Critical analysis of Vataja Gulma

Gulma is the chronic disease of Annavaha Srotas where in Vata Dosha vitiation is typically observed. It is a Vata Pradhana Vyadhi mentioned separately in Charaka Samhita, Sushrutha Samhita, Astanga Hrudaya, Astanga Sangraha and in Madhava Nidana. Because of its shape like that of Gulma (Shrub or Bush) disease is named as Gulma. It is a Sparshopalabhya (palpable mass), Paripinditatwath (hard and round in shape). Nidana (etiological factors), Poorvaroopa (premorbid symptoms), Roopa (signs and symptoms), Upashaya Anupashaya (aggravating and relieving factors), Samprapti (Pathogenesis), Samprapti Ghataka, Upadrava, Arista Lakshanas of Vataja Gulma is discussed in detail in this article with its above possible contemporary correlation

Phase transition from a dx2−y2d_{x^2-y^2} to dx2−y2+dxyd_{x^2-y^2}+d_{xy} superconductor

We study the phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$ superconductor using the tight-binding model of two-dimensional cuprates. As the temperature is lowered past the critical temperature $T_c$, first a $d_{x^2-y^2}$ superconducting phase is created. With further reduction of temperature, the $d_{x^2-y^2}+d_{xy}$ phase is created at temperature $T=T_{c1}$. We study the temperature dependencies of the order parameter, specific heat and spin susceptibility in these mixed-angular-momentum states on square lattice and on a lattice with orthorhombic distortion. The above-mentioned phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$.Comment: Latex file, 5 pages, 6 postscript figures, Accepted in Physical Review

Extended d_{x^2 - y^2}-wave superconductivity

Remarkable anisotropic structures have been recently observed in the order parameter Delta_k of the underdoped superconductor Bi-2212. Such findings are strongly suggestive of deviations from a simple d_{x^2 - y^2}-wave picture of high-Tc superconductivity, i.e. Delta_k ~ cos (k_x) - cos (k_y). In particular, flatter nodes in Delta_k are observed along the k_x = (+/-) k_y directions in k-space, than within this simple model for a d-wave gap. We argue that nonlinear corrections in the k-dependence of Delta_k near the nodes introduce new energy scales, which would lead to deviations in the predicted power-law asymptotic behaviour of several measurable quantities, at low or intermediate temperatures. We evaluate such deviations, either analytically or numerically, within the interlayer pair-tunneling model, and within yet another phenomenological model for a d-wave order parameter. We find that such deviations are expected to be of different sign in the two cases. Moreover, the doping dependence of the flatness of the gap near the nodes is also attributable to Fermi surface effects, in addition to possible screening effects modifying the in-plane pairing kernel, as recently proposed.Comment: 7 pages, 4 embedded PostScript figures. Uses svjour, epsfig, amsmath, amssymb, xspace. To be published in Eur. Phys. J.

d_{x^2-y^2} Pair Domain Walls

Using the density matrix renormalization group, we study domain wall structures in the t-J model at a hole doping of x=1/8. We find that the domain walls are composed of d_{x^2-y^2} pairs and that the regions between the domain walls have antiferromagnetic correlations that are pi phase shifted across a domain wall. At x=1/8, the hole filling corresponds to one hole per two domain wall unit cells. When the pairs in a domain wall are pinned by an external field, the d_{x^2-y^2} pairing response is suppressed, but when the pinning is weakened, d_{x^2-y^2} pair-field correlations can develop.Comment: 11 pages, with 3 Postscript figure

Self-consistent electronic structure of a dx2−y2d_{x^2-y^2} and a dx2−y2+idxyd_{x^2-y^2}+id_{xy} vortex

We investigate quasiparticle states associated with an isolated vortex in a d-wave superconductor using a self-consistent Bogoliubov-de Gennes formalism. For a pure $d_{x^2-y^2}$ superconductor we find that there exist no bound states in the core; all the states are extended with continuous energy spectrum. This result is inconsistent with the existing experimental data on cuprates. We propose an explanation for this data in terms of a magnetic-field-induced $d_{x^2-y^2}+id_{xy}$ state recently invoked in connection with the thermal conductivity measurements on Bi$_2$Sr$_2$CaCu$_2$O$_8$.Comment: 4 pages REVTeX, 3 .ps figures included. Version to appear in PRL, May 24, 1998. Minor changes, references adde

Eigenvalues and eigenfunctions of the anharmonic oscillator V(x,y)=x2y2V(x,y)=x^{2}y^{2}

We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential $V(x,y)=x^{2}y^{2}$ by means of three different methods. Our results strongly suggest that the spectrum of this oscillator is discrete in agreement with early rigorous mathematical proofs and against a recent statement that cast doubts about it