63,983 research outputs found
Survey of electrical resistivity measurements on 8 additional pure metals in the temperature range 0 to 273 K
Electrical resistivity measurements on pure metals in temperature range 0 to 273
Gravitating semirelativistic N-boson systems
Analytic energy bounds for N-boson systems governed by semirelativistic
Hamiltonians of the form H=\sum_{i=1}^N(p_i^2 + m^2)^{1/2} - sum_{1=i<j}^N
v/r_{ij}, with v>0, are derived by use of Jacobi relative coordinates. For
gravity v=c/N, these bounds are substantially tighter than earlier bounds and
they are shown to coincide with known results in the nonrelativistic limit.Comment: 7 pages, 2 figures It is now proved that the reduced Hamiltonian is
bounded below by the simple N/2 Hamiltonia
Asymptotic iteration method for eigenvalue problems
An asymptotic interation method for solving second-order homogeneous linear
differential equations of the form y'' = lambda(x) y' + s(x) y is introduced,
where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to
Schroedinger type problems, including some with highly singular potentials, are
presented.Comment: 14 page
Closed-form sums for some perturbation series involving associated Laguerre polynomials
Infinite series sum_{n=1}^infty {(alpha/2)_n / (n n!)}_1F_1(-n, gamma, x^2),
where_1F_1(-n, gamma, x^2)={n!_(gamma)_n}L_n^(gamma-1)(x^2), appear in the
first-order perturbation correction for the wavefunction of the generalized
spiked harmonic oscillator Hamiltonian H = -d^2/dx^2 + B x^2 + A/x^2 +
lambda/x^alpha 0 0, A >= 0. It is proved that the
series is convergent for all x > 0 and 2 gamma > alpha, where gamma = 1 +
(1/2)sqrt(1+4A). Closed-form sums are presented for these series for the cases
alpha = 2, 4, and 6. A general formula for finding the sum for alpha/2 = 2 + m,
m = 0,1,2, ..., in terms of associated Laguerre polynomials, is also provided.Comment: 16 page
Semirelativistic stability of N-boson systems bound by 1/r pair potentials
We analyze a system of self-gravitating identical bosons by means of a
semirelativistic Hamiltonian comprising the relativistic kinetic energies of
the involved particles and added (instantaneous) Newtonian gravitational pair
potentials. With the help of an improved lower bound to the bottom of the
spectrum of this Hamiltonian, we are able to enlarge the known region for
relativistic stability for such boson systems against gravitational collapse
and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation,
remainder of the paper unchange
Coulomb plus power-law potentials in quantum mechanics
We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the
Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q >
-2 and q \ne 0. We show by envelope theory that the discrete eigenvalues
E_{n\ell} of H may be approximated by the semiclassical expression
E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}.
Values of mu and nu are prescribed which yield upper and lower bounds.
Accurate upper bounds are also obtained by use of a trial function of the form,
psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for
V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with
comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure
Spoken words
Chiefly tablesIncludes bibliographical referencesSupported in part by the National Institute of Education under contract no. US-NIE-C-400-76-011
General energy bounds for systems of bosons with soft cores
We study a bound system of N identical bosons interacting by model pair
potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a
variational trial function and the `equivalent 2-body method', we find explicit
upper and lower bound formulas for the N-particle ground-state energy in
arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is
demonstrated that the upper bound can be systematically improved with the aid
of a special large-N limit in collective field theory
Semiclassical energy formulas for power-law and log potentials in quantum mechanics
We study a single particle which obeys non-relativistic quantum mechanics in
R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2,
then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may
be represented exactly by the semiclassical expression E_{n\ell}(q) =
min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) =
ln(r). By writing one power as a smooth transformation of another, and using
envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are
monotone increasing. Recent refinements to the comparison theorem of QM in
which comparison potentials can cross over, allow us to prove for n = 1 that
Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q}
is monotone decreasing. Thus P(q) cannot increase too slowly. This result
yields some sharper estimates for power-potential eigenvlaues at the bottom of
each angular-momentum subspace.Comment: 20 pages, 5 figure
Regulation of AQP0 water permeability is enhanced by cooperativity.
Aquaporin 0 (AQP0), essential for lens clarity, is a tetrameric protein composed of four identical monomers, each of which has its own water pore. The water permeability of AQP0 expressed in Xenopus laevis oocytes can be approximately doubled by changes in calcium concentration or pH. Although each monomer pore functions as a water channel, under certain conditions the pores act cooperatively. In other words, the tetramer is the functional unit. In this paper, we show that changes in external pH and calcium can induce an increase in water permeability that exhibits either a positive cooperativity switch-like increase in water permeability or an increase in water permeability in which each monomer acts independently and additively. Because the concentrations of calcium and hydrogen ions increase toward the center of the lens, a concentration signal could trigger a regulatory change in AQP0 water permeability. It thus seems plausible that the cooperative modes of water permeability regulation by AQP0 tetramers mediated by decreased pH and elevated calcium are the physiologically important ones in the living lens
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