1,136 research outputs found
Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions
We present an algorithm for enumerating exactly the number of Hamiltonian
chains on regular lattices in low dimensions. By definition, these are sets of
k disjoint paths whose union visits each lattice vertex exactly once. The
well-known Hamiltonian circuits and walks appear as the special cases k=0 and
k=1 respectively. In two dimensions, we enumerate chains on L x L square
lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results
for three dimensions are also given. Using our data we extract several
quantities of physical interest
Superconformal Algebras and Mock Theta Functions
It is known that characters of BPS representations of extended superconformal
algebras do not have good modular properties due to extra singular vectors
coming from the BPS condition. In order to improve their modular properties we
apply the method of Zwegers which has recently been developed to analyze
modular properties of mock theta functions. We consider the case of N=4
superconformal algebra at general levels and obtain the decomposition of
characters of BPS representations into a sum of simple Jacobi forms and an
infinite series of non-BPS representations.
We apply our method to study elliptic genera of hyper-Kahler manifolds in
higher dimensions. In particular we determine the elliptic genera in the case
of complex 4 dimensions of the Hilbert scheme of points on K3 surfaces K^{[2]}
and complex tori A^{[[3]]}.Comment: 28 page
Optimal shapes of compact strings
Optimal geometrical arrangements, such as the stacking of atoms, are of
relevance in diverse disciplines. A classic problem is the determination of the
optimal arrangement of spheres in three dimensions in order to achieve the
highest packing fraction; only recently has it been proved that the answer for
infinite systems is a face-centred-cubic lattice. This simply stated problem
has had a profound impact in many areas, ranging from the crystallization and
melting of atomic systems, to optimal packing of objects and subdivision of
space. Here we study an analogous problem--that of determining the optimal
shapes of closely packed compact strings. This problem is a mathematical
idealization of situations commonly encountered in biology, chemistry and
physics, involving the optimal structure of folded polymeric chains. We find
that, in cases where boundary effects are not dominant, helices with a
particular pitch-radius ratio are selected. Interestingly, the same geometry is
observed in helices in naturally-occurring proteins.Comment: 8 pages, 3 composite ps figure
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for
with arbitrary functions and and integer , where and
are boson annihilation and creation operators, satisfying
. This consequently provides the solution for the exponential
generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics
"Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005),
Myczkowce, Poland. 13 pages, 31 reference
Association of knee and ankle osteoarthritis with physical performance
The direct measurement of the ability to perform physical tasks yields information about factors contributing to poor function and insights into strategies for preventing disability. Our goal was to evaluate the relationship of walking speed and balance tests with specific radiographic features of knee and ankle osteoarthritis (OA)
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
We report the results of certain integrations of quantum-theoretic interest,
relying, in this regard, upon recently developed parameterizations of Boya et
al of the n x n density matrices, in terms of squared components of the unit
(n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized
volume elements of the Bures (minimal monotone) metric for n = 2 and 3,
obtaining thereby "Bures prior probability distributions" over the two- and
three-state systems. Then, as an essential first step in extending these
results to n > 3, we determine that the "Hall normalization constant" (C_{n})
for the marginal Bures prior probability distribution over the
(n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices
is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it
follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known
to equal 2/pi.) The constant C_{5} is also found. It too is associated with a
remarkably simple decompositon, involving the product of the eight consecutive
prime numbers from 2 to 23.
We also preliminarily investigate several cases, n > 5, with the use of
quasi-Monte Carlo integration. We hope that the various analyses reported will
prove useful in deriving a general formula (which evidence suggests will
involve the Bernoulli numbers) for the Hall normalization constant for
arbitrary n. This would have diverse applications, including quantum inference
and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in
J. Phys. A. We make a few slight changes from the previous version, but also
add a subsection (III G) in which several variations of the basic problem are
newly studied. Rather strong evidence is adduced that the Hall constants are
related to partial sums of denominators of the even-indexed Bernoulli
numbers, although a general formula is still lackin
Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices
We study various aspects of the dynamics induced by integer matrices on the
invariant rational lattices of the torus in dimension 2 and greater. Firstly,
we investigate the orbit structure when the toral endomorphism is not
invertible on the lattice, characterising the pretails of eventually periodic
orbits. Next we study the nature of the symmetries and reversing symmetries of
toral automorphisms on a given lattice, which has particular relevance to
(quantum) cat maps.Comment: 29 pages, 3 figure
Correlators for the Wigner–Smith time-delay matrix of chaotic cavities
We study the Wigner–Smith time-delay matrix Q of a ballistic quantum dot supporting N scattering channels. We compute the v-point correlators of the power traces Tr Qk for arbitrary v>1 at leading order for large N using techniques from the random matrix theory approach to quantum chromodynamics. We conjecture that the cumulants of the Tr Qkʼs are integer-valued at leading order in N and include a MATHEMATICA code that computes their generating functions recursively
A Study of Time-Dependent CP-Violating Asymmetries and Flavor Oscillations in Neutral B Decays at the Upsilon(4S)
We present a measurement of time-dependent CP-violating asymmetries in
neutral B meson decays collected with the BABAR detector at the PEP-II
asymmetric-energy B Factory at the Stanford Linear Accelerator Center. The data
sample consists of 29.7 recorded at the
resonance and 3.9 off-resonance. One of the neutral B mesons,
which are produced in pairs at the , is fully reconstructed in
the CP decay modes , , , () and , or in flavor-eigenstate
modes involving and (). The flavor of the other neutral B meson is tagged at the time of
its decay, mainly with the charge of identified leptons and kaons. The proper
time elapsed between the decays is determined by measuring the distance between
the decay vertices. A maximum-likelihood fit to this flavor eigenstate sample
finds . The value of the asymmetry amplitude is determined from
a simultaneous maximum-likelihood fit to the time-difference distribution of
the flavor-eigenstate sample and about 642 tagged decays in the
CP-eigenstate modes. We find , demonstrating that CP violation exists in the neutral B meson
system. (abridged)Comment: 58 pages, 35 figures, submitted to Physical Review
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