190 research outputs found
Explicit approximate controllability of the Schr\"odinger equation with a polarizability term
We consider a controlled Schr\"odinger equation with a dipolar and a
polarizability term, used when the dipolar approximation is not valid. The
control is the amplitude of the external electric field, it acts non linearly
on the state. We extend in this infinite dimensional framework previous
techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in
finite dimension. We consider a highly oscillating control and prove the
semi-global weak stabilization of the averaged system using a Lyapunov
function introduced by Nersesyan. Then it is proved that the solutions of the
Schr\"odinger equation and of the averaged equation stay close on every finite
time horizon provided that the control is oscillating enough. Combining these
two results, we get approximate controllability to the ground state for the
polarizability system
New Chiral Universality Class in a Frustrated Three-Leg Spin Ladder
We study a model of three antiferromagnetic Heisenberg spin chains
weakly coupled by on-rung and plaquette-diagonal interchain interactions. It is
shown that the model exhibits a critical phase with central charge C=2 and
belongs to the class of ``chirally stabilized'' liquids recently introduced by
Andrei, Douglas, and Jerez. By allowing anisotropic interactions in spin space,
we find an exact solution at a Toulouse point which captures all universal
properties of the model, including the SU(2) symmetric case. At the new
critical point the massless degrees of freedom are described in terms of an
effective Heisenberg spin chain and two critical Ising models. We
discuss the spectral properties of the model, compute spin-spin correlation
functions and estimate the NMR relaxation rate.Comment: 4 page
Phase Diagram of the Half-Filled Extended Hubbard Model in Two Dimensions
We consider an extended Hubbard model of interacting fermions on a lattice.
The fermion kinetic energy corresponds to a tight binding Hamiltonian with
nearest neighbour (-t) and next nearest neighbour (t') hopping matrix elements.
In addition to the onsite Hubbard interaction (U) we also consider a nearest
neighbour repulsion (V). We obtain the zero temperature phase diagram of our
model within the Hartree-Fock approximation. We consider ground states having
charge and spin density wave ordering as well as states with orbital
antiferromagnetism or spin nematic order. The latter two states correspond to
particle-hole binding with symmetry in the charge and spin
channels respectively. For , only the charge density wave and spin
density wave states are energetically stable. For non-zero t', we find that
orbital antiferromagnetism (or spin nematic) order is stable over a finite
portion of the phase diagram at weak coupling. This region of stability is seen
to grow with increasing values of t'.Comment: Latex file, 10 output pages, 3 Figures (available on request to
[email protected]), to appear in Phys. Rev. B (BR
Quasiparticle Localization in Disordered d-Wave Superconductors
An extensive numerical study is reported on disorder effect in
two-dimensional d-wave superconductors with random impurities in the unitary
limit. It is found that a sharp resonant peak shows up in the density of states
at zero energy and correspondingly the finite-size spin conductance is strongly
enhanced which results in a non-universal feature in one-parameter scaling.
However, all quasiparticle states remain localized, indicating that the
resonant density peak alone is not sufficient to induce delocalization. In the
weak disorder limit, the localization length is so long that the spin
conductance at small sample size is close to the universal value predicted by
Lee (Phys. Rev. Lett. {\bf 71}, 1887 (1993)).Comment: 4 pages, 3 figure
Conductivity in Two-Dimensional Disordered Model with Anisotropic Long-Range Hopping
We consider two-dimensional system of particles localized on randomly
distributed sites of squared lattice with anisotropic transfer matrix elements
between localized sites. By summing of "diffusion ladder" and "cooperon ladder"
type vertices we calculated the conductivity for various sites and particles
densities.Comment: Latex, 10 page
The angular dependent magnetoresistance in alpha-(BEDT-TTF)_2KHg(SCN)_4
In spite of extensive experimental studies of the angular dependent
magnetoresistance (ADMR) of the low temperature phase (LTP) of
alpha-(BEDT-TTF)_2KHg(SCN)_4 about a decade ago, the nature of LTP remains
elusive. Here we present a new study of ADMR of LTP in alpha-(ET)_2 salts
assuming that LTP is unconventional charge density wave (UCDW). In the presence
of magnetic field the quasiparticle spectrum in UCDW is quantized, which gives
rise to striking ADMR in UCDW. The present model appears to account for many
existing ADMR data of alpha-(BEDT-TTF)_2KHg(SCN)_4 remarkably well.Comment: 6 pages, 4 figure
Spin Gap Fixed Points in the Double Chain Problem
Applying the bosonization procedure to weakly coupled Hubbard chains we
discuss the fixed points of the renormalization group flow where all spin
excitations are gapful and a singlet pairing becomes the dominant instability.Comment: 15 pages, TeX, C Version 3.
Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions
We consider Dirac fermions interacting with a disordered non-Abelian vector
potential. The exact solution is obtained through a special type of conformal
field theory including logarithmic correlators, without resorting to the
replica or supersymmetry approaches. It is shown that the proper treatment of
the conformal theory leads to a different multifractal scaling behaviour than
initially expected. Moreover, the previous replica solution is found to be
incorrect at the level of higher correlation functions.Comment: 4 pages, no figure
Interacting random Dirac fermions in superconducting cuprates
We study the effects of quasiparticle interactions on disorder-induced
localization of Dirac-like nodal excitations in superconducting high-
cuprates. As suggested by the experimental ARPES and terahertz conductivity
data in , we focus on the interactions mediated by
the order parameter fluctuations near an incipient second pairing transition
. We find interaction corrections to the density of states, specific
heat, and conductivity as well as phase and energy relaxation rates and assess
the applicability of the recent localization scenarios for non-interacting
random Dirac fermions to the cuprates
- …