769 research outputs found
Quasiperiodic Modulated-Spring Model
We study the classical vibration problem of a chain with spring constants
which are modulated in a quasiperiodic manner, {\it i. e.}, a model in which
the elastic energy is , where and is an irrational number. For
, it is shown analytically that the spectrum is absolutely
continuous, {\it i.e.}, all the eigen modes are extended. For ,
numerical scaling analysis shows that the spectrum is purely singular
continuous, {\it i.e.}, all the modes are critical.Comment: REV TeX fil
Novel Heterocyclic Arylidene Derivatives as Anticancer Agents Against U87 Human Glioblastoma
The primary objectives of this interdisciplinary study were the synthesis of novel heterocyclic arylidenes and the investigation of their anticancer activity against U87 glioblastoma cell viability. Recently, novel hybrid derivatives have been considered as potential candidates for treating glioblastoma, demonstrating a synergistic anticancer effect in previous studies. 12 heterocyclic arylidenes with various functional groups, including halogens and boronic acid, were produced via a Knoevenagel condensation. These compounds and their starting reagents were then administered to U87 glioblastoma cancer cells at graded concentrations within a 12-well cell viability assay to determine each compound’s lethal concentration 50 (LC50). The LC50 of each compound was then compared to determine the effects of substituent type and position on anticancer activity. Although these arylidenes displayed some anticancer effects, their high LC50 suggest they have no significant effect on U87 glioblastoma cell viability and proliferation
Non-equivalence between Heisenberg XXZ spin chain and Thirring model
The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are
numerically solved, and the energy eigenvalues are determined for the
anti-ferromagnetic case. We examine the relation between the XXZ spin chain and
the Thirring model, and show that the spectrum of the XXZ spin chain is
different from that of the regularized Thirring model.Comment: 10 pages. 2figure
Density Matrix Renormalization Group Study of the S=1/2 Anisotropic Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation
The low energy behavior of the S=1/2 antiferromagnetic XY-like XXZ chains
with precious mean quasiperiodic exchange modulation is studied by the density
matrix renormalization group method. It is found that the energy gap of the
chain with length N scales as with nonuniversal exponent
if the Ising component of the exhange coupling is antiferromagnetic.
This behavior is expected to be the characteristic feature of the quantum spin
chains with relevant aperiodicity. This is in contrast to the XY chain for
which the precious mean exchange modulation is marginal and the gap scales as
. On the contrary, it is also verified that the energy gap scales as
if the Ising component of the exhange coupling is ferromagnetic. Our
results are not only consistent with the recent bosonization analysis of Vidal,
Mouhanna and Giamarchi but also clarify the nature of the strong coupling
regime which is inaccesssible by the bosonization approach.Comment: 8 pages, 15 figures, 1 table; Proceedings of the workshop 'Frontiers
in Magnetism', Kyoto, Oct. 199
Mode entanglement of electrons in the one-dimensional Frenkel-Kontorova model
We study the mode entanglement in the one-dimensional Frenkel-Kontorova
model, and found that behaviors of quantum entanglement are distinct before and
after the transition by breaking of analyticity. We show that the more extended
the electron is, the more entangled the corresponding state. Finally, a
quantitative relation is given between the average square of the concurrence
quantifying the degree of entanglement and the participation ratio
characterizing the degree of localization.Comment: 4 pages, 4 figures. V
Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field
The wave functions for two dimensional Bloch electrons in a uniform magnetic
field at the mid-band points are studied with the help of the algebraic
structure of the quantum group . A linear combination of its
generators gives the Hamiltonian. We obtain analytical and numerical solutions
for the wave functions by solving the Bethe Ansatz equations, proposed by
Wiegmann and Zabrodin on the basis of above observation. The semi-classical
case with the flux per plaquette is analyzed in detail, by exploring
a structure of the Bethe Ansatz equations. We also reveal the multifractal
structure of the Bethe Ansatz solutions and corresponding wave functions when
is irrational, such as the golden or silver mean.Comment: 30 pages, 11 GIF figures(use xv, or WWW browser
Self-similarity under inflation and level statistics: a study in two dimensions
Energy level spacing statistics are discussed for a two dimensional
quasiperiodic tiling. The property of self-similarity under inflation is used
to write a recursion relation for the level spacing distributions defined on
square approximants to the perfect quasiperiodic structure.
New distribution functions are defined and determined by a combination of
numerical and analytical calculations.Comment: Latex, 13 pages including 6 EPS figures, paper submitted to PR
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