915 research outputs found
"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
Large Disorder Renormalization Group Study of the Anderson Model of Localization
We describe a large disorder renormalization group (LDRG) method for the
Anderson model of localization in one dimension which decimates eigenstates
based on the size of their wavefunctions rather than their energy. We show that
our LDRG scheme flows to infinite disorder, and thus becomes asymptotically
exact. We use it to obtain the disorder-averaged inverse participation ratio
and density of states for the entire spectrum. A modified scheme is formulated
for higher dimensions, which is found to be less efficient, but capable of
improvement
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
Phenomemology of a Realistic Accelerating Universe Using Tracker Fields
We present a realistic scenario of tracking of scalar fields with varying
equation of state. The astrophysical constraints on the evolution of scalar
fields in the physical universe are discussed. The nucleosynthesis and the
galaxy formation constraints have been used to put limits on and
estimate during cosmic evolution. Interpolation techniques have been
applied to estimate at the present epoch. The epoch of
transition from matter to quintessence dominated era and consequent onset of
acceleration in cosmic expansion is calculated and taking the lower limit
as estimated from data, it is shown that the
supernova observations beyond redshift would reveal deceleration in
cosmic expansion.Comment: 10 pages, 4 figures, late
Common path interference in Zener tunneling is a universal phenomenon
We show that the probability of electric field induced interband tunneling in
solid state systems is generically a non-monotonic (oscillatory) function of
the applied field. This unexpected behavior can be understood as arising due to
a common path interference between two distinct tunneling solutions. The
phenomenon is insensitive to magnetic field, and arises whenever the low energy
dispersion relation contains higher order terms in addition to the usual
term. Such higher order terms are generically present, albeit with small
co-efficient, so that the oscillatory Zener tunneling is a universal
phenomenon. However, the first `Zener oscillation' occurs at a transmission
probability which is exponentially small when the co-efficient of the higher
order terms is small. This explains why this oscillatory aspect of Zener
tunneling has been hitherto overlooked, despite its universality. The common
path interference is also destroyed by the presence of odd powers of in the
low energy dispersion relation. Since odd powers of are strictly absent
only when the tunneling barrier lies along an axis of mirror symmetry, it
follows that the robustness of the oscillatory behavior depends on the
orientation of the tunneling barrier. Bilayer graphene is identified as a
particularly good material for observation of common path interference, due to
its unusual nearly isotropic dispersion relation, where the term makes
the leading contribution
Parametrization of dark energy equation of state Revisited
A comparative study of various parametrizations of the dark energy equation
of state is made. Astrophysical constraints from LSS, CMB and BBN are laid down
to test the physical viability and cosmological compatibility of these
parametrizations. A critical evaluation of the 4-index parametrizations reveals
that Hannestad-M\"{o}rtsell as well as Lee parametrizations are simple and
transparent in probing the evolution of the dark energy during the expansion
history of the universe and they satisfy the LSS, CMB and BBN constraints on
the dark energy density parameter for the best fit values.Comment: 11 page
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
Lab-to Land - The success story of betelvine cultivation in Mahoba, Uttar Pradesh
Betel leaf chewing is so common that it is taken for gran ted and most people are oblivious of the problems facing this important segment of plant industry.
 
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