11,669 research outputs found
The Length of a Minimal Tree With a Given Topology: generalization of Maxwell Formula
The classic Maxwell formula calculates the length of a planar locally minimal
binary tree in terms of coordinates of its boundary vertices and directions of
incoming edges. However, if an extreme tree with a given topology and a
boundary has degenerate edges, then the classic Maxwell formula cannot be
applied directly, to calculate the length of the extreme tree in this case it
is necessary to know which edges are degenerate. In this paper we generalize
the Maxwell formula to arbitrary extreme trees in a Euclidean space of
arbitrary dimension. Now to calculate the length of such a tree, there is no
need to know either what edges are degenerate, or the directions of
nondegenerate boundary edges. The answer is the maximum of some special linear
function on the corresponding compact convex subset of the Euclidean space
coinciding with the intersection of some cylinders.Comment: 6 ref
Impurity center in a semiconductor quantum ring in the presence of a radial electric field
The problem of an impurity electron in a quantum ring (QR) in the presence of
a radially directed strong external electric field is investigated in detail.
Both an analytical and a numerical approach to the problem are developed. The
analytical investigation focuses on the regime of a strong wire-electric field
compared to the electric field due to the impurity. An adiabatic and
quasiclassical approximation is employed. The explicit dependencies of the
binding energy of the impurity electron on the electric field strength,
parameters of the QR and position of the impurity within the QR are obtained.
Numerical calculations of the binding energy based on a finite-difference
method in two and three dimensions are performed for arbitrary strengths of the
electric field. It is shown that the binding energy of the impurity electron
exhibits a maximum as a function of the radial position of the impurity that
can be shifted arbitrarily by applying a corresponding wire-electric field. The
maximal binding energy monotonically increases with increasing electric field
strength. The inversion effect of the electric field is found to occur. An
increase of the longitudinal displacement of the impurity typically leads to a
decrease of the binding energy. Results for both low- and high-quantum rings
are derived and discussed. Suggestions for an experimentally accessible set-up
associated with the GaAs/GaAlAs QR are provided.Comment: 16 pages, 8 figure
Constrained superpotentials in harmonic gauge theories with 8 supercharges
We consider D-dimensional supersymmetric gauge theories with 8 supercharges
(D<6,) in the framework of harmonic superspaces. The effective
Abelian low-energy action for D=5 contains the free and Chern-Simons terms.
Effective superfield actions for D<4 can be written in terms of
the superpotentials satisfying the superfield constraints and (6-D)-dimensional
Laplace equations. The role of alternative harmonic structures is discussed.Comment: LATEX file, 9 pages, version published in Teor. Mat. Fi
The ground state of the Lithium atom in strong magnetic fields
The ground and some excited states of the Li atom in external uniform
magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for
field strengths ranging from zero up to 2.35 10^8 T. With increasing field
strength the ground state undergoes two transitions involving three different
electronic configurations: for weak fields the ground state configuration
arises from the field-free 1s^22s configuration, for intermediate fields from
the 1s^22p_{-1} configuration and in high fields the 1s2p_{-1}3d_{-2}
electronic configuration is responsible for the properties of the atom. The
transition field strengths are determined. Calculations on the ground state of
the Li+ ion allow us to describe the field-dependent ionization energy of the
Li atom. Some general arguments on the ground states of multi-electron atoms in
strong magnetic fields are provided.Comment: 11 pages, 6 figures, submitted to Physical Review
Ferrimagnetic mixed-spin ladders in weak and strong coupling limits
We study two similar spin ladder systems with the ferromagnetic leg coupling.
First model includes two sorts of spins, s= 1/2 and s= 1, and the second model
comprises only s=1/2 legs coupled by a "triangular" rung exchange. The
antiferromagnetic (AF) rung coupling destroys the long-range order and
eventually makes the systems equivalent to the AF s=1/2 Heisenberg chain. We
investigate the situation by different methods in weak and strong rung coupling
limits. Particularly we compare the spin-wave theory and the bosonization
method in the weak coupling regime of the second model. We analyze the spectra
and correlations, and discuss the order parameter of these ladder systems.Comment: 12 pages, 4 figure
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