190 research outputs found
Accurate calculation of resonances in multiple-well oscillators
Quantum--mechanical multiple--well oscillators exhibit curious complex
eigenvalues that resemble resonances in models with continuum spectra. We
discuss a method for the accurate calculation of their real and imaginary
parts
Genome Assembly Improvement and Mapping Convergently Evolved Skeletal Traits in Sticklebacks with Genotyping-by-Sequencing.
Marine populations of the threespine stickleback (Gasterosteus aculeatus) have repeatedly colonized and rapidly adapted to freshwater habitats, providing a powerful system to map the genetic architecture of evolved traits. Here, we developed and applied a binned genotyping-by-sequencing (GBS) method to build dense genome-wide linkage maps of sticklebacks using two large marine by freshwater F2 crosses of more than 350 fish each. The resulting linkage maps significantly improve the genome assembly by anchoring 78 new scaffolds to chromosomes, reorienting 40 scaffolds, and rearranging scaffolds in 4 locations. In the revised genome assembly, 94.6% of the assembly was anchored to a chromosome. To assess linkage map quality, we mapped quantitative trait loci (QTL) controlling lateral plate number, which mapped as expected to a 200-kb genomic region containing Ectodysplasin, as well as a chromosome 7 QTL overlapping a previously identified modifier QTL. Finally, we mapped eight QTL controlling convergently evolved reductions in gill raker length in the two crosses, which revealed that this classic adaptive trait has a surprisingly modular and nonparallel genetic basis
The optimized Rayleigh-Ritz scheme for determining the quantum-mechanical spectrum
The convergence of the Rayleigh-Ritz method with nonlinear parameters
optimized through minimization of the trace of the truncated matrix is
demonstrated by a comparison with analytically known eigenstates of various
quasi-solvable systems. We show that the basis of the harmonic oscillator
eigenfunctions with optimized frequency ? enables determination of boundstate
energies of one-dimensional oscillators to an arbitrary accuracy, even in the
case of highly anharmonic multi-well potentials. The same is true in the
spherically symmetric case of V (r) = {\omega}2r2 2 + {\lambda}rk, if k > 0.
For spiked oscillators with k < -1, the basis of the pseudoharmonic oscillator
eigenfunctions with two parameters ? and {\gamma} is more suitable, and
optimization of the latter appears crucial for a precise determination of the
spectrum.Comment: 22 pages,8 figure
A basis for variational calculations in d dimensions
In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for
the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions.
The basis functions in each angular momentum subspace are of the form
phi_i(r)=r^{i+1+(t-d)/2}e^{-r^p/2}, i >= 0, p > 0, t > 0. The matrix elements
are given in terms of the Gamma function for all d. The significance of the
parameters t and p and scale s are discussed. Applications to a variety of
potentials are presented, including potentials with singular repulsive terms of
the form b/r^a, a,b > 0, perturbed Coulomb potentials -D/r + B r + Ar^2, and
potentials with weak repulsive terms, such as -g r^2 + r^4, g > 0.Comment: 22 page
Variational collocation for systems of coupled anharmonic oscillators
We have applied a collocation approach to obtain the numerical solution to
the stationary Schr\"odinger equation for systems of coupled oscillators. The
dependence of the discretized Hamiltonian on scale and angle parameters is
exploited to obtain optimal convergence to the exact results. A careful
comparison with results taken from the literature is performed, showing the
advantages of the present approach.Comment: 14 pages, 10 table
The Fokker-Planck equation for bistable potential in the optimized expansion
The optimized expansion is used to formulate a systematic approximation
scheme to the probability distribution of a stochastic system. The first order
approximation for the one-dimensional system driven by noise in an anharmonic
potential is shown to agree well with the exact solution of the Fokker-Planck
equation. Even for a bistable system the whole period of evolution to
equilibrium is correctly described at various noise intensities.Comment: 12 pages, LATEX, 3 Postscript figures compressed an
Eigenvalue bounds for polynomial central potentials in d dimensions
If a single particle obeys non-relativistic QM in R^d and has the Hamiltonian
H = - Delta + f(r), where f(r)=sum_{i = 1}^{k}a_ir^{q_i}, 2\leq q_i < q_{i+1},
a_i \geq 0P_i =
P_{n\ell}^{(d)}(q_k) and a general approximation formula if P_i =
P_{n\ell}^{(d)}(q_i). For the quantum anharmonic oscillator f(r)=r^2+\lambda
r^{2m},m=2,3,... in d dimension, for example, E = E_{n\ell}^{(d)}(\lambda) is
determined by the algebraic expression
\lambda={1\over \beta}({2\alpha(m-1)\over mE-\delta})^m({4\alpha \over
(mE-\delta)}-{E\over (m-1)}) where \delta={\sqrt{E^2m^2-4\alpha(m^2-1)}} and
\alpha, \beta are constants. An improved lower bound to the lowest eigenvalue
in each angular-momentum subspace is also provided. A comparison with the
recent results of Bhattacharya et al (Phys. Lett. A, 244 (1998) 9) and Dasgupta
et al (J. Phys. A: Math. Theor., 40 (2007) 773) is discussed.Comment: 13 pages, no figure
Spiked oscillators: exact solution
A procedure to obtain the eigenenergies and eigenfunctions of a quantum
spiked oscillator is presented. The originality of the method lies in an
adequate use of asymptotic expansions of Wronskians of algebraic solutions of
the Schroedinger equation. The procedure is applied to three familiar examples
of spiked oscillators
Two approximate formulae for the binding energies in Lambda hypernuclei and light nuclei
Two approximate formulae are given for the binding energies in
Lambda-hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller
and the Gaussian central potentials. Those easily programmable formulae combine
the eigenvalues of the transformed Jacobi eigenequation and an application of
the hypervirial theorems.Comment: Accepted for publication in Europhysics Letter
Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
Recent proofs of the convergence of the linear delta expansion in zero and in
one dimensions have been limited to the analogue of the vacuum generating
functional in field theory. In zero dimensions it was shown that with an
appropriate, -dependent, choice of an optimizing parameter \l, which is an
important feature of the method, the sequence of approximants tends to
with an error proportional to . In the present paper we
establish the convergence of the linear delta expansion for the connected
vacuum function . We show that with the same choice of \l the
corresponding sequence tends to with an error proportional to . The rate of convergence of the latter sequence is governed by
the positions of the zeros of .Comment: 20 pages, LaTeX, Imperial/TP/92-93/5
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