B. Basu

City size distributions for India and China

This paper studies the size distributions of urban agglomerations for India and China. We have estimated the scaling exponent for Zipf’s law with the Indian census data for the years of 1981–2001 and the Chinese census data for 1990 and 2000. Along with the biased linear fit estimate, the maximum likelihood estimate for the Pareto and Tsallis q-exponential distribution has been computed. For India, the scaling exponent is in the range of [1.88, 2.06] and for China, it is in the interval [1.82, 2.29]. The goodness-of-fit tests of the estimated distributions are performed using the Kolmogorov–Smirnov statistic.

Relation between concurrence and Berry phase of an entangled state of two spin-(1/2) particles

We have studied here the influence of the Berry phase generated due to a cyclic evolution of an entangled state of two spin-(1/2) particles. It is shown that the measure of formation of entanglement is related to the cyclic geometric phase of the individual spins.

Inertial effect on spin–orbit coupling and spin transport

Abstract We theoretically study the renormalization of inertial effects on the spin dependent transport of conduction electrons in a semiconductor by taking into account the interband mixing on the basis of k → ⋅ p → perturbation theory. In our analysis, for the generation of spin current we have used the extended Drude model where the spin–orbit coupling plays an important role. We predict enhancement of the spin current resulting from the renormalized spin–orbit coupling effective in our model in cubic and non-cubic crystals. Attention has been paid to clarify the importance of gauge fields in the spin transport of this inertial system. A theoretical proposition of a perfect spin filter has been done through the Aharonov–Casher like phase corresponding to this inertial system. For a time dependent acceleration, effect of k → ⋅ p → perturbation on the spin current and spin polarization has also been addressed. Furthermore, achievement of a tunable source of polarized spin current through the non uniformity of the inertial spin–orbit coupling strength has also been discussed.

Quantum Hall effect in bilayer systems and the noncommutative plane : A toy model approach

Abstract We have presented a quantum mechanical toy model for the study of Coulomb interactions in Quantum Hall (QH) system. Inclusion of Coulomb interaction is essential for the study of bilayer QH system and our model can simulate it, in the compound state, in a perturbative framework. We also show that in the noncommutative plane, the Coulomb interaction is modified at a higher order in the noncommutativity parameter θ , and only if θ varies from layer to layer in the QH system.

Confronting quasi-exponential inflation with WMAP seven

We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.

Inertial spin Hall effect in non-commutative space

In the present Letter the study of inertial spin current (that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. In the Hamiltonian framework, the Dirac Hamiltonian in an accelerating frame is computed in the low energy regime by exploiting the Foldy–Wouthuysen scheme. The NC θ-effect appears from the replacement of normal products and commutators by Moyal ⁎-products and ⁎-commutators. In particular, the commutator between the external magnetic vector potential and the potential induced by acceleration becomes non-trivial. Expressions for θ-corrected inertial spin current and conductivity are derived explicitly. We have provided yet another way of experimentally measuring θ. The θ bound is obtained from the out of plane spin polarization, which is experimentally observable.

Effect of spin rotation coupling on spin transport

Abstract We have studied the spin rotation coupling (SRC) as an ingredient to explain different spin-related issues. This special kind of coupling can play the role of a Dresselhaus like coupling in certain conditions. Consequently, one can control the spin splitting, induced by the Dresselhaus like term, which is unusual in a semiconductor heterostructure. Within this framework, we also study the renormalization of the spin-dependent electric field and spin current due to the k → ⋅ p → perturbation, by taking into account the interband mixing in the rotating system. In this paper we predict the enhancement of the spin-dependent electric field resulting from the renormalized spin rotation coupling. The renormalization factor of the spin electric field is different from that of the SRC or Zeeman coupling. The effect of renormalized SRC on spin current and Berry curvature is also studied. Interestingly, in the presence of this SRC-induced SOC it is possible to describe spin splitting as well as spin galvanic effect in semiconductors.

Noncommutative geometry and geometric phases

We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space. The Ahranov-Bohm effect has been considered in this form of phase space, with operatorial structures of noncommutativity. The physical significance of our results is also discussed.

Quantum gravity effect in torsion driven inflation and CP violation

A bstractWe have derived an effective potential for inflationary scenario from torsion and quantum gravity correction in terms of the scalar field hidden in torsion. A strict bound on the CP violating θ parameter, O10−10<θ<O10−9