7,217 research outputs found
Factorisation of Macdonald polynomials
We discuss the problem of factorisation of the symmetric Macdonald
polynomials and present the obtained results for the cases of 2 and 3
variables.Comment: 13 pages, LaTex, no figure
photoproduction on the quasi-free nucleons in the chiral quark model
A chiral quark-model approach is adopted to study the photoproduction
off the quasi-free neutron and proton from a deuteron target. Good descriptions
of the differential cross sections, total cross sections and beam asymmetries
for these two processes are obtained in the low energy region. For , the dominant resonances are ,
, , and . While for
the process, the dominant resonances are
, , , and
. Furthermore, the channel backgrounds have significant
contributions to the photoproduction processes. The configuration
mixings in the and can be extracted,
i.e. and . It shows that the
narrow bump-like structure around GeV observed in can be naturally explained by the constructive
interferences between and . In contrast, the
destructive interference between and produces the
shallow dip around GeV in . The wave
interfering behaviors in the proton and neutron reactions are correlated with
each other in the quark model framework, and no new exotic nucleon resonances
are needed in these two reactions.Comment: 12 pages, 11 figures, helicity amplitudes are added, to be published
in PR
Eigenproblem for Jacobi matrices: hypergeometric series solution
We study the perturbative power-series expansions of the eigenvalues and
eigenvectors of a general tridiagonal (Jacobi) matrix of dimension d.
The(small) expansion parameters are being the entries of the two diagonals of
length d-1 sandwiching the principal diagonal, which gives the unperturbed
spectrum.
The solution is found explicitly in terms of multivariable (Horn-type)
hypergeometric series of 3d-5 variables in the generic case, or 2d-3 variables
for the eigenvalue growing from a corner matrix element. To derive the result,
we first rewrite the spectral problem for a Jacobi matrix as an equivalent
system of cubic equations, which are then resolved by the application of the
multivariable Lagrange inversion formula. The corresponding Jacobi determinant
is calculated explicitly. Explicit formulae are also found for any monomial
composed of eigenvector's components.Comment: Latex, 20 pages; v2: corrected typos, added section with example
Topological defect formation in quenched ferromagnetic Bose-Einstein condensates
We study the dynamics of the quantum phase transition of a ferromagnetic
spin-1 Bose-Einstein condensate from the polar phase to the broken-axisymmetry
phase by changing magnetic field, and find the spontaneous formation of spinor
domain walls followed by the creation of polar-core spin vortices. We also find
that the spin textures depend very sensitively on the initial noise
distribution, and that an anisotropic and colored initial noise is needed to
reproduce the Berkeley experiment [Sadler et al., Nature 443, 312 (2006)]. The
dynamics of vortex nucleation and the number of created vortices depend also on
the manner in which the magnetic field is changed. We point out an analogy
between the formation of spin vortices from domain walls in a spinor BEC and
that of vortex-antivortex pairs from dark solitons in a scalar BEC.Comment: 10 pages, 11 figure
Random copolymer: Gaussian variational approach
We study the phase transitions of a random copolymer chain with quenched
disorder. We apply a replica variational approach based on a Gaussian trial
Hamiltonian in terms of the correlation functions of monomer Fourier
coordinates. This allows us to study collapse, phase separation and freezing
transitions within the same mean field theory. The effective free energy of the
system is derived analytically and analysed numerically. Such quantities as the
radius of gyration or the average value of the overlap between different
replicas are treated as observables and evaluated by introducing appropriate
external fields to the Hamiltonian. We obtain the phase diagram and show that
this system exhibits a scale dependent freezing transition. The correlations
between replicas appear at different length scales as the temperature
decreases. This indicates the existence of the topological frustration.Comment: 15 pages, 4 Postscript figure
Dark matter-wave solitons in the dimensionality crossover
We consider the statics and dynamics of dark matter-wave solitons in the
dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial
Schr\"{o}dinger mean-field model, we find that the anomalous mode of the
Bogoliubov spectrum has an eigenfrequency which coincides with the soliton
oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that
substantial deviations (of order of 10% or more) from the characteristic
frequency ( being the longitudinal trap
frequency) are possible even in the purely 1D regime.Comment: Phys. Rev. A, in pres
Separation of variables for the Ruijsenaars system
We construct a separation of variables for the classical n-particle
Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser
system). The separated coordinates appear as the poles of the properly
normalised eigenvector (Baker-Akhiezer function) of the corresponding Lax
matrix. Two different normalisations of the BA functions are analysed. The
canonicity of the separated variables is verified with the use of r-matrix
technique. The explicit expressions for the generating function of the
separating canonical transform are given in the simplest cases n=2 and n=3.
Taking nonrelativistic limit we also construct a separation of variables for
the elliptic Calogero-Moser system.Comment: 26 pages, LaTex, no figure
- …