477 research outputs found
Exact Transformation for Spin-Charge Separation of Spin-half Fermions without Constraints
We demonstrate an exact local transformation which maps a purely Fermionic
manybody system to a system of spinfull Bosons and spinless Fermions,
demonstrating a possible path to a non-Fermi liquid state. We apply this to the
half-filled Hubbard model and show how the transformation maps the ordinary
spin half Fermionic degrees of freedom exactly and without introducing Hilbert
space constraints to a charge-like ``quasicharge'' fermion and a spin-like
``quasispin'' Boson while preserving all the symmetries of the model. We
present approximate solutions with localized charge which emerge naturally from
the Hubbard model in this form. Our results strongly suggest that charge tends
to remain localized for large values of the Hubbard U
Density Matrix Renormalization Group of Gapless Systems
We investigate convergence of the density matrix renormalization group (DMRG)
in the thermodynamic limit for gapless systems. Although the DMRG correlations
always decay exponentially in the thermodynamic limit, the correlation length
at the DMRG fixed-point scales as , where is the number
of kept states, indicating the existence of algebraic order for the exact
system. The single-particle excitation spectrum is calculated, using a
Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the
symmetry for translationally invariant half-integer
spin-systems with local interactions. Finally, we provide a method to compute
overlaps between ground states obtained from different DMRG calculations.Comment: 11 pages, RevTex, 5 figure
Excitation and Entanglement Transfer Near Quantum Critical Points
Recently, there has been growing interest in employing condensed matter
systems such as quantum spin or harmonic chains as quantum channels for short
distance communication. Many properties of such chains are determined by the
spectral gap between their ground and excited states. In particular this gap
vanishes at critical points of quantum phase transitions. In this article we
study the relation between the transfer speed and quality of such a system and
the size of its spectral gap. We find that the transfer is almost perfect but
slow for large spectral gaps and fast but rather inefficient for small gaps.Comment: submitted to Optics and Spectroscopy special issue for ICQO'200
Clustering in mixing flows
We calculate the Lyapunov exponents for particles suspended in a random
three-dimensional flow, concentrating on the limit where the viscous damping
rate is small compared to the inverse correlation time. In this limit Lyapunov
exponents are obtained as a power series in epsilon, a dimensionless measure of
the particle inertia. Although the perturbation generates an asymptotic series,
we obtain accurate results from a Pade-Borel summation. Our results prove that
particles suspended in an incompressible random mixing flow can show pronounced
clustering when the Stokes number is large and we characterise two distinct
clustering effects which occur in that limit.Comment: 5 pages, 1 figur
Scale effects for strength, ductility, and toughness in "brittle” materials
Decreasing scales effectively increase nearly all important mechanical properties of at least some "brittle” materials below 100 nm. With an emphasis on silicon nanopillars, nanowires, and nanospheres, it is shown that strength, ductility, and toughness all increase roughly with the inverse radius of the appropriate dimension. This is shown experimentally as well as on a mechanistic basis using a proposed dislocation shielding model. Theoretically, this collects a reasonable array of semiconductors and ceramics onto the same field using fundamental physical parameters. This gives proportionality between fracture toughness and the other mechanical properties. Additionally, this leads to a fundamental concept of work per unit fracture area, which predicts the critical event for brittle fracture. In semibrittle materials such as silicon, this can occur at room temperature when the scale is sufficiently small. When the local stress associated with dislocation nucleation increases to that sufficient to break bonds, an instability occurs resulting in fractur
Landau Ginzburg theory of the d-wave Josephson junction
This letter discusses the Landau Ginzburg theory of a Josephson junction
composed of on one side a pure d-wave superconductor oriented with the
axis normal to the junction and on the other side either s-wave or d-wave
oriented with normal to the junction. We use simple symmetry arguments
to show that the Josephson current as a function of the phase must have the
form . In principle vanishes
for a perfect junction of this type, but anisotropy effects, either due to a-b
axis asymmetry or junction imperfections can easily cause to be
quite large even in a high quality junction. If is sufficiently
small and is negative local time reversal symmetry breaking will appear.
