21,759 research outputs found
Eigenvalue spectrum for single particle in a spheroidal cavity: A Semiclassical approach
Following the semiclassical formalism of Strutinsky et al., we have obtained
the complete eigenvalue spectrum for a particle enclosed in an infinitely high
spheroidal cavity. Our spheroidal trace formula also reproduces the results of
a spherical billiard in the limit . Inclusion of repetition of each
family of the orbits with reference to the largest one significantly improves
the eigenvalues of sphere and an exact comparison with the quantum mechanical
results is observed upto the second decimal place for . The
contributions of the equatorial, the planar (in the axis of symmetry plane) and
the non-planar(3-Dimensional) orbits are obtained from the same trace formula
by using the appropriate conditions. The resulting eigenvalues compare very
well with the quantum mechanical eigenvalues at normal deformation. It is
interesting that the partial sum of equatorial orbits leads to eigenvalues with
maximum angular momentum projection, while the summing of planar orbits leads
to eigenvalues with except for L=1. The remaining quantum mechanical
eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few
spurious eigenvalues arise in these partial sums. This result establishes the
important role of 3D orbits even at normal deformations.Comment: 17 pages, 7 ps figure
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Leveling transparency via situated intermediary learning objectives (SILOs)
When designers set out to create a mathematics learning activity, they have a fair sense of its objectives: students will understand a concept and master relevant procedural skills. In reform-oriented activities, students first engage in concrete situations, wherein they achieve situated, intermediary learning objectives (SILOs), and only then they rearticulate their solutions formally. We define SILOs as heuristics learners devise to accommodate contingencies in an evolving problem space, e.g., monitoring and repairing manipulable structures so that they model with fidelity a source situation. Students achieve SILOs through problem-solving with media, instructors orient toward SILOs via discursive solicitation, and designers articulate SILOs via analyzing implementation data. We describe the emergence of three SILOs in developing the activity Giant Steps for Algebra. Whereas the notion of SILOs emerged spontaneously as a framework to organize a system of practice, i.e. our collaborative design, it aligns with phenomenological theory of knowledge as instrumented action
Jastrow-Correlated Wavefunctions for Flat-Band Lattices
The electronic band structure of many compounds, e.g., carbon-based
structures, can exhibit essentially no dispersion. Models of electrons in
flat-band lattices define non-perturbative strongly correlated problems by
default. We construct a set of Jastrow-correlated ansatz wavefunctions to
capture the low energy physics of interacting particles in flat bands. We test
the ansatz in a simple Coulomb model of spinless electrons in a honeycomb
ribbon. We find that the wavefunction accurately captures the ground state in a
transition from a crystal to a uniform quantum liquid.Comment: 5 pages, 4 figures, update context, references and publication
informatio
Adaptation dynamics of the quasispecies model
We study the adaptation dynamics of an initially maladapted population
evolving via the elementary processes of mutation and selection. The evolution
occurs on rugged fitness landscapes which are defined on the multi-dimensional
genotypic space and have many local peaks separated by low fitness valleys. We
mainly focus on the Eigen's model that describes the deterministic dynamics of
an infinite number of self-replicating molecules. In the stationary state, for
small mutation rates such a population forms a {\it quasispecies} which
consists of the fittest genotype and its closely related mutants. The
quasispecies dynamics on rugged fitness landscape follow a punctuated (or
step-like) pattern in which a population jumps from a low fitness peak to a
higher one, stays there for a considerable time before shifting the peak again
and eventually reaches the global maximum of the fitness landscape. We
calculate exactly several properties of this dynamical process within a
simplified version of the quasispecies model.Comment: Proceedings of Statphys conference at IIT Guwahati, to be published
in Praman
An improved inequality for k-th derivative of a polynomial
For a polynomial p(z) of degree n, we have obtained a refinement of the well known Bernstein\u27s inequality
max|z|=1 |p(k)(z)| ≤ n(n -1)(n -2)(n -k+1) max|z|=1 |p(z)|
Integral inequalities for polynomials having a zero of order m at the origin
For a polynomial p(z) of degree n, it holds the Zygmund\u27s inequality. We have obtained inequalities in the reverse direction for the polynomials having a zero of order m at the origin
Integral inequalities for polynomials having a zero of order m at the origin
For a polynomial p(z) of degree n, it holds the Zygmund\u27s inequality. We have obtained inequalities in the reverse direction for the polynomials having a zero of order m at the origin
A generalization of a result on maximum modulus of polynomials
For an arbitrary entire function f(z)$, let M(f,d) = max|z|=d |f(z)|. It is known that if the geometric mean of the moduli of the zeros of a polynomial p(z) of degree n is at least 1, and M(p,1) = 1, then for R > 1, M(p,R) R/2 + 1/2 if n = 1,
M(p,R) Rn/2 + (3+22)Rn-2/2 if n 2.
We have obtained a generalization of this result, by assuming the geometric mean of the moduli of the zeros of the polynomial to be at least k, (k > 0)
Logarithmic temperature dependence of conductivity at half-integer filling factors: Evidence for interaction between composite fermions
We have studied the temperature dependence of diagonal conductivity in
high-mobility two-dimensional samples at filling factors and 3/2 at
low temperatures. We observe a logarithmic dependence on temperature, from our
lowest temperature of 13 mK up to 400 mK. We attribute the logarithmic
correction to the effects of interaction between composite fermions, analogous
to the Altshuler-Aronov type correction for electrons at zero magnetic field.
The paper is accepted for publication in Physical Review B, Rapid
Communications.Comment: uses revtex macro
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