Quantum Scattering Theory in the light of an exactly solvable model with rearrangement collisions

We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In the light of the exact solutions constructed, we discuss various issues and assumptions in quantum scattering theory, including the isometry of the M\"oller wave matrix, the normalization and completeness of asymptotic states, and the non-orthogonality of basis states. We show that these common assertions do not obtain in this model. We suggest a general formalism for scattering theory which overcomes these, and other, shortcomings and limitations of the existing formalisms in the literature.Comment: 74 pages, uuencoded postscript fil

The Influence of Quantum Critical Fluctuations of Circulating Current Order Parameters on the Normal State Properties of Cuprates

We study a model of the quantum critical point of cuprates associated with the "circulating current" order parameter proposed by Varma. An effective action of the order parameter in the quantum disordered phase is derived using functional integral method, and the physical properties of the normal state are studied based on the action. The results derived within the ladder approximation indicate that the system is like Fermi liquid near the quantum critical point and in disordered regime up to minor corrections. This implies that the suggested marginal Fermi liquid behavior induced by the circulating current fluctuations will come in from beyond the ladder diagrams.Comment: 7pages, 1 figure included in RevTex file. To appear in Phys. Rev.

A Theory of the Pseudogap State of the Cuprates

The phase diagram for a general model for Cuprates is derived in a mean-field approximation. A phase violating time-reversal without breaking translational symmetry is possible when both the ionic interactions and the local repulsions are large compared to the energy difference between the Cu and O single-particle levels. It ends at a quantum critical point as the hole or electron doping is increased. Such a phase is necessarily accompanied by singular forward scattering such that, in the stable phase, the density of states at the chemical potential, projected to a particular point group symmetry of the lattice is zero producing thereby an anisotropic gap in the single-particle spectrum. It is suggested that this phase occupies the "pseudogap" region of the phase diagram of the cuprates. The temperature dependence of the single-particle spectra, the density of states, the specific heat and the magnetic susceptibility are calculated with rather remarkable correspondence with the experimental results. The importance of further direct experimental verification of such a phase in resolving the principal issues in the theory of the Cuprate phenomena is pointed out. To this end, some predictions are provided.Comment: 41 pages, 8 figure

Phase Transitions in the Symmetric Kondo Lattice Model in Two and Three Dimensions

We present an application of high-order series expansion in the coupling constants for the ground state properties of correlated lattice fermion systems. Expansions have been generated up to order $(t/J)^{14}$ for $d=1$ and $(t/J)^8$ for $d=2,\ 3$ for certain properties of the symmetric Kondo lattice model. Analyzing the susceptibility series, we find evidence for a continuous phase transition from the ``spin liquid'' phase characteristic of a ``Kondo Insulator'' to an antiferromagnetically ordered phase in dimensions $d\ge2$ as the antiferromagnetic Kondo coupling is decreased. The critical point is estimated to be at $(t/J)_c\approx0.7$ for square lattice and $(t/J)_c\approx0.5$ for simple-cubic lattice.Comment: 12 pages, Revtex, replace previous corrupted fil

Heavy-Fermions in a Transition-Metal Compound: LiV2O4LiV_2O_4

The recent discovery of heavy-Fermion properties in Lithium Vanadate and the enormous difference in its properties from the properties of Lithium Titanate as well as of the manganite compounds raise some puzzling questions about strongly correlated Fermions. These are disscussed as well as a solution to the puzzles provided.Comment: late

Spectroscopic evidences of quantum critical charge fluctuations in cuprates

We calculate the optical conductivity in a clean system of quasiparticles coupled to charge-ordering collective modes. The absorption induced by these modes may produce an anomalous frequency and temperature dependence of low-energy optical absorption in some cuprates. However, the coupling with lattice degrees of freedom introduces a non-universal energy scale leading to scaling violation in low-temperature optical conductivity.Comment: Proceedings of M2S 2006. To appear in Physica

Narasimham Committee Report - Some Further Ramifications and Suggestions

This paper while agreeing with the general thrust of the Narasimham Committee Report. Calls attention to some logical corollaries of the Report and analyses some possible fallout from implementing the Report. We agree with the view that control of banking system should be under an autonomous body supervised by the RBI. However at the level of individual banks, closer scrutiny of lending procedures may be called for than is envisaged in the Report. In a freely functioning capital market the potential of government bonds is enormous, but this necessitates restructuring of the government bond market. The government bonds may then also be used as suitable hedging mechanisms by introducing options and futures trading. We recommend freeing up the operation of pension and provident fund to enable at least partial investment of such funds in risky securities. In the corporate sector, we believe that the current 2:1 debt equity norm is too high and not sustainable in the long term. We envisage that high debt levels and higher interest rates, combined with higher business risk may result in greater incidence of corporate sickness. This may call for various schemes for retrenched workers and amendment to land laws for easy exit of companies. On account of interdependencies across different policies, any sequencing of their implementation may be highly problematic. We therefore suggest a near simultaneity in the implementation of various reforms in order to build up a momentum which would be irreversible if people are to have confidence that the reforms will endure, and if we are to retain our credibility with international financial institutions.

Spontaneous time reversal symmetry breaking in the pseudogap state of high-Tc superconductors

When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped high-Tc superconductors is rather unusual, in that it is not a mean-field transition as other superconducting transitions are. Instead, it is observed that a pseudo-gap in the electronic excitation spectrum appears at temperatures T* higher than Tc, while phase coherence, and superconductivity, are established at Tc (Refs. 1, 2). One would then wish to understand if T* is just a crossover, controlled by fluctuations in order which will set in at the lower Tc (Refs. 3, 4), or whether some symmetry is spontaneously broken at T* (Refs. 5-10). Here, using angle-resolved photoemission with circularly polarized light, we find that, in the pseudogap state, left-circularly polarized photons give a different photocurrent than right-circularly polarized photons, and therefore the state below T* is rather unusual, in that it breaks time reversal symmetry11. This observation of a phase transition at T* provides the answer to a major mystery of the phase diagram of the cuprates. The appearance of the anomalies below T* must be related to the order parameter that sets in at this characteristic temperature .Comment: 11 pages, 4 figure