctuations and favored by two-dimensionality and
by the proximity to the transition to the insulating state. A general character
of the observed phenomenon provides a powerful tool to discriminate between
fluctuations as the origin of the pseudogap state, and other contributions in
the layered high temperature superconductor compounds.Comment: 26 pages, 4 figure
Quantum biology on the edge of quantum chaos
We give a new explanation for why some biological systems can stay quantum
coherent for long times at room temperatures, one of the fundamental puzzles of
quantum biology. We show that systems with the right level of complexity
between chaos and regularity can increase their coherence time by orders of
magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition
(MIT) can have long coherence times and coherent transport at the same time.
The new theory tested in a realistic light harvesting system model can
reproduce the scaling of critical fluctuations reported in recent experiments.
Scaling of return probability in the FMO light harvesting complex shows the
signs of universal return probability decay observed at critical MIT. The
results may open up new possibilities to design low loss energy and information
transport systems in this Poised Realm hovering reversibly between quantum
coherence and classicality
Complex spectral evolution in a BCS superconductor, ZrB12
We investigate the electronic structure of a complex conventional superconductor, ZrB12 employing high resolution photoemission spectroscopy and ab initio band structure calculations. The experimental valence band spectra could be described reasonably well within the local density approximation. Energy bands close to the Fermi level possess t2g symmetry and the Fermi level is found to be in the proximity of quantum fluctuation regime. The spectral lineshape in the high resolution spectra is complex exhibiting signature of a deviation from Fermi liquid behavior. A dip at the Fermi level emerges above the superconducting transition temperature that gradually grows with the decrease in temperature. The spectral simulation of the dip and spectral lineshape based on a phenomenological self energy suggests finite electron pair lifetime and a pseudogap above the superconducting transition temperature
Algebraic charge liquids
High temperature superconductivity emerges in the cuprate compounds upon
changing the electron density of an insulator in which the electron spins are
antiferromagnetically ordered. A key characteristic of the superconductor is
that electrons can be extracted from them at zero energy only if their momenta
take one of four specific values (the `nodal points'). A central enigma has
been the evolution of the zero energy electrons in the metallic state between
the antiferromagnet and the superconductor, and recent experiments yield
apparently contradictory results. The oscillation of the resistance in this
metal as a function of magnetic field indicate that the zero energy electrons
carry momenta which lie on elliptical `Fermi pockets', while ejection of
electrons by high intensity light indicates that the zero energy electrons have
momenta only along arc-like regions. We present a theory of new states of
matter, which we call `algebraic charge liquids', which arise naturally between
the antiferromagnet and the superconductor, and reconcile these observations.
Our theory also explains a puzzling dependence of the density of
superconducting electrons on the total electron density, and makes a number of
unique predictions for future experiments.Comment: 6+8 pages, 2 figures; (v2) Rewritten for broader accessibility; (v3)
corrected numerical error in Eq. (5
Dynamics of localization in a waveguide
This is a review of the dynamics of wave propagation through a disordered
N-mode waveguide in the localized regime. The basic quantities considered are
the Wigner-Smith and single-mode delay times, plus the time-dependent power
spectrum of a reflected pulse. The long-time dynamics is dominated by resonant
transmission over length scales much larger than the localization length. The
corresponding distribution of the Wigner-Smith delay times is the Laguerre
ensemble of random-matrix theory. In the power spectrum the resonances show up
as a 1/t^2 tail after N^2 scattering times. In the distribution of single-mode
delay times the resonances introduce a dynamic coherent backscattering effect,
that provides a way to distinguish localization from absorption.Comment: 18 pages including 8 figures; minor correction
Modeling the quantum evolution of the universe through classical matter
It is well known that the canonical quantization of the
Friedmann-Lema\^itre-Robertson-Walker (FLRW) filled with a perfect fluid leads
to nonsingular universes which, for later times, behave as their classical
counterpart. This means that the expectation value of the scale factor
never vanishes and, as , we recover the classical expression for
the scale factor. In this paper, we show that such universes can be reproduced
by classical cosmology given that the universe is filled with an exotic matter.
In the case of a perfect fluid, we find an implicit equation of state (EoS). We
then show that this single fluid with an implict EoS is equivalent to two
non-interacting fluids, one of them representing stiff matter with negative
energy density. In the case of two non-interacting scalar fields, one of them
of the phantom type, we find their potential energy. In both cases we find that
quantum mechanics changes completely the configuration of matter for small
values of time, by adding a fluid or a scalar field with negative energy
density. As time passes, the density of negative energy decreases and we
recover the ordinary content of the classical universe. The more the initial
wave function of the universe is concentrated around the classical big bang
singularity, the more it is necessary to add negative energy, since this type
of energy will be responsible for the removal of the classical singularity.Comment: updated version as accepted by Gen. Relativ. Gravi
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