3,167 research outputs found
A realization of the Lie algebra associated to a Kantor triple system
We present a nonlinear realization of the 5-graded Lie algebra associated to
a Kantor triple system. Any simple Lie algebra can be realized in this way,
starting from an arbitrary 5-grading. In particular, we get a unified
realization of the exceptional Lie algebras f_4, e_6, e_7, e_8, in which they
are respectively related to the division algebras R, C, H, O.Comment: 11 page
Statistics of Largest Loops in a Random Walk
We report further findings on the size distribution of the largest neutral
segments in a sequence of N randomly charged monomers [D. Ertas and Y. Kantor,
Phys. Rev. E53, 846 (1996); cond-mat/9507005]. Upon mapping to one--dimensional
random walks (RWs), this corresponds to finding the probability distribution
for the size L of the largest segment that returns to its starting position in
an N--step RW. We primarily focus on the large N, \ell = L/N << 1 limit, which
exhibits an essential singularity. We establish analytical upper and lower
bounds on the probability distribution, and numerically probe the distribution
down to \ell \approx 0.04 (corresponding to probabilities as low as 10^{-15})
using a recursive Monte Carlo algorithm. We also investigate the possibility of
singularities at \ell=1/k for integer k.Comment: 5 pages and 4 eps figures, requires RevTeX, epsf and multicol.
Postscript file also available at
http://cmtw.harvard.edu/~deniz/publications.htm
A Model Ground State of Polyampholytes
The ground state of randomly charged polyampholytes is conjectured to have a
structure similar to a necklace, made of weakly charged parts of the chain,
compacting into globules, connected by highly charged stretched `strings'. We
suggest a specific structure, within the necklace model, where all the neutral
parts of the chain compact into globules: The longest neutral segment compacts
into a globule; in the remaining part of the chain, the longest neutral segment
(the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so
on. We investigate the size distributions of the longest neutral segments in
random charge sequences, using analytical and Monte Carlo methods. We show that
the length of the n-th longest neutral segment in a sequence of N monomers is
proportional to N/(n^2), while the mean number of neutral segments increases as
sqrt(N). The polyampholyte in the ground state within our model is found to
have an average linear size proportional to sqrt(N), and an average surface
area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.
MUBs inequivalence and affine planes
There are fairly large families of unitarily inequivalent complete sets of
N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The
number of such sets is not bounded above by any polynomial as a function of N.
While it is standard that there is a superficial similarity between complete
sets of MUBs and finite affine planes, there is an intimate relationship
between these large families and affine planes. This note briefly summarizes
"old" results that do not appear to be well-known concerning known families of
complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical
Physics 53, 032204 (2012) except for format changes due to the journal's
style policie
Theta-point universality of polyampholytes with screened interactions
By an efficient algorithm we evaluate exactly the disorder-averaged
statistics of globally neutral self-avoiding chains with quenched random charge
in monomer i and nearest neighbor interactions on
square (22 monomers) and cubic (16 monomers) lattices. At the theta transition
in 2D, radius of gyration, entropic and crossover exponents are well compatible
with the universality class of the corresponding transition of homopolymers.
Further strong indication of such class comes from direct comparison with the
corresponding annealed problem. In 3D classical exponents are recovered. The
percentage of charge sequences leading to folding in a unique ground state
approaches zero exponentially with the chain length.Comment: 15 REVTEX pages. 4 eps-figures . 1 tabl
Rotochemical Heating of Neutron Stars: Rigorous Formalism with Electrostatic Potential Perturbations
The electrostatic potential that keeps approximate charge neutrality in
neutron star matter is self-consistently introduced into the formalism for
rotochemical heating presented in a previous paper by Fernandez and
Reisenegger. Although the new formalism is more rigorous, we show that its
observable consequences are indistinguishable from those of the previous one,
leaving the conclusions of the previous paper unchanged.Comment: 14 pages, including 4 eps figures. Accepted for publication in The
Astrophysical Journa
Quasi-normal modes of superfluid neutron stars
We study non-radial oscillations of neutron stars with superfluid baryons, in
a general relativistic framework, including finite temperature effects. Using a
perturbative approach, we derive the equations describing stellar oscillations,
which we solve by numerical integration, employing different models of nucleon
superfluidity, and determining frequencies and gravitational damping times of
the quasi-normal modes. As expected by previous results, we find two classes of
modes, associated to superfluid and non-superfluid degrees of freedom,
respectively. We study the temperature dependence of the modes, finding that at
specific values of the temperature, the frequencies of the two classes of
quasi-normal modes show avoided crossings, and their damping times become
comparable. We also show that, when the temperature is not close to the avoided
crossings, the frequencies of the modes can be accurately computed by
neglecting the coupling between normal and superfluid degrees of freedom. Our
results have potential implications on the gravitational wave emission from
neutron stars.Comment: 16 pages, 7 figures, 2 table
Dissipation in relativistic superfluid neutron stars
We analyze damping of oscillations of general relativistic superfluid neutron
stars. To this aim we extend the method of decoupling of superfluid and normal
oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R)
(2011)]. All calculations are made self-consistently within the finite
temperature superfluid hydrodynamics. The general analytic formulas are derived
for damping times due to the shear and bulk viscosities. These formulas
describe both normal and superfluid neutron stars and are valid for oscillation
modes of arbitrary multipolarity. We show that: (i) use of the ordinary
one-fluid hydrodynamics is a good approximation, for most of the stellar
temperatures, if one is interested in calculation of the damping times of
normal f-modes; (ii) for radial and p-modes such an approximation is poor;
(iii) the temperature dependence of damping times undergoes a set of rapid
changes associated with resonance coupling of neighboring oscillation modes.
The latter effect can substantially accelerate viscous damping of normal modes
in certain stages of neutron-star thermal evolution.Comment: 25 pages, 9 figures, 1 table, accepted for publication in MNRA
From Collapse to Freezing in Random Heteropolymers
We consider a two-letter self-avoiding (square) lattice heteropolymer model
of N_H (out ofN) attracting sites. At zero temperature, permanent links are
formed leading to collapse structures for any fraction rho_H=N_H/N. The average
chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H -->
0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H <
1, entropy approaches zero as N --> infty (being finite for a homopolymer). An
abrupt decrease in entropy occurs at the phase boundary between the swollen (R
~ N^nu) and collapsed region. Scaling arguments predict different regimes
depending on the ensemble of crosslinks. Some implications to the protein
folding problem are discussed.Comment: 4 pages, Revtex, figs upon request. New interpretation and emphasis.
Submitted to Europhys.Let
Bundles of Interacting Strings in Two Dimensions
Bundles of strings which interact via short-ranged pair potentials are
studied in two dimensions. The corresponding transfer matrix problem is solved
analytically for arbitrary string number N by Bethe ansatz methods. Bundles
consisting of N identical strings exhibit a unique unbinding transition. If the
string bundle interacts with a hard wall, the bundle may unbind from the wall
via a unique transition or a sequence of N successive transitions. In all
cases, the critical exponents are independent of N and the density profile of
the strings exhibits a scaling form that approaches a mean-field profile in the
limit of large N.Comment: 8 pages (latex) with two figure
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