Arbitrary values of the flux would then be pinned to corners between such
junctions and occasionally on junction faces, which is consistent with
experiments by Kirtley et al
Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix
In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that
the many-particle eigenvalues and eigenstates of the many-body density matrix
of a block of sites cut out from an infinite chain of
noninteracting spinless fermions can all be constructed out of the one-particle
eigenvalues and one-particle eigenstates respectively. In this paper we
developed a statistical-mechanical analogy between the density matrix
eigenstates and the many-body states of a system of noninteracting fermions.
Each density matrix eigenstate corresponds to a particular set of occupation of
single-particle pseudo-energy levels, and the density matrix eigenstate with
the largest weight, having the structure of a Fermi sea ground state,
unambiguously defines a pseudo-Fermi level. We then outlined the main ideas
behind an operator-based truncation of the density matrix eigenstates, where
single-particle pseudo-energy levels far away from the pseudo-Fermi level are
removed as degrees of freedom. We report numerical evidence for scaling
behaviours in the single-particle pseudo-energy spectrum for different block
sizes and different filling fractions \nbar. With the aid of these
scaling relations, which tells us that the block size plays the role of an
inverse temperature in the statistical-mechanical description of the density
matrix eigenstates and eigenvalues, we looked into the performance of our
operator-based truncation scheme in minimizing the discarded density matrix
weight and the error in calculating the dispersion relation for elementary
excitations. This performance was compared against that of the traditional
density matrix-based truncation scheme, as well as against a operator-based
plane wave truncation scheme, and found to be very satisfactory.Comment: 22 pages in RevTeX4 format, 22 figures. Uses amsmath, amssymb,
graphicx and mathrsfs package
Altered protein dynamics of disease-associated lamin A mutants
BACKGROUND: Recent interest in the function of the nuclear lamina has been provoked by the discovery of lamin A/C mutations in the laminopathy diseases. However, it is not understood why mutations in lamin A give such a range of tissue-specific phenotypes. Part of the problem in rationalising genotype-phenotype correlations in the laminopathies is our lack of understanding of the function of normal and mutant lamin A. To investigate this we have used photobleaching in human cells to analyse the dynamics of wild-type and mutant lamin A protein at the nuclear periphery. RESULTS: We have found that a large proportion of wild-type lamin A at the nuclear periphery is immobile, but that there is some slow movement of lamin A within the nuclear lamina. The mobility of an R482W mutant lamin A was indistinguishable from wild-type, but increased mobility of L85R and L530P mutant proteins within the nuclear lamina was found. However, the N195K mutant shows the most enhanced protein mobility, both within the nucleoplasm and within the lamina. CONCLUSION: The slow kinetics of lamin A movement is compatible with its incorporation into a stable polymer that only exchanges subunits very slowly. All of the myopathy-associated lamin A mutants that we have studied show increased protein movement compared with wild-type. In contrast, the dynamic behaviour of the lipodystrophy-associated lamin A mutant was indistinguishable from wild-type. This supports the hypothesis that the underlying defect in lamin A function is quite distinct in the laminopathies that affect striated muscle, compared to the diseases that affect adipose tissue. Our data are consistent with an alteration in the stability of the lamin A molecules within the higher-order polymer at the nuclear lamina in myopathies
Unmixing in Random Flows
We consider particles suspended in a randomly stirred or turbulent fluid.
When effects of the inertia of the particles are significant, an initially
uniform scatter of particles can cluster together. We analyse this 'unmixing'
effect by calculating the Lyapunov exponents for dense particles suspended in
such a random three-dimensional flow, concentrating on the limit where the
viscous damping rate is small compared to the inverse correlation time of the
random flow (that is, the regime of large Stokes number). In this limit
Lyapunov exponents are obtained as a power series in a parameter which is a
dimensionless measure of the inertia. We report results for the first seven
orders. The perturbation series is divergent, but we obtain accurate results
from a Pade-Borel summation. We deduce that particles can cluster onto a
fractal set and show that its dimension is in satisfactory agreement with
previously reported in simulations of turbulent Navier-Stokes flows. We also
investigate the rate of formation of caustics in the particle flow.Comment: 39 pages, 8 figure
- …