301,444 research outputs found
-pairing interaction, number of states, and nine- sum rules of four identical particles
In this paper we study -pairing Hamiltonian and find that the sum of
eigenvalues of spin states equals sum of norm matrix elements within the
pair basis for four identical particles such as four fermions in a single-
shell or four bosons with spin . We relate number of states to sum rules of
nine- coefficients. We obtained sum rules for nine- coefficients
summing
over (1) even and , (2) even and odd , (3) odd and odd ,
and (4) both even and odd , where is a half integer and is an
integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review
C, in pres
Formation mechanisms and phase stability of solid-state grown cspbi3 perovskites
CsPbI3 inorganic perovskite is synthesized by a solvent-free, solid-state reaction, and its structural and optical properties can be deeply investigated using a multi-technique approach. X-ray Diffraction (XRD) and Raman measurements, optical absorption, steady-time and time-resolved luminescence, as well as High-Resolution Transmission Electron Microscopy (HRTEM) imaging, were exploited to understand phase evolution as a function of synthesis time length. Nanoparticles with multiple, well-defined crystalline domains of different crystalline phases were observed, usually surrounded by a thin, amorphous/out-of-axis shell. By increasing the synthesis time length, in addition to the pure α phase, which was rapidly converted into the δ phase at room temperature, a secondary phase, Cs4PbI6, was observed, together with the 715 nm-emitting γ phase
Two-point correlation function with pion in QCD sum rules
Within the framework of the conventional QCD sum rules, we study the pion
two-point correlation function, , beyond the soft-pion limit. We construct sum rules from the
three distinct Dirac structures, i \gamma_5 \notp, i \gamma_5, \gamma_5
\sigma_{\mu \nu} {q^\mu p^\nu} and study the reliability of each sum rule. The
sum rule from the third structure is found to be insensitive to the continuum
threshold, , and contains relatively small contribution from the
undetermined single pole which we denote as . The sum rule from the structure is very different even though it contains similar
contributions from and as the ones coming from the structure. On the other hand, the sum rule from
the i \gamma_5 \notp structure has strong dependence on both and ,
which is clearly in constrast with the sum rule for . We identify the source of the sensitivity for each of the sum
rules by making specific models for higher resonance contributions and discuss
the implication.Comment: slightly revised. version accepted for publication in Physical Review
Negative and Nonlinear Response in an Exactly Solved Dynamical Model of Particle Transport
We consider a simple model of particle transport on the line defined by a
dynamical map F satisfying F(x+1) = 1 + F(x) for all x in R and F(x) = ax + b
for |x| < 0.5. Its two parameters a (`slope') and b (`bias') are respectively
symmetric and antisymmetric under reflection x -> R(x) = -x. Restricting
ourselves to the chaotic regime |a| > 1 and therein mainly to the part a>1 we
study not only the `diffusion coefficient' D(a,b), but also the `current'
J(a,b). An important tool for such a study are the exact expressions for J and
D as obtained recently by one of the authors. These expressions allow for a
quite efficient numerical implementation, which is important, because the
functions encountered typically have a fractal character. The main results are
presented in several plots of these functions J(a,b) and D(a,b) and in an
over-all `chart' displaying, in the parameter plane, all possibly relevant
information on the system including, e.g., the dynamical phase diagram as well
as invariants such as the values of topological invariants (kneading numbers)
which, according to the formulas, determine the singularity structure of J and
D. Our most significant findings are: 1) `Nonlinear Response': The parameter
dependence of these transport properties is, throughout the `ergodic' part of
the parameter plane (i.e. outside the infinitely many Arnol'd tongues)
fractally nonlinear. 2) `Negative Response': Inside certain regions with an
apparently fractal boundary the current J and the bias b have opposite signs.Comment: corrected typos and minor reformulations; 28 pages (revtex) with 7
figures (postscript); accepted for publication in JS
Chebyshev Series Expansion of Inverse Polynomials
An inverse polynomial has a Chebyshev series expansion
1/\sum(j=0..k)b_j*T_j(x)=\sum'(n=0..oo) a_n*T_n(x) if the polynomial has no
roots in [-1,1]. If the inverse polynomial is decomposed into partial
fractions, the a_n are linear combinations of simple functions of the
polynomial roots. If the first k of the coefficients a_n are known, the others
become linear combinations of these with expansion coefficients derived
recursively from the b_j's. On a closely related theme, finding a polynomial
with minimum relative error towards a given f(x) is approximately equivalent to
finding the b_j in f(x)/sum_(j=0..k)b_j*T_j(x)=1+sum_(n=k+1..oo) a_n*T_n(x),
and may be handled with a Newton method providing the Chebyshev expansion of
f(x) is known.Comment: LaTeX2e, 24 pages, 1 PostScript figure. More references. Corrected
typos in (1.1), (3.4), (4.2), (A.5), (E.8) and (E.11
Number of states for nucleons in a single- shell
In this paper we obtain number of states with a given spin and a given
isospin for systems with three and four nucleons in a single- orbit, by
using sum rules of six- and nine- symbols obtained in earlier works.Comment: to be published in Physical Review
Power laws of complex systems from Extreme physical information
Many complex systems obey allometric, or power, laws y=Yx^{a}. Here y is the
measured value of some system attribute a, Y is a constant, and x is a
stochastic variable. Remarkably, for many living systems the exponent a is
limited to values +or- n/4, n=0,1,2... Here x is the mass of a randomly
selected creature in the population. These quarter-power laws hold for many
attributes, such as pulse rate (n=-1). Allometry has, in the past, been
theoretically justified on a case-by-case basis. An ultimate goal is to find a
common cause for allometry of all types and for both living and nonliving
systems. The principle I - J = extrem. of Extreme physical information (EPI) is
found to provide such a cause. It describes the flow of Fisher information J =>
I from an attribute value a on the cell level to its exterior observation y.
Data y are formed via a system channel function y = f(x,a), with f(x,a) to be
found. Extremizing the difference I - J through variation of f(x,a) results in
a general allometric law f(x,a)= y = Yx^{a}. Darwinian evolution is presumed to
cause a second extremization of I - J, now with respect to the choice of a. The
solution is a=+or-n/4, n=0,1,2..., defining the particular powers of biological
allometry. Under special circumstances, the model predicts that such biological
systems are controlled by but two distinct intracellular information sources.
These sources are conjectured to be cellular DNA and cellular transmembrane ion
gradient
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