1,969 research outputs found
Lattice Green Function (at 0) for the 4d Hypercubic Lattice
The generating function for recurrent Polya walks on the four dimensional
hypercubic lattice is expressed as a Kampe-de-Feriet function. Various
properties of the associated walks are enumerated.Comment: latex, 5 pages, Res. Report 1
Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
We introduce a family of strongly-correlated spin wave functions on arbitrary
spin-1/2 and spin-1 lattices in one and two dimensions. These states are
lattice analogues of Moore-Read states of particles at filling fraction 1/q,
which are non-Abelian Fractional Quantum Hall states in 2D. One parameter
enables us to perform an interpolation between the continuum limit, where the
states become continuum Moore-Read states of bosons (odd q) and fermions (even
q), and the lattice limit. We show numerical evidence that the topological
entanglement entropy stays the same along the interpolation for some of the
states we introduce in 2D, which suggests that the topological properties of
the lattice states are the same as in the continuum, while the 1D states are
critical states. We then derive exact parent Hamiltonians for these states on
lattices of arbitrary size. By deforming these parent Hamiltonians, we
construct local Hamiltonians that stabilize some of the states we introduce in
1D and in 2D.Comment: 15 pages, 7 figure
Lattice Green functions in all dimensions
We give a systematic treatment of lattice Green functions (LGF) on the
-dimensional diamond, simple cubic, body-centred cubic and face-centred
cubic lattices for arbitrary dimensionality for the first three
lattices, and for for the hyper-fcc lattice. We show that there
is a close connection between the LGF of the -dimensional hypercubic lattice
and that of the -dimensional diamond lattice. We give constant-term
formulations of LGFs for all lattices and dimensions. Through a still
under-developed connection with Mahler measures, we point out an unexpected
connection between the coefficients of the s.c., b.c.c. and diamond LGFs and
some Ramanujan-type formulae for Comment: 30 page
Green's function of a finite chain and the discrete Fourier transform
A new expression for the Green's function of a finite one-dimensional lattice
with nearest neighbor interaction is derived via discrete Fourier transform.
Solution of the Heisenberg spin chain with periodic and open boundary
conditions is considered as an example. Comparison to Bethe ansatz clarifies
the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20,
No. 5 (2006) 593-60
Exact results for some Madelung type constants in the finite-size scaling theory
A general formula is obtained from which the madelung type constant: extensively used in the finite-size
scaling theory is computed analytically for some particular cases of the
parameters and . By adjusting these parameters one can obtain
different physical situations corresponding to different geometries and
magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added
New results on the limit for the width of the exotic Theta^+ resonance
We investigate the impact of the \Theta^+(1540) resonance on differential and
integrated cross sections for the reaction K^+d{\to}K^0pp, where experimental
information is available at kaon momenta below 640 MeV/c. The calculation
utilizes the J\"ulich KN model and extensions of it that include contributions
from a \Theta^+(1540) state with different widths. The evaluation of the
reaction K^+d{\to}K^0pp takes into account effects due to the Fermi motion of
the nucleons within the deuteron and the final three-body kinematics. We
conclude that the available data constrain the width of the \Theta^+(1540) to
be less than 1 MeV.Comment: 5 pages, 5 figures, updated version, accepted for publication in
Phys. Lett.
Diffusion-Limited One-Species Reactions in the Bethe Lattice
We study the kinetics of diffusion-limited coalescence, A+A-->A, and
annihilation, A+A-->0, in the Bethe lattice of coordination number z.
Correlations build up over time so that the probability to find a particle next
to another varies from \rho^2 (\rho is the particle density), initially, when
the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic
limit. As a result, the particle density decays inversely proportional to time,
\rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant
value.Comment: To be published in JPCM, special issue on Kinetics of Chemical
Reaction
Uniform tiling with electrical resistors
The electric resistance between two arbitrary nodes on any infinite lattice
structure of resistors that is a periodic tiling of space is obtained. Our
general approach is based on the lattice Green's function of the Laplacian
matrix associated with the network. We present several non-trivial examples to
show how efficient our method is. Deriving explicit resistance formulas it is
shown that the Kagom\'e, the diced and the decorated lattice can be mapped to
the triangular and square lattice of resistors. Our work can be extended to the
random walk problem or to electron dynamics in condensed matter physics.Comment: 22 pages, 14 figure
Point vortices on the sphere: a case with opposite vorticities
We study systems formed of 2N point vortices on a sphere with N vortices of
strength +1 and N vortices of strength -1. In this case, the Hamiltonian is
conserved by the symmetry which exchanges the positive vortices with the
negative vortices. We prove the existence of some fixed and relative
equilibria, and then study their stability with the ``Energy Momentum Method''.
Most of the results obtained are nonlinear stability results. To end, some
bifurcations are described.Comment: 35 pages, 9 figure
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