The Significance of Multiple Saturation Points in the Context of Polybaric Near-fractional Melting

Experimental petrologists have successfully located basaltic liquid compositions parental to mid-ocean ridge basalt that are, within experimental resolution, multiply saturated with three-phase harzburgite or four-phase lherzolite assemblages on their liquidus at some elevated pressure. Such an experimental result is a necessary consequence of any paradigm in which erupted basalts derive from single-batch primary liquids that equilibrate with a mantle residue and undergo no subsequent magma mixing before differentiation and eruption. Here we investigate whether, conversely, such evidence of multiple saturation is sufficient to exclude dynamic melting models wherein increments of melt are mixed after segregation from residues, during melt transport or in magma chambers. Using two independent models of crystal–liquid equilibria to simulate polybaric near-fractional peridotite melting, we find that aggregate liquids from such melting processes can display near-intersections of liquidus surfaces too close to distinguish experimentally from exact multiple saturation points. Given uncertainties in glass compositions, fractionation corrections, experimental temperature and pressure conditions, and achievement of equilibrium, these results suggest that polybaric mixtures can in fact masquerade as mantle-equilibrated single-batch primary liquids. Multiple saturation points on the liquidus surfaces of primitive basalts do, however, preserve information about the average pressure of extraction of their constituent increments of liquid

Optical analogue of population trapping in the continuum: classical and quantum interference effects

A quantum theory of light propagation in two optical channel waveguides tunnelling-coupled to a common continuum of modes (such as those of a slab waveguide) is presented, and classical and quantum interference effects are investigated. For classical light, the photonic system realizes an optical analogue of coherent population trapping in the continuum encountered in atomic physics, where destructive interference between different light leakage channels leads to the appearance of a trapped state embedded in the continuum. For nonclassical light, two-photon interference effects are predicted, such as the tendency of photon pairs to bunch when decaying into the continuum.Comment: 12 pages, 2 figure

Experimental petrology and origin of Fra Mauro rocks and soil

Melting experiments over the pressure range 0 to 20 kilobars were conducted on Apollo 14 igneous rocks 14310 and 14072 and on comprehensive fines 14259. The mineralogy and textures of rocks 14310 and 14072 are presumed to be the result of near-surface crystallization. The chemical compositions of the samples show special relationships to multiply-saturated liquids in the system: anorthite-forsterite-fayalite-silica at low pressure. Partial melting of a lunar crust consisting largely of plagioclase, low calcium pyroxene, and olivine, followed by crystal fractionation at the lunar surface is proposed as a mechanism for the production of the igneous rocks and soil glasses sampled by Apollo 14

Spectral-discrete solitons and localization in frequency space

We report families of discrete optical solitons in frequency space, or spectral-discrete solitons existing in a dispersive Raman medium, where individual side-bands are coupled by coherence. The associated time-domain patterns correspond to either trains of ultrashort pulses, or weakly modulated waves. We describe the physics behind the spectral localization and study soliton bifurcations, stability and dynamics.Comment: 4 pages, 4 figures, submitted to Opt. Let

Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR

Coupled-mode theory for photonic band-gap inhibition of spatial instabilities

We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane

Loschmidt echo and fidelity decay near an exceptional point

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating

Classical realization of two-site Fermi-Hubbard systems

A classical wave optics realization of the two-site Hubbard model, describing the dynamics of interacting fermions in a double-well potential, is proposed based on light transport in evanescently-coupled optical waveguides.Comment: 4 page