35,138 research outputs found
Fractional statistics in the fractional quantum Hall effect
A microscopic confirmation of the fractional statistics of the {\em
quasiparticles} in the fractional quantum Hall effect has so far been lacking.
We calculate the statistics of the composite-fermion quasiparticles at
and by evaluating the Berry phase for a closed loop
encircling another composite-fermion quasiparticle. A careful consideration of
subtle perturbations in the trajectory due to the presence of an additional
quasiparticle is crucial for obtaining the correct value of the statistics. The
conditions for the applicability of the fractional statistics concept are
discussed.Comment: Phys. Rev. Lett., in pres
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
Nonuniversal exponents in sandpiles with stochastic particle number transfer
We study fixed density sandpiles in which the number of particles transferred
to a neighbor on relaxing an active site is determined stochastically by a
parameter . Using an argument, the critical density at which an
active-absorbing transition occurs is found exactly. We study the critical
behavior numerically and find that the exponents associated with both static
and time-dependent quantities vary continuously with .Comment: Some parts rewritten, results unchanged. To appear in Europhys. Let
Band Structure of the Fractional Quantum Hall Effect
The eigenstates of interacting electrons in the fractional quantum Hall phase
typically form fairly well defined bands in the energy space. We show that the
composite fermion theory gives insight into the origin of these bands and
provides an accurate and complete microscopic description of the strongly
correlated many-body states in the low-energy bands. Thus, somewhat like in
Landau's fermi liquid theory, there is a one-to-one correspondence between the
low energy Hilbert space of strongly interacting electrons in the fractinal
quantum Hall regime and that of weakly interacting electrons in the integer
quantum Hall regime.Comment: 10 page
Shorted Operators Relative to a Partial Order in a Regular Ring
In this paper, the explicit form of maximal elements, known as shorted
operators, in a subring of a von Neumann regular ring has been obtained. As an
application of the main theorem, the unique shorted operator (of electrical
circuits) which was introduced by Anderson-Trapp has been derived.Comment: There was a small mistake in the published version which has been
corrected her
Decision Sheet and Learning Diary: New Tools for Improved Learning Through the Case Method
Of the three phases of learning through the case method, instructors have focused on the in-class phase in training of both teachers and participants. The other two phases, pre-class preparation and post class-reflection, have not received much attention leading to lack of exploitation of the full learning potential from the method. This paper shares continued efforts to conceptualize and develop two tools, decision sheet and learning diary, to strengthen the two phases. These were designed and tested in three executive development programmes. The results and our reflections suggest that the tools enhance the process of learning and the learning itself.
Synchronization in Networks of Identical Systems via Pinning: Application to Distributed Secondary Control of Microgrids
Motivated by the need for fast synchronized operation of power microgrids, we
analyze the problem of single and multiple pinning in networked systems. We
derive lower and upper bounds on the algebraic connectivity of the network with
respect to the reference signal. These bounds are utilized to devise a
suboptimal algorithm with polynomial complexity to find a suitable set of nodes
to pin the network effectively and efficiently. The results are applied to
secondary voltage pinning control design for a microgrid in islanded operation
mode. Comparisons with existing single and multiple pinning strategies clearly
demonstrates the efficacy of the obtained results.Comment: 11 pages, 9 figures, submitted to Transactions on Control Systems
Technolog
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
Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect
Motivated by the discovery of extremely low energy collective modes in the
fractional quantum Hall effect (Kang, Pinczuk {\em et al.}), with energies
below the Zeeman energy, we study theoretically the spin reversed excitations
for fractional quantum Hall states at and 3/7 and find qualitatively
different behavior than for . We find that a low-energy,
charge-neutral "spin roton," associated with spin reversed excitations that
involve a change in the composite-fermion Landau level index, has energy in
reasonable agreement with experiment.Comment: Postscript figures included. Accepted in Phys. Rev. B (Rapid
Communication
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