Multiplicity of periodic solutions for systems of weakly coupled parametrized second order differential equations

We prove a multiplicity result of periodic solutions for a system of second order differential equations having asymmetric nonlinearities. The proof is based on a recent generalization of the Poincar\ue9\u2013Birkhoff fixed point theorem provided by Fonda and Ure\uf1a

Quantum dynamics and statistics of two coupled down-conversion processes

In the framework of Heisenberg-Langevin theory the dynamical and statistical effects arising from the linear interaction of two nondegenerate down-conversion processes are investigated. Using the strong-pumping approximation the analytical solution of equations of motion is calculated. The phenomena reminiscent of Zeno and anti-Zeno effects are examined. The possibility of phase-controlled and mismatch-controlled switching is illustrated.Comment: 17 pages, 7 figure

INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION

It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at [email protected] (internet)

An Integrated XRF/XRD Instrument for Mars Exobiology and Geology Experiments

By employing an integrated x-ray instrument on a future Mars mission, data obtained will greatly augment those returned by Viking; details characterizing the past and present environment on Mars and those relevant to the possibility of the origin and evolution of life will be acquired. A combined x-ray fluorescence/x-ray diffraction (XRF/XRD) instrument was breadboarded and demonstrated to accommodate important exobiology and geology experiment objectives outlined for MESUR and future Mars missions. Among others, primary objectives for the exploration of Mars include the intense study of local areas on Mars to establish the chemical, mineralogical, and petrological character of different components of the surface material; to determine the distribution, abundance, and sources and sinks of volatile materials, including an assessment of the biologic potential, now and during past epoches; and to establish the global chemical and physical characteristics of the Martian surface. The XRF/XRD breadboard instrument identifies and quantifies soil surface elemental, mineralogical, and petrological characteristics and acquires data necessary to address questions on volatile abundance and distribution. Additionally, the breadboard is able to characterize the biogenic element constituents of soil samples providing information on the biologic potential of the Mars environment. Preliminary breadboard experiments confirmed the fundamental instrument design approach and measurement performance

Suppression of Zeno effect for distant detectors

We describe the influence of continuous measurement in a decaying system and the role of the distance from the detector to the initial location of the system. The detector is modeled first by a step absorbing potential. For a close and strong detector, the decay rate of the system is reduced; weaker detectors do not modify the exponential decay rate but suppress the long-time deviations above a coupling threshold. Nevertheless, these perturbing effects of measurement disappear by increasing the distance between the initial state and the detector, as well as by improving the efficiency of the detector.Comment: 4 pages, 4 figure

Quantum Zeno effect in a probed downconversion process

The distorsion of a spontaneous downconvertion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the downconversion in the nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of downconversion. These effects are interpreted as being manifestations of quantum Zeno or anti-Zeno effects, respectively, and they are understood by using the dressed modes picture of the device. The possibility of using the coupling as a nontrivial phase--matching technique is pointed out.Comment: 11 pages, 4 figure

Interface geometry of binary mixtures on curved substrates

Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting from the J\"ulicher-Lipowsky generalization of the Canham-Helfrich free energy to multicomponent membranes, we derive a number of exact relations governing the structure of an interface separating two lipid phases on arbitrarily shaped substrates and its stability. We then restrict our analysis to four classes of surfaces of both applied and conceptual interest: the sphere, axisymmetric surfaces, minimal surfaces and developable surfaces. For each class we investigate how the structure of the geometry and topology of the interface is affected by the shape of the substrate and we make various testable predictions. Our work sheds light on the subtle interaction mechanism between membrane shape and its chemical composition and provides a solid framework for interpreting results from experiments on supported lipid bilayers.Comment: 26 pages, 10 figure

Thermodynamic equilibrium of binary mixtures on curved surfaces

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on non-trivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical sub-diagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as antimixed states below the critical temperature. We corroborate our semi-analytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multi-component lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.Comment: 20 Pages, 7 Figures; comments and references added, typos correcte