A Study of D.C. Resistivity of Calcutta Soil

The paper reports the results of study of d c. resistivity of soil in and around the city of Calcutta and of its variation with time, temperature and humidity The effect of endosmosis has also been ascertained

Statistical Geometry in Quantum Mechanics

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the Hilbert space H. By consideration of the square-root density function we can regard M as a submanifold of the unit sphere in H. Therefore, H embodies the `state space' of the probability distributions, and the geometry of M can be described in terms of the embedding of in H. The geometry in question is characterised by a natural Riemannian metric (the Fisher-Rao metric), thus allowing us to formulate the principles of classical statistical inference in a natural geometric setting. In particular, we focus attention on the variance lower bounds for statistical estimation, and establish generalisations of the classical Cramer-Rao and Bhattacharyya inequalities. The statistical model M is then specialised to the case of a submanifold of the state space of a quantum mechanical system. This is pursued by introducing a compatible complex structure on the underlying real Hilbert space, which allows the operations of ordinary quantum mechanics to be reinterpreted in the language of real Hilbert space geometry. The application of generalised variance bounds in the case of quantum statistical estimation leads to a set of higher order corrections to the Heisenberg uncertainty relations for canonically conjugate observables.Comment: 32 pages, LaTex file, Extended version to include quantum measurement theor

Interest Rates and Information Geometry

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discount function with respect to the maturity date gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that the general arbitrage-free yield curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. We also derive the dynamics for the central moments associated with the distribution determined by the yield curve.Comment: 20 pages, 3 figure

Tunnelling time and tunnelling dynamics

The concept of 'tunnelling time' in the context of quantum particle tunnelling is reviewed. Various suggestions of linking the tunnelling dynamics with a characteristic time (real or complex) like the phase time, barrier interaction time (bounce time), presence time, etc. are analysed. A simple but fully quantal method of defining and estimating a real tunnelling time is examined in a variety of situations. The recently proposed idea of interpreting 'tunnelling time' as the cavity lifetime of a particle is also explored. We emphasize that proton or H-atom transfer reactions in double or triple wells offer systems in which the signature of the tunnelling time should be recognizable not just indirectly through the tunnelling splitting of spectral lines, but by following the relaxation dynamics of the subsystem that the proton or H atom leaves by tunnelling

Weak Field Black Hole Formation in Asymptotically AdS Spacetimes

We use the AdS/CFT correspondence to study the thermalization of a strongly coupled conformal field theory that is forced out of its vacuum by a source that couples to a marginal operator. The source is taken to be of small amplitude and finite duration, but is otherwise an arbitrary function of time. When the field theory lives on $R^{d-1,1}$, the source sets up a translationally invariant wave in the dual gravitational description. This wave propagates radially inwards in $AdS_{d+1}$ space and collapses to form a black brane. Outside its horizon the bulk spacetime for this collapse process may systematically be constructed in an expansion in the amplitude of the source function, and takes the Vaidya form at leading order in the source amplitude. This solution is dual to a remarkably rapid and intriguingly scale dependent thermalization process in the field theory. When the field theory lives on a sphere the resultant wave either slowly scatters into a thermal gas (dual to a glueball type phase in the boundary theory) or rapidly collapses into a black hole (dual to a plasma type phase in the field theory) depending on the time scale and amplitude of the source function. The transition between these two behaviors is sharp and can be tuned to the Choptuik scaling solution in $R^{d,1}$.Comment: 50 pages + appendices, 6 figures, v2: Minor revisions, references adde

Deciphering Universal Extra Dimension from the top quark signals at the CERN LHC

Models based on Universal Extra Dimensions predict Kaluza-Klein (KK) excitations of all Standard Model (SM) particles. We examine the pair production of KK excitations of top- and bottom-quarks at the Large Hadron Collider. Once produced, the KK top/bottom quarks can decay to $b$-quarks, leptons and the lightest KK-particle, $\gamma_1$, resulting in 2 $b$-jets, two opposite sign leptons and missing transverse momentum, thereby mimicing top-pair production. We show that, with a proper choice of kinematic cuts, an integrated luminosity of 100 fb$^{-1}$ would allow a discovery for an inverse radius upto $R^{-1} = 750$ GeV.Comment: 18 pages, 14 figures, Accepted for publication in JHE

Negative specific heat in a thermodynamic model of multifragmentation

We consider a soluble model of multifragmentation which is similar in spirit to many models which have been used to fit intermediate energy heavy ion collision data. In this model $c_v$ is always positive but for finite nuclei $c_p$ can be negative for some temperatures and pressures. Furthermore, negative values of $c_p$ can be obtained in canonical treatment. One does not need to use the microcanonical ensemble. Negative values for $c_p$ can persist for systems as large as 200 paticles but this depends upon parameters used in the model calculation. As expected, negative specific heats are absent in the thermodynamic limit.Comment: Revtex, 13 pages including 6 figure

Anopheline fauna of parts of Tirap district, Arunachal Pradesh with reference to malaria transmission

In a survey on the anopheline fauna in highly malaria endemic areas of the Tirap district of Arunachal Pradesh, 7476 anophelines belonging to 17 species were collected, including seven species of anophelines which are recognized malaria vectors in India. Anopheles tessellatus and A. jamesii were recorded for the first time in this area. The parasitological survey revealed that the area was endemic for malaria particularly P. falciparum. the slide positivity rate and slide falciparum rate being 25.63 and 19.21 per cent respectively. On dissection of 10 anopheies species, malarial infection was detected in two viz., A. minimus and A. dirus