The scattering of light in quartz

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The phosphorescence of diamond

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The thermoluminescence of diamond

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Alternative Dispute Resolution in India - ADR: status/effectiveness study

This study focuses on the effectiveness of Alternative Dispute Resolution mechanisms in India. The broad targets included (a) a comparative analysis of institutional ADRs and ad-hoc ADR, (b) cost and time benefit analysis of ADRs in comparison with adjudication through courts; (c) study of the effectiveness of pre-trial mediation centres; and (e) to make concrete suggestions. The study proves that ADR in India has not been that effective when compared to adjudication through courts. The report favored institutional ADRs given the high rate of corruption and bureaucratic hitches prevalent in ad-hoc ADRs. The study also found that pre-trial mediation centres were developing in the right track

Non-perturbative Quantum Dynamics of the Order Parameter in the Pairing Model

We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different Hilbert spaces of single-particle and paired/empty states. This allows us to factorize the full thermodynamic partition function into a combination of simple terms associated with real spins on singly-occupied states and the partition function of the quantum XY-model for Anderson pseudospins associated with the paired/empty states. Using coherent-state path-integral, we calculate the effects of superconducting phase fluctuations exactly. The contribution of superconducting amplitude fluctuations to the partition function in the broken-symmetry phase is shown to follow from the Bogoliubov-de Gennes equations in imaginary time. These equations in turn allow several interesting mappings, e.g., they are shown to be in a one-to-one correspondence with the one-dimensional Schr\"odinger equation in supersymmetric Quantum Mechanics. However, the most practically useful approach to calculate functional determinants is found to be via an analytical continuation of the quantum order parameter to real time, \Delta(\tau -> it), such that the problem maps onto that of a driven two-level system. The contribution of a particular dynamic order parameter to the partition function is shown to correspond to the sum of the Berry phase and dynamic phase accumulated by the pseudospin. We also examine a family of exact solutions for two-level-system dynamics on a class of elliptic functions and suggest a compact expression to estimate the functional determinants on such trajectories. The possibility of having quantum soliton solutions co-existing with classical BCS mean-field is discussed.Comment: 34 pages (v2: Typos corrected, references added

Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet

Identifying the correct low-energy effective theory for magnons and holes in an antiferromagnet has remained an open problem for a long time. In analogy to the effective theory for pions and nucleons in QCD, based on a symmetry analysis of Hubbard and t-J-type models, we construct a systematic low-energy effective field theory for magnons and holes located inside pockets centered at lattice momenta (\pm pi/2a,\pm pi/2a). The effective theory is based on a nonlinear realization of the spontaneously broken spin symmetry and makes model-independent universal predictions for the entire class of lightly doped antiferromagnetic precursors of high-temperature superconductors. The predictions of the effective theory are exact, order by order in a systematic low-energy expansion. We derive the one-magnon exchange potentials between two holes in an otherwise undoped system. Remarkably, in some cases the corresponding two-hole Schr\"odinger equations can even be solved analytically. The resulting bound states have d-wave characteristics. The ground state wave function of two holes residing in different hole pockets has a d_{x^2-y^2}-like symmetry, while for two holes in the same pocket the symmetry resembles d_{xy}.Comment: 35 pages, 11 figure

Failure of Mean Field Theory at Large N

We study strongly coupled lattice QCD with $N$ colors of staggered fermions in 3+1 dimensions. While mean field theory describes the low temperature behavior of this theory at large $N$, it fails in the scaling region close to the finite temperature second order chiral phase transition. The universal critical region close to the phase transition belongs to the 3d XY universality class even when $N$ becomes large. This is in contrast to Gross-Neveu models where the critical region shrinks as $N$ (the number of flavors) increases and mean field theory is expected to describe the phase transition exactly in the limit of infinite $N$. Our work demonstrates that close to second order phase transitions infrared fluctuations can sometimes be important even when $N$ is strictly infinite.Comment: 4 pages, 3 figure

Vortex distribution in the Lowest Landau Level

We study the vortex distribution of the wave functions minimizing the Gross Pitaevskii energy for a fast rotating condensate in the Lowest Landau Level (LLL): we prove that the minimizer cannot have a finite number of zeroes thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of ``invisible'' vortices: the distortion of the lattice is very small in the Thomas Fermi region but quite large outside, where the "invisible" vortices lie.Comment: 4 pages, 1 figur