1,141 research outputs found
On the equivalence of modes of convergence for log-concave measures
An important theme in recent work in asymptotic geometric analysis is that
many classical implications between different types of geometric or functional
inequalities can be reversed in the presence of convexity assumptions. In this
note, we explore the extent to which different notions of distance between
probability measures are comparable for log-concave distributions. Our results
imply that weak convergence of isotropic log-concave distributions is
equivalent to convergence in total variation, and is further equivalent to
convergence in relative entropy when the limit measure is Gaussian.Comment: v3: Minor tweak in exposition. To appear in GAFA seminar note
Molecular orientation entanglement and temporal Bell-type inequalities
We detail and extend the results of [Milman {\it et al.}, Phys. Rev. Lett.
{\bf 99}, 130405 (2007)] on Bell-type inequalities based on correlations
between measurements of continuous observables performed on trapped molecular
systems. We show that for some observables with a continuous spectrum which is
bounded, one is able to construct non-locality tests sharing common properties
with those for two-level systems. The specific observable studied here is
molecular spatial orientation, and it can be experimentally measured for single
molecules, as required in our protocol. We also provide some useful general
properties of the derived inequalities and study their robustness to noise.
Finally, we detail possible experimental scenarii and analyze the role played
by different experimental parameters.Comment: 10 pages and 5 figure
Phase space measure concentration for an ideal gas
We point out that a special case of an ideal gas exhibits concentration of
the volume of its phase space, which is a sphere, around its equator in the
thermodynamic limit. The rate of approach to the thermodynamic limit is
determined. Our argument relies on the spherical isoperimetric inequality of
L\'{e}vy and Gromov.Comment: 15 pages, No figures, Accepted by Modern Physics Letters
Parity-dependent State Engineering and Tomography in the ultrastrong coupling regime
Reaching the strong coupling regime of light-matter interaction has led to an
impressive development in fundamental quantum physics and applications to
quantum information processing. Latests advances in different quantum
technologies, like superconducting circuits or semiconductor quantum wells,
show that the ultrastrong coupling regime (USC) can also be achieved, where
novel physical phenomena and potential computational benefits have been
predicted. Nevertheless, the lack of effective decoupling mechanism in this
regime has so far hindered control and measurement processes. Here, we propose
a method based on parity symmetry conservation that allows for the generation
and reconstruction of arbitrary states in the ultrastrong coupling regime of
light-matter interactions. Our protocol requires minimal external resources by
making use of the coupling between the USC system and an ancillary two-level
quantum system.Comment: Improved version. 9 pages, 5 figure
Spacecraft drag-free technology development: On-board estimation and control synthesis
Estimation and control methods for a Drag-Free spacecraft are discussed. The functional and analytical synthesis of on-board estimators and controllers for an integrated attitude and translation control system is represented. The framework for detail definition and design of the baseline drag-free system is created. The techniques for solution of self-gravity and electrostatic charging problems are applicable generally, as is the control system development
Autonomous frequency domain identification: Theory and experiment
The analysis, design, and on-orbit tuning of robust controllers require more information about the plant than simply a nominal estimate of the plant transfer function. Information is also required concerning the uncertainty in the nominal estimate, or more generally, the identification of a model set within which the true plant is known to lie. The identification methodology that was developed and experimentally demonstrated makes use of a simple but useful characterization of the model uncertainty based on the output error. This is a characterization of the additive uncertainty in the plant model, which has found considerable use in many robust control analysis and synthesis techniques. The identification process is initiated by a stochastic input u which is applied to the plant p giving rise to the output. Spectral estimation (h = P sub uy/P sub uu) is used as an estimate of p and the model order is estimated using the produce moment matrix (PMM) method. A parametric model unit direction vector p is then determined by curve fitting the spectral estimate to a rational transfer function. The additive uncertainty delta sub m = p - unit direction vector p is then estimated by the cross spectral estimate delta = P sub ue/P sub uu where e = y - unit direction vectory y is the output error, and unit direction vector y = unit direction vector pu is the computed output of the parametric model subjected to the actual input u. The experimental results demonstrate the curve fitting algorithm produces the reduced-order plant model which minimizes the additive uncertainty. The nominal transfer function estimate unit direction vector p and the estimate delta of the additive uncertainty delta sub m are subsequently available to be used for optimization of robust controller performance and stability
Quantum phase gate and controlled entanglement with polar molecules
We propose an alternative scenario for the generation of entanglement between rotational quantum states of two polar molecules. This entanglement arises from dipole-dipole interaction, and is controlled by a sequence of laser pulses simultaneously exciting both molecules. We study the efficiency of the process, and discuss possible experimental implementations with cold molecules trapped in optical lattices or in solid matrices. Finally, various entanglement detection procedures are presented, and their suitability for these two physical situations is analyzed
Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems
We obtain new principles for transferring log-Sobolev and Spectral-Gap
inequalities from a source metric-measure space to a target one, when the
curvature of the target space is bounded from below. As our main application,
we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of
various conservative spin system models, consisting of non-interacting and
weakly-interacting particles, constrained to conserve the mean-spin. When the
self-interaction is a perturbation of a strongly convex potential, this
partially recovers and partially extends previous results of Caputo,
Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg
and Yau. When the self-interaction is only assumed to be (non-strongly) convex,
as in the case of the two-sided exponential measure, we obtain sharp estimates
on the system's spectral-gap as a function of the mean-spin, independently of
the size of the system.Comment: 57 page
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