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S. Richard

Publications and source records attributed to S. Richard.

46 records · Page 3Linked to original sources
arXiv2009

Magnetic pseudodifferential operators with coefficients in C*-algebras

In previous articles, a magnetic pseudodifferential calculus and a family of C*-algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol classes of Hörmander type with an x-behavior modelized by an abelian C*-algebra. Some of these classes generate C*-algebras associated with the twisted dynamical system. We show the relevance of these classes to the spectral analysis of pseudodifferential operators with anisotropic symbols and magnetic fields.

math-ph↗
arXiv2008

New formulae for the Aharonov-Bohm wave operators

It is proved that the wave operators corresponding to Schroedinger operators with Aharonov-Bohm type magnetic fields can be rewritten in terms of explicit functions of the generator of dilations and of the Laplacian.

math-ph↗
arXiv2006

Spectral analysis for adjacency operators on graphs

We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there is at most an eigenvalue located at the origin. Among other examples, the one-dimensional XY model of solid-state physics is covered. The proofs rely on commutators methods.

math-ph↗
arXiv2003

Momentum Spectroscopy of Phase Fluctuations of an Elongated Bose-Einstein Condensate

We have measured the momentum distribution of an elongated BEC (aspect ratio of 152), for temperatures below the critical temperature. The corresponding coherence length is significantly smaller than the condensate length in a wide range of temperature, in quantitative agreement with theoretical predictions. The Lorentzian shape of the momentum spectrum supports the image of a phase fluctuating quasicondensate.

cond-mat.stat-mech↗
arXiv2003

Momentum distribution and correlation function of quasicondensates in elongated traps

We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate, in a trap and in free expansion. We take the inhomogeneous density profile into account {\it{via}} a local density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate.

cond-mat↗
arXiv2003

Momentum spectroscopy of 1D phase fluctuations in Bose-Einstein condensates

We measure the axial momentum distribution of Bose-Einstein condensates with an aspect ratio of 152 using Bragg spectroscopy. We observe the Lorentzian momentum distribution characteristic of one-dimensional phase fluctuations. The temperature dependence of the width of this distribution provides a quantitative test of quasi-condensate theory. In addition, we observe a condensate length consistent with the absence of density fluctuations, even when phase fluctuations are large.

cond-mat.soft↗
arXiv2002

Phase coherence length of a Bose-Einstein condensate

We report on the measurement of the momentum distribution of an elongated Bose-Einstein condensate. A broadening of the distribution with increasing temperature is observed, which is clear evidence for phase fluctuations in the sample.

cond-mat↗
arXiv2001

Atom laser divergence

We measure the angular divergence of a quasi-continuous, rf-outcoupled, free-falling atom laser as a function of the outcoupling frequency. The data is compared to a Gaussian-beam model of laser propagation that generalizes the standard formalism of photonic lasers. Our treatment includes diffraction, magnetic lensing, and interaction between the atom laser and the condensate. We find that the dominant source of divergence is the condensate-laser interaction.

cond-mat↗