441 research outputs found
Comments on Supersymmetric Vector and Matrix Models
Some results in random matrices are generalized to supermatrices, in
particular supermatrix integration is reduced to an integration over the
eigenvalues and the resulting volume element is shown to be equivalent to a one
dimensional Coulomb gas of both positive and negative charges.It is shown
that,for polynomial potentials, after removing the instability due to the
annihilation of opposite charges, supermatrix models are indistinguishable from
ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and
Manes. It is pointed out however that this may not be true for more general
potentials such as for instance the supersymmetric generalization of the Penner
model.Comment: 6 page
On gonihedric loops and quantum gravity
We present an analysis of the gonihedric loop model, a reformulation of the
two dimensional gonihedric spin model, using two different techniques. First,
the usual regular lattice statistical physics problem is mapped onto a height
model and studied analytically. Second, the gravitational version of this loop
model is studied via matrix models techniques. Both methods lead to the
conclusion that the model has for all values of the parameters
of the model. In this way it is possible to understand the absence of a
continuous transition
The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles
From random matrix theory it is known that for special values of the coupling
constant the Calogero-Moser (CM) equation system is nothing but the radial part
of a generalized harmonic oscillator Schroedinger equation. This allows an
immediate construction of the solutions by means of a Rodriguez relation. The
results are easily generalized to arbitrary values of the coupling constant. By
this the CM equations become nearly trivial.
As an application an expansion for in terms of eigenfunctions of
the CM equation system is obtained, where X and Y are matrices taken from one
of the Gaussian ensembles, and the brackets denote an average over the angular
variables.Comment: accepted by J. Phys.
Replica treatment of non-Hermitian disordered Hamiltonians
We employ the fermionic and bosonic replicated nonlinear sigma models to
treat Ginibre unitary, symplectic, and orthogonal ensembles of non-Hermitian
random matrix Hamiltonians. Using saddle point approach combined with Borel
resummation procedure we derive the exact large-N results for microscopic
density of states in all three ensembles. We also obtain tails of the density
of states as well the two-point function for the unitary ensemble.Comment: REVTeX 3.1, 13 pages, 1 figure; typos fixed (v2
Correlation functions of the BC Calogero-Sutherland model
The BC-type Calogero-Sutherland model (CSM) is an integrable extension of the
ordinary A-type CSM that possesses a reflection symmetry point. The BC-CSM is
related to the chiral classes of random matrix ensembles (RMEs) in exactly the
same way as the A-CSM is related to the Dyson classes. We first develop the
fermionic replica sigma-model formalism suitable to treat all chiral RMEs. By
exploiting ''generalized color-flavor transformation'' we then extend the
method to find the exact asymptotics of the BC-CSM density profile. Consistency
of our result with the c=1 Gaussian conformal field theory description is
verified. The emerging Friedel oscillations structure and sum rules are
discussed in details. We also compute the distribution of the particle nearest
to the reflection point.Comment: 12 pages, no figure, REVTeX4. sect.V updated, references added (v3
Eigenvalue Distributions of the QCD Dirac Operator
We compute by Monte Carlo methods the individual distributions of the th
smallest Dirac operator eigenvalues in QCD, and compare them with recent
analytical predictions. We do this for both massless and massive quarks in an
SU(3) gauge theory with staggered fermions. Very precise agreement is found in
all cases. As a simple by-product we also extract the microscopic spectral
density of the Dirac operator in SU(3) gauge theory with dynamical massive
fermions for and 2, and obtain high-accuracy agreement with analytical
expressions.Comment: LaTeX, 8 pages, 9 postscript figures. Very minor correction
Universal Massive Spectral Correlators and QCD_3
Based on random matrix theory in the unitary ensemble, we derive the
double-microscopic massive spectral correlators corresponding to the Dirac
operator of QCD_3 with an even number of fermions N_f. We prove that these
spectral correlators are universal, and demonstrate that they satisfy exact
massive spectral sum rules of QCD_3 in a phase where flavor symmetries are
spontaneously broken according to U(N_f) -> U(N_f/2) x U(N_f/2).Comment: 5 pages, REVTeX. Misprint correcte
An Efficient Ligation Method in the Making of an in vitro Virus for in vitro Protein Evolution
The “in vitro virus” is a molecular construct to perform evolutionary protein engineering. The “virion (=viral particle)” (mRNA-peptide fusion), is made by bonding a nascent protein with its coding mRNA via puromycin in a test tube for in vitro translation. In this work, the puromycin-linker was attached to mRNA using the Y-ligation, which was a method of two single-strands ligation at the end of a double-stranded stem to make a stem-loop structure. This reaction gave a yield of about 95%. We compared the Y-ligation with two other ligation reactions and showed that the Y-ligation gave the best productivity. An efficient amplification of the in vitro virus with this “viral genome” was demonstrated
"Single Ring Theorem" and the Disk-Annulus Phase Transition
Recently, an analytic method was developed to study in the large limit
non-hermitean random matrices that are drawn from a large class of circularly
symmetric non-Gaussian probability distributions, thus extending the existing
Gaussian non-hermitean literature. One obtains an explicit algebraic equation
for the integrated density of eigenvalues from which the Green's function and
averaged density of eigenvalues could be calculated in a simple manner. Thus,
that formalism may be thought of as the non-hermitean analog of the method due
to Br\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian
random matrices. A somewhat surprising result is the so called "Single Ring"
theorem, namely, that the domain of the eigenvalue distribution in the complex
plane is either a disk or an annulus. In this paper we extend previous results
and provide simple new explicit expressions for the radii of the eigenvalue
distiobution and for the value of the eigenvalue density at the edges of the
eigenvalue distribution of the non-hermitean matrix in terms of moments of the
eigenvalue distribution of the associated hermitean matrix. We then present
several numerical verifications of the previously obtained analytic results for
the quartic ensemble and its phase transition from a disk shaped eigenvalue
distribution to an annular distribution. Finally, we demonstrate numerically
the "Single Ring" theorem for the sextic potential, namely, the potential of
lowest degree for which the "Single Ring" theorem has non-trivial consequences.Comment: latex, 5 eps figures, 41 page
Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories
It has been conjectured that spontaneous chiral symmetry breaking in strongly
coupled vectorlike gauge theories falls into only three different classes,
depending on the gauge group and the representations carried by the fermions.
We test this proposal by studying SU(2), SU(3) and SU(4) lattice gauge theories
with staggered fermions in different irreducible representations. Staggered
fermions away from the continuum limit should, for all complex representations,
still belong to the continuum class of spontaneous symmetry breaking. But for
all real and pseudo-real representations we show that staggered fermions should
belong to incorrect symmetry breaking classes away from the continuum, thus
generalizing previous results. As an unambiguous signal for whether chiral
symmetry breaks, and which breaking pattern it follows, we look at the smallest
Dirac eigenvalue distributions. We find that the patterns of symmetry breaking
are precisely those conjectured.Comment: LaTeX, 17 pages. Typos in eq (17) correcte
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