Joseph L. Birman

Clebsch−Gordan coefficients for crystal space groups

A practical method for calculating Clebsch−Gordan coefficients for crystal space groups is presented. It is based on properties of the space group irreducible representations as induced from ray representations of subgroups. Using this method, we obtain all Clebsch−Gordan coefficients for a family of representations in a single calculation: For space groups, for a given triangle of stars *k, *k′, *k″, where *k ⊗ *k′ ‐ *k″, the coefficients for all allowable little group representations l, l′, l″ are obtained. In the following paper this is applied to rocksalt O5h−Fm3m and diamond O7h−Fd3m space groups.

Clebsch−Gordan coefficients for *X ⊗ *X in diamond O7h−Fd3m and rocksalt O5n−Fm3m

By using the method described in the previous paper, based on properties of space group irreducible representations as induced from ray representations of subgroups, Clebsch−Gordan coefficients are calculated for *X ⊗ *X in diamond O7h−Fd3m and rocksalt O5h−Fm3m structures. Tables of coefficients for these stars are presented. An example of explicit calculation of the coefficients is given for these symmorphic and nonsymmorphic groups with multiplicity included in the former.

Irreducible Vector and Ray Representations of Some Cubic Crystal Point Groups in Four Dimensions

A new, and computationally simple, method is given for obtaining the characters of all the inequivalent irreducible vector representations of a finite group. The method was applied to determine the characters of the irreducible vector and ray representations of the four‐dimensional cubic crystal point groups: group 47 and group 45. These groups are of order 384 and 1152, respectively, and contain the cubic point group in three dimensions Oh[3] as a subgroup. Tables are given of the irreducible representations of Oh subduced by the irreducible representations of group 47 and group 45. These tables may be useful in testing the conjecture that accidental degeneracy in problems in solid state physics in three dimensions reflects a higher symmetry in four dimensions.

Orthogonality catastrophe and decoherence of a confined Bose-Einstein condensate at finite temperature

We discuss mechanisms of decoherence of a confined Bose-Einstein condensate at finite temperatures under the explicit condition of conservation of the total number of bosons

Implications of SU(2) symmetry on the dynamics of population difference in the two-component atomic vapor.

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Theory of multipole-dipole resonance Raman scattering by phonons

in the trap. A criterion for the irreversible decay of the condensate two-time correlator is formulated in terms of the {\it Orthogonality Catastrophe} (OC) for the exact N-body eigenstates, so that no irreversible decay occurs without the OC. If an infinite external bath contacts a finite condensate, the OC should practically always occur as long as the bath degrees o freedom are interacting with each other. We claim that, if no external bath is present and the role of the bath is played by the normal component, no irreversible decay occurs. We discuss the role of the effect of the {\it level repulsion} in eliminating the OC. At finite temperatures, the time-correlations of the condensate isolated from the environment are dominated by the reversible dephasing which results from the thermal ensemble averaging over realizations of the normal component. Accordingly, the correlator exhibits the gaussian decay with certain decay time

An SU(8) model for the unification of superconductivity, charge, and spin density waves

\tau_d

Structure of the magnetoexciton and optical properties in fractional quantum Hall systems

dependent on temperature as well as on intensity of the shot noise determined by the statistical uncertainty in the number of bosons

QUANTUM DEPHASING OF NORMAL MODES OF A BOSE-EINSTEIN CONDENSATE IN A MAGNETIC TRAP

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Theory of resonant Raman enhancement of a forbidden phonon in Cu2O

deposited into the trap. We estimate