1,292 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
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
Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials
Nonsymmetric Askey-Wilson polynomials are usually written as Laurent
polynomials. We write them equivalently as 2-vector-valued symmetric Laurent
polynomials. Then the Dunkl-Cherednik operator of which they are
eigenfunctions, is represented as a 2x2 matrix-valued operator. As a new result
made possible by this approach we obtain positive definiteness of the inner
product in the orthogonality relations, under certain constraints on the
parameters. A limit transition to nonsymmetric little q-Jacobi polynomials also
becomes possible in this way. Nonsymmetric Jacobi polynomials are considered as
limits both of the Askey-Wilson and of the little q-Jacobi case.Comment: 16 pages. Dedicated to Paul Butzer on the occasion of his 80th
birthday. v4: minor correction in (4.14
Equilibration in long-range quantum spin systems from a BBGKY perspective
The time evolution of -spin reduced density operators is studied for a
class of Heisenberg-type quantum spin models with long-range interactions. In
the framework of the quantum Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY)
hierarchy, we introduce an unconventional representation, different from the
usual cluster expansion, which casts the hierarchy into the form of a
second-order recursion. This structure suggests a scaling of the expansion
coefficients and the corresponding time scales in powers of with the
system size , implying a separation of time scales in the large system
limit. For special parameter values and initial conditions, we can show
analytically that closing the BBGKY hierarchy by neglecting -spin
correlations does never lead to equilibration, but gives rise to quasi-periodic
time evolution with at most independent frequencies. Moreover, for the
same special parameter values and in the large- limit, we solve the complete
recursion relation (the full BBGKY hierarchy), observing a superexponential
decay to equilibrium in rescaled time .Comment: 3 figure
Topological quantum phase transition in the BEC-BCS crossover phenomena
A crossover between the Bose Einstein condensation (BEC) and BCS
superconducting state is described topologically in the chiral symmetric
fermion system with attractive interaction. Using a local Z_2 Berry phase, we
found a quantum phase transition between the BEC and BCS phases without
accompanying the bulk gap closing.Comment: 4 pages, 5 figure
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
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
On There Being Infinitely Many Thinkable Thoughts: A Reply to Porpora and a Defence of Tegmark
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