110 research outputs found
Level curvatures, spectral statistics and scaling for interacting particles
The mobility of two interacting particles in a random potential is studied,
using the sensitivity of their levels to a change of boundary conditions. The
delocalization in Hilbert space induced by the interaction of the two particle
Fock states is shown to decrease the mobility in metals and to increase it in
insulators. In contrast to the single particle case, the spectral rigidity is
not directly related to the level curvature. Therefore, another curvature of
topological origin is introduced, which defines the energy scale below which
the spectrum has the universal Wigner-Dyson rigidity.Comment: 4 pages, RevTe
Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the -matrix
Using the Fokker-Planck equation describing the evolution of the transmission
eigenvalues for Dyson's Brownian motion ensemble, we calculate the
magnetoconductance of a ballistic chaotic dot in in the crossover regime from
the orthogonal to the unitary symmetry. The correlation functions of the
transmission eigenvalues are expressed in terms of quaternion determinants for
arbitrary number of scattering channels. The corresponding average,
variance and autocorrelation function of the magnetoconductance are given as a
function of the Brownian motion time . A microscopic derivation of this
-Brownian motion approach is discussed and is related to the applied
flux. This exactly solvable random matrix model yields the right expression for
the suppression of the weak localization corrections in the large -limit and
for small applied fluxes. An appropriate rescaling of could extend its
validity to larger magnetic fluxes for the averages, but not for the
correlation functions.Comment: 33 pages, 7 postscript figure
Coulomb repulsion versus Hubbard repulsion in a disordered chain
We study the difference between on site Hubbard and long range Coulomb
repulsions for two interacting particles in a disordered chain. While Hubbard
repulsion can only yield weak critical chaos with intermediate spectral
statistics, Coulomb repulsion can drive the two particle system to quantum
chaos with Wigner-Dyson spectral statistics. For intermediate strengths U of
the two repulsions in one dimension, there is a crossover regime where
delocalization and spectral rigidity are maximum, whereas the limits of weak
and strong U are characterized by a stronger localization and uncorrelated
energy levels.Comment: 8 pages, 10 figure
From independent particle towards collective motion in two electron square lattices
The two dimensional crossover from independent particle towards collective
motion is studied using 2 spinless fermions interacting via a U/r Coulomb
repulsion in a LxL square lattice with periodic boundary conditions and nearest
neighbor hopping t. Three regimes characterize the ground state when U/t
increases. Firstly, when the fluctuation of the spacing r between
the two particles is larger than the lattice spacing, there is a scaling length
such that the relative fluctuation is a
universal function of the dimensionless ratio L/Lo, up to finite size
corrections of order . LLo are respectively the limits of the
free particle Fermi motion and of the correlated motion of a Wigner molecule.
Secondly, when U/t exceeds a threshold U*(L)/t, becomes smalller
than the lattice spacing, giving rise to a correlated lattice regime where the
previous scaling breaks down and analytical expansions in powers of (t/U)
become valid. A weak random potential reduces the scaling length and favors the
correlated motion.Comment: 8 pages, 11 figures, to be published in EP
Universal Scaling of the Quantum Conductance of an Inversion-Symmetric Interacting Model
We consider quantum transport of spinless fermions in a 1D lattice embedding
an interacting region (two sites with inter-site repulsion U and inter-site
hopping td, coupled to leads by hopping terms tc). Using the numerical
renormalization group for the particle-hole symmetric case, we study the
quantum conductance g as a function of the inter-site hopping td. The
interacting region, which is perfectly reflecting when td -> 0 or td ->
infinity, becomes perfectly transmitting if td takes an intermediate value
\tau(U,tc) which defines the characteristic energy of this interacting model.
When td < tc sqrt(U), g is given by a universal function of the dimensionless
ratio X=td/\tau. This universality characterizes the non-interacting regime
where \tau=tc^2, the perturbative regime (U < tc^2) where \tau can be obtained
using Hartree-Fock theory, and the non-perturbative regime (U > tc^2) where
\tau is twice the characteristic temperature TK of an orbital Kondo effect
induced by the inversion symmetry. When td < \tau, the expression
g(X)=4/(X+1/X)^2 valid without interaction describes also the conductance in
the presence of the interaction. To obtain those results, we map this spinless
model onto an Anderson model with spins, where the quantum impurity is at the
end point of a semi-infinite 1D lead and where td plays the role of a magnetic
field h. This allows us to describe g(td) using exact results obtained for the
magnetization m(h) of the Anderson model at zero temperature. We expect this
universal scaling to be valid also in models with 2D leads, and observable
using 2D semi-conductor heterostructures and an interacting region made of two
identical quantum dots with strong capacitive inter-dot coupling and connected
via a tunable quantum point contact.Comment: 14 pages, 18 figure
Brownian motion ensembles and parametric correlations of the transmission eigenvalues: Application to coupled quantum billiards and to disordered wires
The parametric correlations of the transmission eigenvalues of a
-channel quantum scatterer are calculated assuming two different Brownian
motion ensembles. The first one is the original ensemble introduced by Dyson
and assumes an isotropic diffusion for the -matrix. The second Brownian
motion ensemble assumes for the transfer matrix an isotropic diffusion
yielded by a multiplicative combination law. We review the qualitative
differences between transmission through two weakly coupled quantum dots and
through a disordered line and we discuss the mathematical analogies between the
Fokker-Planck equations of the two Brownian motion models.Comment: 33 pages, 7 postscript figures, the presented abstract is shortened
in comparison to the abstract of the pape
Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements
For interacting particles in a one dimensional random potential, we study
the structure of the corresponding network in Hilbert space. The states without
interaction play the role of the ``sites''. The hopping terms are induced by
the interaction. When the one body states are localized, we numerically find
that the set of directly connected ``sites'' is multifractal. For the case of
two interacting particles, the fractal dimension associated to the second
moment of the hopping term is shown to characterize the Golden rule decay of
the non interacting states and the enhancement factor of the localization
length.Comment: First paper of a serie of four, to appear in Eur. Phys.
Effect of measurement probes upon the conductance of an interacting nanosystem: Detection of an attached ring by non local many body effects
We consider a nanosystem connected to measurement probes via leads. When a
magnetic flux is varied through a ring attached to one lead at a distance Lc
from the nanosystem, the effective nanosystem transmission |ts|^2 exhibits
Aharonov-Bohm oscillations if the electrons interact inside the nanosystem.
These oscillations can be very large if Lc is small and if the nanosystem has
almost degenerate levels which are put near the Fermi energy by a local gate
Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II
In this second paper, using N=3 polarized electrons (spinless fermions)
interacting via a U/r Coulomb repulsion on a two dimensional L * L square
lattice with periodic boundary conditions and nearest neighbor hopping, we show
that a single unpaired fermion can co-exist with a correlated two particle
Wigner molecule for intermediate values of the Coulomb energy to kinetic energy
ratio r_s.Comment: 15 pages, 28 postscript figure
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