Phase Distribution in a Disordered Chain and the Emergence of a Two-parameter Scaling in the Quasi-ballistic to the Mildly Localized Regime

We study the phase distribution of the complex reflection coefficient in different configurations as a disordered 1D system evolves in length, and its effect on the distribution of the 4-probe resistance $R_4$. The stationary ($L \to \infty$) phase distribution is almost always strongly non-uniform and is in general double-peaked with their separation decaying algebraically with growing disorder strength to finally give rise to a single narrow peak at infinitely strong disorder. Further in the length regime where the phase distribution still evolves with length (i.e., in the quasi-ballistic to the mildly localized regime), the phase distribution affects the distribution of the resistance in such a way as to make the mean and the variance of $log(1+R_4)$ diverge independently with length with different exponents. As $L \to \infty$, these two exponents become identical (unity). Obviously, these facts imply two relevant parameters for scaling in the quasi-ballistic to the mildly localized regime finally crossing over to one-parameter scaling in the strongly localized regime.Comment: 12 LaTeX pages plus 3 EPS figure

Electronic transport in a randomly amplifying and absorbing chain

We study localization properties of a one-dimensional disordered system characterized by a random non-hermitean hamiltonian where both the randomness and the non-hermiticity arises in the local site-potential; its real part being ordered (fixed), and a random imaginary part implying the presence of either a random absorption or amplification at each site. The transmittance (forward scattering) decays exponentially in either case. In contrast to the disorder in the real part of the potential (Anderson localization), the transmittance with the disordered imaginary part may decay slower than that in the case of ordered imaginary part.Comment: 7 LaTex pages plus 2 PS figures; e-mail: [email protected]

Spherically confined isotropic harmonic oscillator

The generalized pseudospectral Legendre method is used to carry out accurate calculations of eigenvalues of the spherically confined isotropic harmonic oscillator with impenetrable boundaries. The energy of the confined state is found to be equal to that of the unconfined state when the radius of confinement is suitably chosen as the location of the radial nodes in the unconfined state. This incidental degeneracy condition is numerically shown to be valid in general. Further, the full set of pairs of confined states defined by the quantum numbers [(n+1, \ell) ; (n, \ell+2)], n = 1,2,.., and with the radius of confinement {(2 \ell +3)/2}^{1/2} a.u., which represents the single node in the unconfined (1, \ell) state, is found to display a constant energy level separation exactly given by twice the oscillator frequency. The results of similar numerical studies on the confined Davidson oscillator with impenetrable boundary as well as the confined isotropic harmonic oscillator with finite potential barrier are also reported .The significance of the numerical results are discussed.Comment: 28 pages, 4 figure

Dr. Biman Bagchi a bibliometric portrait

Analyses bibliometrically 226 publications [Papers Published in journals-220, thesis [others 4] by Biman Bagchi, a renowned physical chemist from India, published during 1981 to 2002. The first contribution of the author was in 1981 at the age of 27. The number of his contributions in a year peaked in 1999 and 2002 when it touched 19. The author is highly productive in as much as on average the author has produced 10 papers per year. In the byline of authorship, Bagchi occupies the first authorship position in 69 cases. His collaborator A. Chandra occupies the first authorship position in 30 papers thus becoming Bagchi's closest collaborator. The journal has been the most preferred channel of communication of the author in as much as 220 papers out of 226 have been praced in journals. J. Chem. Phys. is found to be the most preferred journal that carried 91 papers of the author, followed by Chem. Phys. Lett. (21 papers). J. Phys. Chem. (19 papers), Proc. Indian Acad. Sci. - Chem. Sci. (13 papers), and others. Of the papers, 179 received 4030 citations and 47 received no citations. It is expected that more than 20 uncited papers till 2002 will receive citations in future. Three papers of the author have received more than 200 citations each, and another three received between 100-200 citations each. The number of papers receiving 10 citations or more total 92. On four different years the scientist has received more than 300 citations and his citation rate per paper has peaked at 18.98. The article shows with a concrete example the growth, peaking and declining of citation rate. A few new terms such as citation gain, citation loss, gaining citation rate and losing citation rate have been introduced and described