1,024 research outputs found
Search for Tracker Potentials in Quintessence Theory
We report a significant finding in Quintessence theory that the the scalar
fields with tracker potentials have a model-independent scaling behaviour in
the expanding universe. So far widely discussed exponential,power law or
hyperbolic potentials can simply mimic the tracking behaviour over a limited
range of redshift. In the small redshift range where the variation of the
tracking parameter may be taken to be negligible, the differential
equation of generic potentials leads to hyperbolic sine and hyperbolic cosine
potentials which may approximate tracker field in the present day universe. We
have plotted the variation of tracker potential and the equation of state of
the tracker field as function of the redshift for the model-independent
relation derived from tracker field theory; we have also plotted the variation
of in terms of the scalar field for the chosen hyperbolic
cosine function and have compared with the curves obtained by reconstruction of
from the real observational data from the supernovae.Comment: 11 pages, 3 figures, late
"Rare" Fluctuation Effects in the Anderson Model of Localization
We discuss the role of rare fluctuation effects in quantum condensed matter
systems. In particular, we present recent numerical results of the effect of
resonant states in Anderson's original model of electron localization. We find
that such resonances give rise to anomalous behavior of eigenstates not just
far in the Lifshitz tail, but rather for a substantial fraction of eigenstates,
especially for intermediate disorder. The anomalous behavior includes
non-analyticity in various properties as a characteristic. The effect of
dimensionality on the singularity, which is present in all dimensions, is
described, and the behavior for bounded and unbounded disorder is contrasted
Singular Behavior of Eigenstates in Anderson's Model of Localization
We observe a singularity in the electronic properties of the Anderson Model
of Localization with bounded diagonal disorder, which is clearly distinct from
the well-established mobility edge (localization-delocalization transition)
that occurs in dimensions . We present results of numerical calculations
for Anderson's original (box) distribution of onsite disorder in dimensions
= 1, 2 and 3. To establish this hitherto unreported behavior, and to understand
its evolution with disorder, we contrast the behavior of two different measures
of the localization length of the electronic wavefunctions - the averaged
inverse participation ratio and the Lyapunov exponent. Our data suggest that
Anderson's model exhibits richer behavior than has been established so far.Comment: Correction to v1: Fig.3 caption now displaye
Singular Behavior of Anderson Localized Wavefunctions for a Two-Site Model
We show analytically that the apparent non-analyticity discovered recently in
the inverse participation ratio (IPR) of the eigenstates in Anderson's model of
localization is also present in a simple two-site model, along with a
concurrent non-analyticity in the density of states (DOS) at the same energy.
We demonstrate its evolution from two sites to the thermodynamic limit by
numerical methods. For the two site model, non-analyticity in higher
derivatives of the DOS and IPR is also proven to exist for all bounded
distributions of disorder
Formulation of Mathematical Mode! of Picketing of Liquor Shops and Warehouses
Before getting independence of INDIA from British regime, large number of Leaders of India was required to take strong agitation against British Government for getting freedom. One of the prominent leaders was Mr. M. K. Gandhi. During the period 1920 to 1942 in Central Provinces and Berar specifically pertaining to the period June 1930 to September 1930 [1], strong agitations took place towards reducing income to Government by way of reducing liquor consumption. Several events took place towards this objective. Based on the facts, the attempt is made in this paper to present the entire agitation as one social phenomena in the form of a Mathematical Model co-relating the fall in liquor revenue in terms of various causes responsible for this fall in revenue. It is only through the Mathematical Model that it is possible to get quantitative idea of intensity of interaction of causes on effects of any phenomena may be it be scientific or socio-economic or of any other type. Particularly the approach of Field Data Based Model [2] is applicable in such a situation as this is a Field Phenomena. Such models serve as most reliable tools to plan future such activities. This could be known as a process of PROGNOSIS
Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-stage Tracking Cosmological Nuclear Energy
Recent observations on Type-Ia supernovae and low density () measurement of matter including dark matter suggest that the present-day
universe consists mainly of repulsive-gravity type `exotic matter' with
negative-pressure often said `dark energy' (). But the nature
of dark energy is mysterious and its puzzling questions, such as why, how,
where and when about the dark energy, are intriguing. In the present paper the
authors attempt to answer these questions while making an effort to reveal the
genesis of dark energy and suggest that `the cosmological nuclear binding
energy liberated during primordial nucleo-synthesis remains trapped for a long
time and then is released free which manifests itself as dark energy in the
universe'. It is also explained why for dark energy the parameter . Noting that for stiff matter and for radiation; is for dark energy because is due to `deficiency of
stiff-nuclear-matter' and that this binding energy is ultimately released as
`radiation' contributing , making . When
dark energy is released free at , . But as on present day
at when radiation strength has diminished to , . This, thus almost solves the dark-energy mystery of
negative pressure and repulsive-gravity. The proposed theory makes several
estimates /predictions which agree reasonably well with the astrophysical
constraints and observations. Though there are many candidate-theories, the
proposed model of this paper presents an entirely new approach (cosmological
nuclear energy) as a possible candidate for dark energy.Comment: 17 pages, 4 figures, minor correction
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