Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $\Theta_\pi$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul

Coherent Tunneling of Atoms from Bose-condensed Gases at Finite Temperatures

Tunneling of atoms between two trapped Bose-condensed gases at finite temperatures is explored using a many-body linear response tunneling formalism similar to that used in superconductors. To lowest order, the tunneling currents can be expressed quite generally in terms of the single-particle Green's functions of the isolated Bose gases. A coherent first-order tunneling Josephson current between two atomic Bose-condensates is found, in addition to coherent and dissipative contributions from second-order condensate-noncondensate and noncondensate-noncondensate tunneling. Our work is a generalization of Meier and Zwerger, who recently treated tunneling between uniform atomic Bose gases. We apply our formalism to the analysis of an out-coupling experiment induced by light wave fields, using a simple Bogoliubov-Popov quasiparticle approximation for the trapped Bose gas. For tunneling into the vacuum, we recover the results of Japha, Choi, Burnett and Band, who recently pointed out the usefulness of studying the spectrum of out-coupled atoms. In particular, we show that the small tunneling current of noncondensate atoms from a trapped Bose gas has a broad spectrum of energies, with a characteristic structure associated with the Bogoliubov quasiparticle u^2 and v^2 amplitudes.Comment: 26 pages, 5 figures, minor changes, to appear in PR

Measurement of one-particle correlations and momentum distributions for trapped 1D gases

van Hove's theory of scattering of probe particles by a macroscopic target is generalized so as to relate the differential cross section for atomic ejection via stimulated Raman transitions to one-particle momentum-time correlations and momentum distributions of 1D trapped gases. This method is well suited to probing the longitudinal momentum distributions of 1D gases in situ, and examples are given for bosonic and fermionic atoms.Comment: 4 pages, 2 .eps figure

Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolution

A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength become larger. The number of density matrices required is given by $3^{M}$ where $M$ is the number of timesteps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.Comment: 14 pages, 9 figure

Rupture of multiple parallel molecular bonds under dynamic loading

Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root or logarithmic.Comment: 8 pages, 2 figure

On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

Atom laser coherence and its control via feedback

We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.Comment: 15 pages, 6 figures, revtex

Generic model of an atom laser

We present a generic model of an atom laser by including a pump and loss term in the Gross-Pitaevskii equation. We show that there exists a threshold for the pump above which the mean matter field assumes a non-vanishing value in steady-state. We study the transient regime of this atom laser and find oscillations around the stationary solution even in the presence of a loss term. These oscillations are damped away when we introduce a position dependent loss term. For this case we present a modified Thomas-Fermi solution that takes into account the pump and loss. Our generic model of an atom laser is analogous to the semi-classical theory of the laser.Comment: 15 pages, including 5 figures, submitted to Phys. Rev. A, revised manuscript, file also available at http://www.physik.uni-ulm.de/quan/users/kne

Neuroimaging Evidence of Major Morpho-Anatomical and Functional Abnormalities in the BTBR T+TF/J Mouse Model of Autism

BTBR T+tf/J (BTBR) mice display prominent behavioural deficits analogous to the defining symptoms of autism, a feature that has prompted a widespread use of the model in preclinical autism research. Because neuro-behavioural traits are described with respect to reference populations, multiple investigators have examined and described the behaviour of BTBR mice against that exhibited by C57BL/6J (B6), a mouse line characterised by high sociability and low self-grooming. In an attempt to probe the translational relevance of this comparison for autism research, we used Magnetic Resonance Imaging (MRI) to map in both strain multiple morpho-anatomical and functional neuroimaging readouts that have been extensively used in patient populations. Diffusion tensor tractography confirmed previous reports of callosal agenesis and lack of hippocampal commissure in BTBR mice, and revealed a concomitant rostro-caudal reorganisation of major cortical white matter bundles. Intact inter-hemispheric tracts were found in the anterior commissure, ventro-medial thalamus, and in a strain-specific white matter formation located above the third ventricle. BTBR also exhibited decreased fronto-cortical, occipital and thalamic gray matter volume and widespread reductions in cortical thickness with respect to control B6 mice. Foci of increased gray matter volume and thickness were observed in the medial prefrontal and insular cortex. Mapping of resting-state brain activity using cerebral blood volume weighted fMRI revealed reduced cortico-thalamic function together with foci of increased activity in the hypothalamus and dorsal hippocampus of BTBR mice. Collectively, our results show pronounced functional and structural abnormalities in the brain of BTBR mice with respect to control B6 mice. The large and widespread white and gray matter abnormalities observed do not appear to be representative of the neuroanatomical alterations typically observed in autistic patients. The presence of reduced fronto-cortical metabolism is of potential translational relevance, as this feature recapitulates previously-reported clinical observations

Quantum dynamical theory for squeezing the output of a Bose-Einstein condensate

A linear quantum dynamical theory for squeezing the output of the trapped Bose-Einstein condensate is presented with the Bogoliubov approximation. We observe that the non-classical properties, such as sub-Poisson distribution and quadrature squeezing effect, mutually oscillate between the quantum states of the applied optical field and the resulting atom laser beam with time. In particular, it is shown that an initially squeezed optical field will lead to squeezing in the outcoupled atomic beam at later times.Comment: 6 pages, Latex file, Phys.Rev.A 63(2001)1560