1,394 research outputs found
Berezinians, Exterior Powers and Recurrent Sequences
We study power expansions of the characteristic function of a linear operator
in a -dimensional superspace . We show that traces of exterior
powers of satisfy universal recurrence relations of period .
`Underlying' recurrence relations hold in the Grothendieck ring of
representations of \GL(V). They are expressed by vanishing of certain Hankel
determinants of order in this ring, which generalizes the vanishing of
sufficiently high exterior powers of an ordinary vector space. In particular,
this allows to explicitly express the Berezinian of an operator as a rational
function of traces. We analyze the Cayley--Hamilton identity in a superspace.
Using the geometric meaning of the Berezinian we also give a simple formulation
of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and
expanded, new results include
Collapse of Randomly Self-Interacting Polymers
We use complete enumeration and Monte Carlo techniques to study
self--avoiding walks with random nearest--neighbor interactions described by
, where is a quenched sequence of ``charges'' on the
chain. For equal numbers of positive and negative charges (), the
polymer with undergoes a transition from self--avoiding behavior to a
compact state at a temperature . The collapse temperature
decreases with the asymmetry Comment: 8 pages, TeX, 4 uuencoded postscript figures, MIT-CMT-
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
Two-Dimensional Polymers with Random Short-Range Interactions
We use complete enumeration and Monte Carlo techniques to study
two-dimensional self-avoiding polymer chains with quenched ``charges'' .
The interaction of charges at neighboring lattice sites is described by . We find that a polymer undergoes a collapse transition at a temperature
, which decreases with increasing imbalance between charges. At the
transition point, the dependence of the radius of gyration of the polymer on
the number of monomers is characterized by an exponent , which is slightly larger than the similar exponent for homopolymers. We
find no evidence of freezing at low temperatures.Comment: 4 two-column pages, 6 eps figures, RevTex, Submitted to Phys. Rev.
EXTENDED SUPERCONFORMAL SYMMETRY, FREUDENTHAL TRIPLE SYSTEMS AND GAUGED WZW MODELS
We review the construction of extended ( N=2 and N=4 ) superconformal
algebras over triple systems and the gauged WZW models invariant under them.
The N=2 superconformal algebras (SCA) realized over Freudenthal triple systems
(FTS) admit extension to ``maximal'' N=4 SCA's with SU(2)XSU(2)XU(1) symmetry.
A detailed study of the construction and classification of N=2 and N=4 SCA's
over Freudenthal triple systems is given. We conclude with a study and
classification of gauged WZW models with N=4 superconformal symmetry.Comment: Invited talk presented at the Gursey Memorial Conference I in
Istanbul, Turkiye (June 6-10, 1994). To appear in the proceedings of the
conference. (21 pages. Latex document.
Collapse of Stiff Polyelectrolytes due to Counterion Fluctuations
The effective elasticity of highly charged stiff polyelectrolytes is studied
in the presence of counterions, with and without added salt. The rigid polymer
conformations may become unstable due to an effective attraction induced by
counterion density fluctuations. Instabilities at the longest, or intermediate
length scales may signal collapse to globule, or necklace states, respectively.
In the presence of added-salt, a generalized electrostatic persistence length
is obtained, which has a nontrivial dependence on the Debye screening length.Comment: 4 pages RevTex, 3 ps figures included using epsf, final version as
appeared in PR
Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries
An intrinsic curvature model is investigated using the canonical Monte Carlo
simulations on dynamically triangulated spherical surfaces of size upto N=4842
with two fixed-vertices separated by the distance 2L. We found a first-order
transition at finite curvature coefficient \alpha, and moreover that the order
of the transition remains unchanged even when L is enlarged such that the
surfaces become sufficiently oblong. This is in sharp contrast to the known
results of the same model on tethered surfaces, where the transition weakens to
a second-order one as L is increased. The phase transition of the model in this
paper separates the smooth phase from the crumpled phase. The surfaces become
string-like between two point-boundaries in the crumpled phase. On the
contrary, we can see a spherical lump on the oblong surfaces in the smooth
phase. The string tension was calculated and was found to have a jump at the
transition point. The value of \sigma is independent of L in the smooth phase,
while it increases with increasing L in the crumpled phase. This behavior of
\sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu,
where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled
phase. We should note that a possibility of a continuous transition is not
completely eliminated.Comment: 15 pages with 10 figure
No N=4 Strings on Wolf Spaces
We generalize the standard supersymmetric Kazama-Suzuki coset
construction to the case by requiring the {\it non-linear}
(Goddard-Schwimmer) quasi-superconformal algebra to be realized on
cosets. The constraints that we find allow very simple geometrical
interpretation and have the Wolf spaces as their natural solutions. Our results
obtained by using components-level superconformal field theory methods are
fully consistent with standard results about supersymmetric
two-dimensional non-linear sigma-models and WZNW models on Wolf spaces.
We construct the actions for the latter and express the quaternionic structure,
appearing in the coset solution, in terms of the symplectic structure
associated with the underlying Freudenthal triple system. Next, we gauge the
QSCA and build a quantum BRST charge for the string propagating on
a Wolf space. Surprisingly, the BRST charge nilpotency conditions rule out the
non-trivial Wolf spaces as consistent string backgrounds.Comment: 31 pages, LaTeX, special macros are include
Phase transition of triangulated spherical surfaces with elastic skeletons
A first-order transition is numerically found in a spherical surface model
with skeletons, which are linked to each other at junctions. The shape of the
triangulated surfaces is maintained by skeletons, which have a one-dimensional
bending elasticity characterized by the bending rigidity , and the surfaces
have no two-dimensional bending elasticity except at the junctions. The
surfaces swell and become spherical at large and collapse and crumple at
small . These two phases are separated from each other by the first-order
transition. Although both of the surfaces and the skeleton are allowed to
self-intersect and, hence, phantom, our results indicate a possible phase
transition in biological or artificial membranes whose shape is maintained by
cytoskeletons.Comment: 15 pages with 10 figure
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