679 research outputs found
One-parameter extension of the Doi-Peliti formalism and relation with orthogonal polynomials
An extension of the Doi-Peliti formalism for stochastic chemical kinetics is
proposed. Using the extension, path-integral expressions consistent with
previous studies are obtained. In addition, the extended formalism is naturally
connected to orthogonal polynomials. We show that two different orthogonal
polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to
express the Doi-Peliti formalism explicitly.Comment: 10 page
Nucleus-Electron Model for States Changing from a Liquid Metal to a Plasma and the Saha Equation
We extend the quantal hypernetted-chain (QHNC) method, which has been proved
to yield accurate results for liquid metals, to treat a partially ionized
plasma. In a plasma, the electrons change from a quantum to a classical fluid
gradually with increasing temperature; the QHNC method applied to the electron
gas is in fact able to provide the electron-electron correlation at arbitrary
temperature. As an illustrating example of this approach, we investigate how
liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV
at a fixed normal ion-density . The electron-ion
radial distribution function (RDF) in liquid Rb has distinct inner-core and
outer-core parts. Even at a temperature of 1 eV, this clear distinction remains
as a characteristic of a liquid metal. At a temperature of 3 eV, this
distinction disappears, and rubidium becomes a plasma with the ionization 1.21.
The temperature variations of bound levels in each ion and the average
ionization are calculated in Rb plasmas at the same time. Using the
density-functional theory, we also derive the Saha equation applicable even to
a high-density plasma at low temperatures. The QHNC method provides a procedure
to solve this Saha equation with ease by using a recursive formula; the charge
population of differently ionized species are obtained in Rb plasmas at several
temperatures. In this way, it is shown that, with the atomic number as the only
input, the QHNC method produces the average ionization, the electron-ion and
ion-ion RDF's, and the charge population which are consistent with the atomic
structure of each ion for a partially ionized plasma.Comment: 28 pages(TeX) and 11 figures (PS
Pressure formulas for liquid metals and plasmas based on the density-functional theory
At first, pressure formulas for the electrons under the external potential
produced by fixed nuclei are derived both in the surface integral and volume
integral forms concerning an arbitrary volume chosen in the system; the surface
integral form is described by a pressure tensor consisting of a sum of the
kinetic and exchange-correlation parts in the density-functional theory, and
the volume integral form represents the virial theorem with subtraction of the
nuclear virial. Secondly on the basis of these formulas, the thermodynamical
pressure of liquid metals and plasmas is represented in the forms of the
surface integral and the volume integral including the nuclear contribution.
From these results, we obtain a virial pressure formula for liquid metals,
which is more accurate and simpler than the standard representation. From the
view point of our formulation, some comments are made on pressure formulas
derived previously and on a definition of pressure widely used.Comment: 18 pages, no figur
Polynomial solutions of nonlinear integral equations
We analyze the polynomial solutions of a nonlinear integral equation,
generalizing the work of C. Bender and E. Ben-Naim. We show that, in some
cases, an orthogonal solution exists and we give its general form in terms of
kernel polynomials.Comment: 10 page
Probing Ion-Ion and Electron-Ion Correlations in Liquid Metals within the Quantum Hypernetted Chain Approximation
We use the Quantum Hypernetted Chain Approximation (QHNC) to calculate the
ion-ion and electron-ion correlations for liquid metallic Li, Be, Na, Mg, Al,
K, Ca, and Ga. We discuss trends in electron-ion structure factors and radial
distribution functions, and also calculate the free-atom and metallic-atom
form-factors, focusing on how bonding effects affect the interpretation of
X-ray scattering experiments, especially experimental measurements of the
ion-ion structure factor in the liquid metallic phase.Comment: RevTeX, 19 pages, 7 figure
Phase Diagram for Anderson Disorder: beyond Single-Parameter Scaling
The Anderson model for independent electrons in a disordered potential is
transformed analytically and exactly to a basis of random extended states
leading to a variant of augmented space. In addition to the widely-accepted
phase diagrams in all physical dimensions, a plethora of additional, weaker
Anderson transitions are found, characterized by the long-distance behavior of
states. Critical disorders are found for Anderson transitions at which the
