Ordered and disordered dynamics in monolayers of rolling particles

We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles with an offset center of mass and a non-isotropic inertia tensor. The rolling constraint is considered as a simplified model of a very strong, but rapidly decaying bond with the surface, preventing application of the standard tools of statistical mechanics. We show the existence and nonlinear stability of ordered lattice states, as well as disturbance propagation through and chaotic vibrations of these states. We also investigate the dynamics of disordered gas states and show that there is a surprising and robust linear connection between distributions of angular and linear velocity for both lattice and gas states, allowing to define the concept of temperature

Observation of long-lived polariton states in semiconductor microcavities across the parametric threshold

The excitation spectrum around the pump-only stationary state of a polariton optical parametric oscillator (OPO) in semiconductor microcavities is investigated by time-resolved photoluminescence. The response to a weak pulsed perturbation in the vicinity of the idler mode is directly related to the lifetime of the elementary excitations. A dramatic increase of the lifetime is observed for a pump intensity approaching and exceeding the OPO threshold. The observations can be explained in terms of a critical slowing down of the dynamics upon approaching the threshold and the following onset of the soft Goldstone mode

An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow

In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed earlier by the authors. We discuss various aspects of the Hamiltonian structure of the Euler equations and show in particular that the optimal control approach leads to a standard formulation of the Euler equations -- the so-called impulse equations in their Lagrangian form. We discuss various other aspects of the Euler equations from a pedagogical point of view. We show that the Hamiltonian in the maximum principle is given by the pairing of the Eulerian impulse density with the velocity. We provide a comparative discussion of the flow equations in their Eulerian and Lagrangian form and describe how these forms occur naturally in the context of optimal control. We demonstrate that the extremal equations corresponding to the optimal control problem for the flow have a natural canonical symplectic structure.Comment: 6 pages, no figures. To appear in Proceedings of the 39th IEEEE Conference on Decision and Contro

An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons

We report an experimental study of superfluid hydrodynamic effects in a one-dimensional polariton fluid flowing along a laterally patterned semiconductor microcavity and hitting a micron-sized engineered defect. At high excitation power, superfluid propagation effects are observed in the polariton dynamics, in particular, a sharp acoustic horizon is formed at the defect position, separating regions of sub- and super-sonic flow. Our experimental findings are quantitatively reproduced by theoretical calculations based on a generalized Gross-Pitaevskii equation. Promising perspectives to observe Hawking radiation via photon correlation measurements are illustrated.Comment: 5 pages Main + 5 pages Supplementary, 8 figure

A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

Sub-Doppler resonances in the back-scattered light from random porous media infused with Rb vapor

We report on the observation of sub-Doppler resonances on the back-scattered light from a random porous glass medium with rubidium vapor filling its interstices. The sub-Doppler spectral lines are the consequence of saturated absorption where the incident laser beam saturates the atomic medium and the back-scattered light probes it. Some specificities of the observed spectra reflect the transient atomic evolution under confinement inside the pores. Simplicity, robustness and potential miniaturization are appealing features of this system as a spectroscopic reference.Comment: 6 pages, 4 figure

K -> pi pi and a light scalar meson

We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi transitions using a Dyson-Schwinger equation model. Exploiting the feature that QCD penguin operators direct K^0_S transitions through 0^{++} intermediate states, we find an explanation of the enhancement of I=0 K -> pi pi transitions in the contribution of a light sigma-meson. This mechanism also affects epsilon'/epsilon.Comment: 7 pages, REVTE

Isentropic Curves at Magnetic Phase Transitions

Experiments on cold atom systems in which a lattice potential is ramped up on a confined cloud have raised intriguing questions about how the temperature varies along isentropic curves, and how these curves intersect features in the phase diagram. In this paper, we study the isentropic curves of two models of magnetic phase transitions- the classical Blume-Capel Model (BCM) and the Fermi Hubbard Model (FHM). Both Mean Field Theory (MFT) and Monte Carlo (MC) methods are used. The isentropic curves of the BCM generally run parallel to the phase boundary in the Ising regime of low vacancy density, but intersect the phase boundary when the magnetic transition is mainly driven by a proliferation of vacancies. Adiabatic heating occurs in moving away from the phase boundary. The isentropes of the half-filled FHM have a relatively simple structure, running parallel to the temperature axis in the paramagnetic phase, and then curving upwards as the antiferromagnetic transition occurs. However, in the doped case, where two magnetic phase boundaries are crossed, the isentrope topology is considerably more complex

Controllable diffusion of cold atoms in a harmonically driven and tilted optical lattice: Decoherence by spontaneous emission

We have studied some transport properties of cold atoms in an accelerated optical lattice in the presence of decohering effects due to spontaneous emission. One new feature added is the effect of an external AC drive. As a result we obtain a tunable diffusion coefficient and it's nonlinear enhancement with increasing drive amplitude. We report an interesting maximum diffusion condition.Comment: 16 pages, 7 figures, revised versio