Eisenstein integrals and induction of relations

I give a survey of joint work with Henrik Schlichtkrull on the induction of certain relations among (partial) Eisenstein integrals for the minimal principal series of a reductive symmetric space. I explain the application of this principle of induction to the proofs of a Fourier inversion formula and a Paley-Wiener theorem. Finally, the relation with the Plancherel decomposition is discussed.Comment: Latex2e, 22 pp, Proc. Conf. `Analyse Harmonique Non Commutative (colloque en l'honneur de Jacques Carmona)' CIRM, Luminy, 20-24 Mai, 200

A Paley-Wiener theorem for reductive symmetric spaces

Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-finite compactly supported smooth functions on X is characterized.Comment: 31 pages, published versio

KK-invariant cusp forms for reductive symmetric spaces of split rank one

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms coincides with the closure of the $K$-finite generalized matrix coefficients of discrete series representations if and only if there exist no $K$-spherical discrete series representations. Moreover, we prove that every $K$-spherical discrete series representation occurs with multiplicity $1$ in the Plancherel decomposition of $G/H$.Comment: 12 page

Fully self-consistent calculations of nuclear Schiff moments

We calculate the Schiff moments of the nuclei 199Hg and 211Ra in completely self-consistent odd-nucleus mean-field theory by modifying the Hartree-Fock-Bogoliubov code HFODD. We allow for arbitrary shape deformation, and include the effects of nucleon dipole moments alongside those of a CP-violating pion-exchange nucleon-nucleon interaction. The results for 199Hg differ significantly from those of previous calculations when the CP-violating interaction is of isovector character.Comment: 7 pages, 2 figure

Unified Treatment of Heterodyne Detection: the Shapiro-Wagner and Caves Frameworks

A comparative study is performed on two heterodyne systems of photon detectors expressed in terms of a signal annihilation operator and an image band creation operator called Shapiro-Wagner and Caves' frame, respectively. This approach is based on the introduction of a convenient operator $\hat \psi$ which allows a unified formulation of both cases. For the Shapiro-Wagner scheme, where $[\hat \psi, \hat \psi^{\dag}] =0$, quantum phase and amplitude are exactly defined in the context of relative number state (RNS) representation, while a procedure is devised to handle suitably and in a consistent way Caves' framework, characterized by $[\hat \psi, \hat \psi^{\dag}] \neq 0$, within the approximate simultaneous measurements of noncommuting variables. In such a case RNS phase and amplitude make sense only approximately.Comment: 25 pages. Just very minor editorial cosmetic change

Optimization of Short Coherent Control Pulses

The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the non-commutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $\pi$ and $\frac{\pi}{2}$ pulses.Comment: 9 pages, 6 figures; published versio

Theory of multiwave mixing and decoherence control in qubit array system

We develop a theory to analyze the decoherence effect in a charged qubit array system with photon echo signals in the multiwave mixing configuration. We present how the decoherence suppression effect by the {\it bang-bang} control with the $\pi$ pulses can be demonstrated in laboratory by using a bulk ensemble of exciton qubits and optical pulses whose pulse area is even smaller than $\pi$. Analysis is made on the time-integated multiwave mixing signals diffracted into certain phase matching directions from a bulk ensemble. Depending on the pulse interval conditions, the cross over from the decoherence acceleration regime to the decoherence suppression regime, which is a peculiar feature of the coherent interaction between a qubit and the reservoir bosons, may be observed in the time-integated multiwave mixing signals in the realistic case including inhomogeneous broadening effect. Our analysis will successfully be applied to precise estimation of the reservoir parameters from experimental data of the direction resolved signal intensities obtained in the multiwave mixing technique.Comment: 19 pages, 11 figure