Letter from H. V. Andrews to John Muir, 1905 Apr 19.

THE COUNTRYCALENDER13ASTOR PLACE NEWYORKApril 19, 1905.Mr. John Muir, Martinez, California. Dear Sir:- We have pleasure in sending you under separate cover a copy of the first issue of our now magazine.Would you be interested to prepare for some future number of it (not too far in the future we hope) an article which might be called The Life of a River , tracing a stream from its source in a glacier to its fall into the sea? We hope the idea will appeal to you, and if it does we promise to provide an appropriate setting of fine typography and beautiful illustration to do it justice. Very truly yours, [illegible]Managing Editor.0355

Letter from H. V. Andrews to John Muir, 1905 Apr 19.

THE COUNTRYCALENDER13ASTOR PLACE NEWYORKApril 19, 1905.Mr. John Muir, Martinez, California. Dear Sir:- We have pleasure in sending you under separate cover a copy of the first issue of our now magazine.Would you be interested to prepare for some future number of it (not too far in the future we hope) an article which might be called The Life of a River , tracing a stream from its source in a glacier to its fall into the sea? We hope the idea will appeal to you, and if it does we promise to provide an appropriate setting of fine typography and beautiful illustration to do it justice. Very truly yours, [illegible]Managing Editor.0355

Letter from H. V. Andrews to John Muir, 1905 Apr 19.

THE COUNTRYCALENDER13ASTOR PLACE NEWYORKApril 19, 1905.Mr. John Muir, Martinez, California. Dear Sir:- We have pleasure in sending you under separate cover a copy of the first issue of our now magazine.Would you be interested to prepare for some future number of it (not too far in the future we hope) an article which might be called The Life of a River , tracing a stream from its source in a glacier to its fall into the sea? We hope the idea will appeal to you, and if it does we promise to provide an appropriate setting of fine typography and beautiful illustration to do it justice. Very truly yours, [illegible]Managing Editor.0355

qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions

To show a mechanism leading to the breakdown of a particle picture for the multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high dimensions, we investigate the corresponding 2-$d$ nonlinear Schr{\"o}dinger equation (Gross-Pitaevskii equation) with use of a modified variational principle. A molecule of two identical Gaussian wavepackets has two degrees of freedom(DFs), the separation of center-of-masses and the wavepacket width. Without the inter-component interaction(ICI) these DFs show independent regular oscillations with the degenerate eigen-frequencies. The inclusion of ICI strongly mixes these DFs, generating a fat mode that breaks a particle picture, which however can be recovered by introducing a time-periodic ICI with zero average. In case of the molecule of three wavepackets for a three-component BEC, the increase of amplitude of ICI yields a transition from regular to chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure

The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond

There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the Gross-Pitaevskii equation to obtain optimum two-mode parameters. We find that by using the lowest symmetric and antisymmetric wavefunctions, it is possible to derive equations for a more exact two-mode model that provides for a variable tunneling rate depending on the instantaneous values of the number of atoms and phase differences. Especially for larger values of the nonlinear interaction term and larger barrier heights, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in 1D and 3D, as compared with previous models with constant tunneling, and better agreement with experimental results for the tunneling oscillation frequency [Albiez et al., cond-mat/0411757]. We also show how this approach can be used to obtain modified equations for a second quantized version of the Bose double well problem.Comment: RevTeX, 14 pages, 14 figure

Level density of a Fermi gas: average growth and fluctuations

We compute the level density of a two--component Fermi gas as a function of the number of particles, angular momentum and excitation energy. The result includes smooth low--energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy--Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low--lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur

Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table