asymptotically dominant sector of augmented space changes for all states at the
same disorder. At fixed disorder, critical energies are also found at which the
localization properties of states are singular. Under the approximation of
single-parameter scaling, this phase diagram reduces to the widely-accepted one
in 1, 2 and 3 dimensions. In two dimensions, in addition to the Anderson
transition at infinitesimal disorder, there is a transition between two
localized states, characterized by a change in the nature of wave function
decay.Comment: 51 pages including 4 figures, revised 30 November 200
Wigner quantization of some one-dimensional Hamiltonians
Recently, several papers have been dedicated to the Wigner quantization of
different Hamiltonians. In these examples, many interesting mathematical and
physical properties have been shown. Among those we have the ubiquitous
relation with Lie superalgebras and their representations. In this paper, we
study two one-dimensional Hamiltonians for which the Wigner quantization is
related with the orthosymplectic Lie superalgebra osp(1|2). One of them, the
Hamiltonian H = xp, is popular due to its connection with the Riemann zeros,
discovered by Berry and Keating on the one hand and Connes on the other. The
Hamiltonian of the free particle, H_f = p^2/2, is the second Hamiltonian we
will examine. Wigner quantization introduces an extra representation parameter
for both of these Hamiltonians. Canonical quantization is recovered by
restricting to a specific representation of the Lie superalgebra osp(1|2)
Escort mean values and the characterization of power-law-decaying probability densities
Escort mean values (or -moments) constitute useful theoretical tools for
describing basic features of some probability densities such as those which
asymptotically decay like {\it power laws}. They naturally appear in the study
of many complex dynamical systems, particularly those obeying nonextensive
statistical mechanics, a current generalization of the Boltzmann-Gibbs theory.
They recover standard mean values (or moments) for . Here we discuss the
characterization of a (non-negative) probability density by a suitable set of
all its escort mean values together with the set of all associated normalizing
quantities, provided that all of them converge. This opens the door to a
natural extension of the well known characterization, for the instance,
of a distribution in terms of the standard moments, provided that {\it all} of
them have {\it finite} values. This question would be specially relevant in
connection with probability densities having {\it divergent} values for all
nonvanishing standard moments higher than a given one (e.g., probability
densities asymptotically decaying as power-laws), for which the standard
approach is not applicable. The Cauchy-Lorentz distribution, whose second and
higher even order moments diverge, constitutes a simple illustration of the
interest of this investigation. In this context, we also address some
mathematical subtleties with the aim of clarifying some aspects of an
interesting non-linear generalization of the Fourier Transform, namely, the
so-called -Fourier Transform.Comment: 20 pages (2 Appendices have been added
Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]
The quantization of phase is still an open problem. In the approach of
Susskind and Glogower so called cosine and sine operators play a fundamental
role. Their eigenstates in the Fock representation are related with the
Chebyshev polynomials of the second kind. Here we introduce more general cosine
and sine operators whose eigenfunctions in the Fock basis are related in a
similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1].
To each polynomial set defined in terms of a weight function there corresponds
a pair of cosine and sine operators. Depending on the symmetry of the weight
function we distinguish generalized or extended operators. Their eigenstates
are used to define cosine and sine representations and probability
distributions. We consider also the inverse arccosine and arcsine operators and
use their eigenstates to define cosine-phase and sine-phase distributions,
respectively. Specific, numerical and graphical results are given for the
classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure
Almost perfect state transfer in quantum spin chains
The natural notion of almost perfect state transfer (APST) is examined. It is
applied to the modelling of efficient quantum wires with the help of spin
chains. It is shown that APST occurs in mirror-symmetric systems, when the
1-excitation energies of the chains are linearly independent over rational
numbers. This result is obtained as a corollary of the Kronecker theorem in
Diophantine approximation. APST happens under much less restrictive conditions
than perfect state transfer (PST) and moreover accommodates the unavoidable
imperfections. Some examples are discussed.Comment: 11 page
- âŠ