Magnetic polarizability of hadrons from lattice QCD in the background field method

We present a calculation of hadron magnetic polarizability using the techniques of lattice QCD. This is carried out by introducing a uniform external magnetic field on the lattice and measuring the quadratic part of a hadron's mass shift. The calculation is performed on a $24^4$ lattice with standard Wilson actions at beta=6.0 (spacing $a=0.1$ fm) and pion mass down to about 500 MeV. Results are obtained for 30 particles covering the entire baryon octet ($n$, $p$, $\Sigma^0$, $\Sigma^-$, $\Sigma^+$, $\Xi^-$, $\Xi^0$, $\Lambda$) and decuplet ($\Delta^0$, $\Delta^-$, $\Delta^+$, $\Delta^{++}$, $\Sigma^{*0}$, $\Sigma^{*-}$, $\Sigma^{*+}$, $\Xi^{*0}$, $\Xi^{*-}$, $\Omega^-$), plus selected mesons ($\pi^0$, $\pi^+$, $\pi^-$, $K^0$, $K^+$, ${K}^-$, $\rho^0$, $\rho^+$, $\rho^-$, $K^{*0}$, $K^{*+}$, $K^{*-}$). The results are compared with available values from experiments and other theoretical calculations.Comment: 30 pages, 23 figures, 5 table

Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE

The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996-2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue distribution of the cross-correlation matrix, $\mathbf{C}$, of NSE is found to be similar to that of developed markets, such as the New York Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds expected for a random matrix constructed from mutually uncorrelated time series. Of the few largest eigenvalues that deviate from the bulk, the largest is identified with market-wide movements. The intermediate eigenvalues that occur between the largest and the bulk have been associated in NYSE with specific business sectors with strong intra-group interactions. However, in the Indian market, these deviating eigenvalues are comparatively very few and lie much closer to the bulk. We propose that this is because of the relative lack of distinct sector identity in the market, with the movement of stocks dominantly influenced by the overall market trend. This is shown by explicit construction of the interaction network in the market, first by generating the minimum spanning tree from the unfiltered correlation matrix, and later, using an improved method of generating the graph after filtering out the market mode and random effects from the data. Both methods show, compared to developed markets, the relative absence of clusters of co-moving stocks that belong to the same business sector. This is consistent with the general belief that emerging markets tend to be more correlated than developed markets.Comment: 15 pages, 8 figures, to appear in Proceedings of International Workshop on "Econophysics & Sociophysics of Markets & Networks" (Econophys-Kolkata III), Mar 12-15, 200

Hydrogen atom in a spherical well: linear approximation

We discuss the boundary effects on a quantum system by examining the problem of a hydrogen atom in a spherical well. By using an approximation method which is linear in energy we calculate the boundary corrections to the ground-state energy and wave function. We obtain the asymptotic dependence of the ground-state energy on the radius of the well.Comment: Revised version to appear in European Journal of Physic

Operator method in solving non-linear equations of the Hartree-Fock type

The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron ground-state energy. Energies for 2s- and 3s-states are also calculated. The other excited states are briefly discussed.Comment: 7 page

Time evolution, cyclic solutions and geometric phases for general spin in an arbitrarily varying magnetic field

A neutral particle with general spin and magnetic moment moving in an arbitrarily varying magnetic field is studied. The time evolution operator for the Schr\"odinger equation can be obtained if one can find a unit vector that satisfies the equation obeyed by the mean of the spin operator. There exist at least $2s+1$ cyclic solutions in any time interval. Some particular time interval may exist in which all solutions are cyclic. The nonadiabatic geometric phase for cyclic solutions generally contains extra terms in addition to the familiar one that is proportional to the solid angle subtended by the closed trace of the spin vector.Comment: revtex4, 8 pages, no figur

Nuclear Octupole Correlations and the Enhancement of Atomic Time-Reversal Violation

We examine the time-reversal-violating nuclear ``Schiff moment'' that induces electric dipole moments in atoms. After presenting a self-contained derivation of the form of the Schiff operator, we show that the distribution of Schiff strength, an important ingredient in the ground-state Schiff moment, is very different from the electric-dipole-strength distribution, with the Schiff moment receiving no strength from the giant dipole resonance in the Goldhaber-Teller model. We then present shell-model calculations in light nuclei that confirm the negligible role of the dipole resonance and show the Schiff strength to be strongly correlated with low-lying octupole strength. Next, we turn to heavy nuclei, examining recent arguments for the strong enhancement of Schiff moments in octupole-deformed nuclei over that of 199Hg, for example. We concur that there is a significant enhancement while pointing to effects neglected in previous work (both in the octupole-deformed nuclides and 199Hg) that may reduce it somewhat, and emphasizing the need for microscopic calculations to resolve the issue. Finally, we show that static octupole deformation is not essential for the development of collective Schiff moments; nuclei with strong octupole vibrations have them as well, and some could be exploited by experiment.Comment: 25 pages, 4 figures embedded in tex

