686 research outputs found
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
Structure Factor and Electronic Structure of Compressed Liquid Rubidium
We have applied the quantal hypernetted-chain equations in combination with
the Rosenfeld bridge-functional to calculate the atomic and the electronic
structure of compressed liquid-rubidium under high pressure (0.2, 2.5, 3.9, and
6.1 GPa); the calculated structure factors are in good agreement with
experimental results measured by Tsuji et al. along the melting curve. We found
that the Rb-pseudoatom remains under these high pressures almost unchanged with
respect to the pseudoatom at room pressure; thus, the effective ion-ion
interaction is practically the same for all pressure-values. We observe that
all structure factors calculated for this pressure-variation coincide almost
into a single curve if wavenumbers are scaled in units of the Wigner-Seitz
radius although no corresponding scaling feature is observed in the
effective ion-ion interaction.This scaling property of the structure factors
signifies that the compression in liquid-rubidium is uniform with increasing
pressure; in absolute Q-values this means that the first peak-position ()
of the structure factor increases proportionally to ( being the
specific volume per ion), as was experimentally observed by Tsuji et al.Comment: 18 pages, 11 figure
How to construct spin chains with perfect state transfer
It is shown how to systematically construct the quantum spin chains with
nearest-neighbor interactions that allow perfect state transfer (PST). Sets of
orthogonal polynomials (OPs) are in correspondence with such systems. The key
observation is that for any admissible one-excitation energy spectrum, the
weight function of the associated OPs is uniquely prescribed. This entails the
complete characterization of these PST models with the mirror symmetry property
arising as a corollary. A simple and efficient algorithm to obtain the
corresponding Hamiltonians is presented. A new model connected to a special
case of the symmetric -Racah polynomials is offered. It is also explained
how additional models with PST can be derived from a parent system by removing
energy levels from the one-excitation spectrum of the latter. This is achieved
through Christoffel transformations and is also completely constructive in
regards to the Hamiltonians.Comment: 7 page
Radial Bargmann representation for the Fock space of type B
Let be the probability and orthogonality measure for the
-Meixner-Pollaczek orthogonal polynomials, which has appeared in
\cite{BEH15} as the distribution of the -Gaussian process (the
Gaussian process of type B) over the -Fock space (the Fock space of
type B). The main purpose of this paper is to find the radial Bargmann
representation of . Our main results cover not only the
representation of -Gaussian distribution by \cite{LM95}, but also of
-Gaussian and symmetric free Meixner distributions on . In
addition, non-trivial commutation relations satisfied by -operators
are presented.Comment: 13 pages, minor changes have been mad
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)
Lowering and raising operators for the free Meixner class of orthogonal polynomials
We compare some properties of the lowering and raising operators for the
classical and free classes of Meixner polynomials on the real line
Exact limiting relation between the structure factors in neutron and x-ray scattering
The ratio of the static matter structure factor measured in experiments on
coherent X-ray scattering to the static structure factor measured in
experiments on neutron scattering is considered. It is shown theoretically that
this ratio in the long-wavelength limit is equal to the nucleus charge at
arbitrary thermodynamic parameters of a pure substance (the system of nuclei
and electrons, where interaction between particles is pure Coulomb) in a
disordered equilibrium state. This result is the exact relation of the quantum
statistical mechanics. The experimental verification of this relation can be
done in the long wavelength X-ray and neutron experiments.Comment: 7 pages, no figure
Birth and death processes and quantum spin chains
This papers underscores the intimate connection between the quantum walks
generated by certain spin chain Hamiltonians and classical birth and death
processes. It is observed that transition amplitudes between single excitation
states of the spin chains have an expression in terms of orthogonal polynomials
which is analogous to the Karlin-McGregor representation formula of the
transition probability functions for classes of birth and death processes. As
an application, we present a characterization of spin systems for which the
probability to return to the point of origin at some time is 1 or almost 1.Comment: 14 page
q-Ultraspherical polynomials for q a root of unity
Properties of the -ultraspherical polynomials for being a primitive
root of unity are derived using a formalism of the algebra. The
orthogonality condition for these polynomials provides a new class of
trigonometric identities representing discrete finite-dimensional analogs of
-beta integrals of Ramanujan.Comment: 7 pages, LATE
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