Computing magnetic anisotropy constants of single molecule magnets

We present here a theoretical approach to compute the molecular magnetic anisotropy parameters, D (M) and E (M) for single molecule magnets in any given spin eigenstate of exchange spin Hamiltonian. We first describe a hybrid constant M (S) valence bond (VB) technique of solving spin Hamiltonians employing full spatial and spin symmetry adaptation and we illustrate this technique by solving the exchange Hamiltonian of the Cu6Fe8 system. Treating the anisotropy Hamiltonian as perturbation, we compute the D (M)and E(M) values for various eigenstates of the exchange Hamiltonian. Since, the dipolar contribution to the magnetic anisotropy is negligibly small, we calculate the molecular anisotropy from the single-ion anisotropies of the metal centers. We have studied the variation of D (M) and E(M) by rotating the single-ion anisotropies in the case of Mn12Ac and Fe-8 SMMs in ground and few low-lying excited states of the exchange Hamiltonian. In both the systems, we find that the molecular anisotropy changes drastically when the single-ion anisotropies are rotated. While in Mn12Ac SMM D (M) values depend strongly on the spin of the eigenstate, it is almost independent of the spin of the eigenstate in Fe-8 SMM. We also find that the D (M)value is almost insensitive to the orientation of the anisotropy of the core Mn(IV) ions. The dependence of D (M) on the energy gap between the ground and the excited states in both the systems has also been studied by using different sets of exchange constants.

Soft gluon k(t)-resummation and the Froissart bound

We study soft gluon k(t)-resurnmation and the relevance of InfraRed (IR) gluons for the energy dependence of total hadronic cross-sections. In our model, consistency with the Froissart bound is directly related to the ansatz that the IR behaviour of the QCD coupling constant follows an inverse power law.

W physics at the ILC with polarized beams as a probe of the Littlest Higgs model

We study the possibility of using W pair production and leptonic decay of one of the W's at the ILC with polarized beams as a probe of the Littlest Higgs Model. We consider cross-sections, polarization fractions of the W's, leptonic decay energy and angular distributions, and left-right polarization asymmetry as probes of the model. With parameter values allowed by present experimental constraints detectable effects on these observables at typical ILC energies of 500 GeV and 800 GeV will be present. Beam polarization is further found to enhance the sensitivity.

The virial expansion of a classical interacting system

We consider N particles interacting pairwise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). For a system placed in a harmonic trap, its classical partition function for the repulsive regime is recognised in the literature. We start by presenting a concise re-derivation of this result. The equation of state is then calculated both for the trapped and the homogeneous gas. Finally, the classical limit of Wu's distribution function for fractional exclusion statistics is obtained and we re-derive the classical virial expansion of the homogeneous gas using this distribution function.

Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

Tuning the Conductance of Dirac Fermions on the Surface of a Topological Insulator

We study the transport properties of the Dirac fermions with a Fermi velocity v(F) on the surface of a topological insulator across a ferromagnetic strip providing an exchange field J over a region of width d. We show that the conductance of such a junction, in the clean limit and at low temperature, changes from oscillatory to a monotonically decreasing function of d beyond a critical J. This leads to the possible realization of a magnetic switch using these junctions. We also study the conductance of these Dirac fermions across a potential barrier of width d and potential V-0 in the presence of such a ferromagnetic strip and show that beyond a critical J, the criteria of conductance maxima changes from chi = eV(0)d/(h) over barv(F) = n pi to chi = (n + 1/2)pi for integer n. We point out that these novel phenomena have no analogs in graphene and suggest experiments which can probe them.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Nonquantum Entanglement Resolves a Basic Issue in Polarization Optics

The issue raised in this Letter is classical, not only in the sense of being nonquantum, but also in the sense of being quite ancient: which subset of 4 X 4 real matrices should be accepted as physical Mueller matrices in polarization optics? Nonquantum entanglement or inseparability between the polarization and spatial degrees of freedom of an electromagnetic beam whose polarization is not homogeneous is shown to provide the physical basis to resolve this issue in a definitive manner.

Power dissipation for systems with junctions of multiple quantum wires

We study power dissipation for systems of multiple quantum wires meeting at a junction, in terms of a current splitting matrix (M) describing the junction. We present a unified framework for studying dissipation for wires with either interacting electrons (i.e., Tomonaga-Luttinger liquid wires with Fermi-liquid leads) or noninteracting electrons. We show that for a given matrix M, the eigenvalues of (MM)-M-T characterize the dissipation, and the eigenvectors identify the combinations of bias voltages which need to be applied to the different wires in order to maximize the dissipation associated with the junction. We use our analysis to propose and study some microscopic models of a dissipative junction which employ the edge states of a quantum Hall liquid. These models realize some specific forms of the M matrix whose entries depends on the tunneling amplitudes between the different edges.

Benchmark scenarios for the NMSSM

We discuss constrained and semi--constrained versions of the next--to--minimal supersymmetric extension of the Standard Model (NMSSM) in which a singlet Higgs superfield is added to the two doublet superfields that are present in the minimal extension (MSSM). This leads to a richer Higgs and neutralino spectrum and allows for many interesting phenomena that are not present in the MSSM. In particular, light Higgs particles are still allowed by current constraints and could appear as decay products of the heavier Higgs states, rendering their search rather difficult at the LHC. We propose benchmark scenarios which address the new phenomenological features, consistent with present constraints from colliders and with the dark matter relic density, and with (semi--)universal soft terms at the GUT scale. We present the corresponding spectra for the Higgs particles, their couplings to gauge bosons and fermions and their most important decay branching ratios. A brief survey of the search strategies for these states at the LHC is given.

Boson-fermion duality in SU(m vertical bar n) supersymmetric Haldane-Shastry spin chain

By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation. (C) 2007 Elsevier B.V. All rights reserved.

QCD and total cross-sections : photons and hadrons

In this contribution, we discuss a total cross-section model which can be applied to both photon and purely hadronic processes. We find that the model can reproduce photo-production cross-sections, as well as extrapolation of gamma*p processes to gamma p using Vector Meson Dominance models, with minimal modifications from the proton case.

Determining the CP Properties of the Higgs Boson

The search and the probe of the fundamental properties of Higgs boson(s) and, in particular, the determination of their charge conjugation and parity (CP) quantum numbers, are the main tasks of future high-energy colliders. We demonstrate that the CP properties of a standard model-like Higgs particle can be unambiguously assessed by measuring just the total cross section and the top polarization in associated Higgs boson production with top quark pairs in e(+)e(-) collisions.