Decuplet Baryon Structure from Lattice QCD

The electromagnetic properties of the SU(3)-flavor baryon decuplet are examined within a lattice simulation of quenched QCD. Electric charge radii, magnetic moments, and magnetic radii are extracted from the E0 and M1 form factors. Preliminary results for the E2 and M3 moments are presented giving the first model independent insight to the shape of the quark distribution in the baryon ground state. As in our octet baryon analysis, the lattice results give evidence of spin-dependent forces and mass effects in the electromagnetic properties. The quark charge distribution radii indicate these effects act in opposing directions. Some baryon dependence of the effective quark magnetic moments is seen. However, this dependence in decuplet baryons is more subtle than that for octet baryons. Of particular interest are the lattice predictions for the magnetic moments of $\Omega^-$ and $\Delta^{++}$ for which new recent experimental measurements are available. The lattice prediction of the $\Delta^{++}/p$ ratio appears larger than the experimental ratio, while the lattice prediction for the $\Omega^-/p$ magnetic moment ratio is in good agreement with the experimental ratio.Comment: RevTeX manuscript, 34 pages plus 21 figures (available upon request

Solvable three-state model of a driven double-well potential and coherent destruction of tunneling

A simple model for a particle in a double well is derived from discretizing its configuration space. The model contains as many free parameters as the original system and it respects all the existing symmetries. In the presence of an external periodic force both the continuous system and the discrete model are shown to possess a generalized time-reversal symmetry in addition to the known generalized parity. The impact of the driving force on the spectrum of the Floquet operator is studied. In particular, the occurrence of degenerate quasienergies causing coherent destruction of tunneling is discussed—to a large extent analytically—for arbitrary driving frequencies and barrier heights

A Perturbative/Variational Approach to Quantum Lattice Hamiltonians

We propose a method to construct the ground state $\psi(\lambda)$ of local lattice hamiltonians with the generic form $H_0 + \lambda H_1$, where $\lambda$ is a coupling constant and $H_0$ is a hamiltonian with a non degenerate ground state $\psi_0$. The method is based on the choice of an exponential ansatz $\psi(\lambda) = {\rm exp}(U(\lambda)) \psi_0$, which is a sort of generalized lattice version of a Jastrow wave function. We combine perturbative and variational techniques to get succesive approximations of the operator $U(\lambda)$. Perturbation theory is used to set up a variational method which in turn produces non perturbative results. The computation with this kind of ansatzs leads to associate to the original quantum mechanical problem a statistical mechanical system defined in the same spatial dimension. In some cases these statistical mechanical systems turn out to be integrable, which allow us to obtain exact upper bounds to the energy. The general ideas of our method are illustrated in the example of the Ising model in a transverse field.Comment: 27 pages, three .ps figures appended, DFTUZ 94-2

Time evolution, cyclic solutions and geometric phases for the generalized time-dependent harmonic oscillator

The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and geometric phases. In this approach, finding the time evolution operator for the Schr\"odinger equation is reduced to solving an ordinary differential equation for a c-number vector which moves on a hyperboloid in a three-dimensional space. Cyclic solutions do not exist for all time intervals. A necessary and sufficient condition for the existence of cyclic solutions is given. There may exist some particular time interval in which all solutions with definite parity, or even all solutions, are cyclic. Criterions for the appearance of such cases are given. The known relation that the nonadiabatic geometric phase for a cyclic solution is proportional to the classical Hannay angle is reestablished. However, this is valid only for special cyclic solutions. For more general ones, the nonadiabatic geometric phase may contain an extra term. Several cases with relatively simple Hamiltonians are solved and discussed in detail. Cyclic solutions exist in most cases. The pattern of the motion, say, finite or infinite, can not be simply determined by the nature of the Hamiltonian (elliptic or hyperbolic, etc.). For a Hamiltonian with a definite nature, the motion can changes from one pattern to another, that is, some kind of phase transition may occur, if some parameter in the Hamiltonian goes through some critical value.Comment: revtex4, 28 pages, no figur