Degenerate Phase Research Articles

Thermal and magnetic properties of integrable spin-1 and spin-3/2 chains with applications to real compounds

The ground state and thermodynamic properties of spin-1 and spin- chains are investigated via exactly solvedsu(3) and su(4) models with physically motivated chemical potential terms. The analysis involves thethermodynamic Bethe ansatz and the high temperature expansion (HTE) methods. For thespin-1 chain with large single-ion anisotropy, a gapped phase occurs which is significantlydifferent from the valence-bond-solid Haldane phase. The theoretical curves for themagnetization, susceptibility and specific heat are favourably compared withexperimental data for a number of spin-1 chain compounds. For the spin- chain a degenerate gapped phase exists starting at zero external magnetic field. A middlemagnetization plateau can be triggered by the single-ion anisotropy term. Overall, ourresults lend further weight to the applicability of integrable models to the physics oflow-dimensional quantum spin systems. They also highlight the utility of the exact HTEmethod.

Decay estimates for weighted oscillatory integrals in R^2

In this paper, we study decay estimates for a two-dimensional scalar oscillatory integral with degenerate real-analytic phase and amplitude. Integrals such as these form a model for certain higher-dimensional degenerate oscillatory integrals, for which it is known that many of the two-dimensional results fail. We define an analogue of the Newton distance in the weighted case, and prove that this gives the optimal rate of decay for the weighted oscillatory integral under certain generic hypotheses. When these hypotheses fail, we provide counterexamples to show that the optimal rate of decay may be faster in general. We have obtained bounds for the rate of decay in some of these exceptional cases.

Systematics of the metallization of low-Z and alkali fluids

Hydrogen, nitrogen, oxygen, cesium, and rubidium undergo nonmetal–metal (NMM) transitions in the degenerate warm fluid phase. It is quite likely that all these fluids are monatomic or very nearly so. For N, O, and H, these NMM transitions occur under quasi-isentropic compression to ∼100 GPa (1 Mbar) pressures and densities of ∼10 times initial liquid density in the case of H. These conditions were achieved with a two-stage gun. In the cases of Cs and Rb, these transitions occur at only ∼0.01 GPa in the expanded fluid at 2000 K. These NMM transitions are Mott transitions. The values of the minimum metallic conductivities are essentially the same for all five because minimum metallic conductivity depends weakly on density of metallization and number of conduction electrons per atom. In contrast, the density dependences of the semiconductivities are very different. In the spirit of Mott, quantum mechanical wave functions of the free atoms are used to estimate the densities at which semiconductivies are appreciable. The radial extents of the charge-density distributions are well correlated with the Mott-scaled density dependences of the semiconductivities. These radial extents depend on the degree to which the filled-electron core screens the valence electron(s) from the nuclear Coulomb force. This simple picture gives a qualitative explanation for the density dependences of the semiconductivities of all five and for the Herzfeld criterion, which predates quantum mechanics.

THERMODYNAMICS OF A BOSE GAS TRAPPED IN A BOUNDED HARMONIC POTENTIAL

Some thermodynamic features of an assembly of a finite number of bosons trapped in a bounded harmonic potential are investigated. P–V isotherms are drawn for both the degenerate and the non-degenerate phases. At any temperature, the pressure is a decreasing function of volume, unlike the free Bose gas for which the pressure becomes independent of volume in the degenerate phase. At the absolute zero of temperature the quantum pressure for a spherical enclosure of radius r0 equal to aho, aho being the characteristic harmonic oscillator length, is found to be of order 10-10 Torr while for [Formula: see text] it is of order 10-12 Torr. The isothermal compressibility has a sharp drop near the critical point and becomes negligibly small for temperatures above the critical temperature, irrespective of the size of the trap. The coefficient of thermal expansion also shows a sudden drop at the critical temperature. The specific heat at constant pressure shows a peak and is well-defined in the degenerate phase, in contradistinction to the ideal Bose gas. Results recently derived by Singh on the basis of local equilibrium theory are found to be in good agreement with our numerical computations.

Magnetic ground-state phase diagram of a multiple-spin exchange model on the triangular lattice

We investigated the ground state of a multiple-spin exchange model, which may describe magnetism of the solid 3 He layers adsorbed on graphite. The model contains four-spin exchange terms together with the conventional Heisenberg ones. Using the mean-field theory we found numerous ground-state phases with large numbers (up to 144) of sublattices. These phases replace the previously reported infinitely degenerate phase. A novel phase with 6-sublattice non-coplanar spin structure, where both vector and scalar chiral orders exist, appears between the 120° Néel and tetrahedral phases. This phase is replaced by a novel 12-sublattice phase under the magnetic field.

Theory and experiment of two-photon $lquot$direct$rquot$ interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump

Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young’s double-slit experiment. In this experiment, a short focal length lens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.

Polarization selective motional holeburning for high efficiency, degenerate optical phase conjugation in rubidium

We have observed high reflectivity (>40) optical phase conjugation for a low pump intensity (100 mW/mm 2), using degenerate four-wave mixing in rubidium vapor. The polarization of the beams were selected such that the diffracting grating was formed in the Zeeman sublevel coherence. We find that only a selected band of atoms moving at non-zero velocities contribute to this process, by forming, in the atom's frame, a non-degenerate double- Λ system. This observation makes it possible to construct a simple, compact, and highly efficient phase conjugator using a semiconductor laser, without any modulators, for many applications, without any concern resulting from frequency mismatch between the probe and the conjugate.

Uniform boundedness of oscillatory singular integrals on Hardy spaces

We prove the uniform $H^1$ boundedness of oscillatory singular integrals with degenerate phase functions.

New buffer layers, large band gap ternary compounds: CuAlTe2

After deposition, by evaporation under vacuum, of Al/Cu/Te. multilayer structures, annealing at 673 K or more for half an hour, under argon flow, allows CuAlTe2 films crystallised in the chalcopyrite structure to be obtained. The optical and electrical properties are interpreted by introducing the influence of impurity foreign phases present in the films. The optical properties are sensitive to the small Al2O3 domains randomly distributed into the CuAlTe2 polycrystalline matrix. The optical band gap is slightly increased (2.35 eV) by the presence of alumina. The conductivity measurements show that a short circuit effect can be induced by a binary Cu Te degenerate phase present at the surface of the films. This effect can be suppressed by KCN etching of the samples that allows the superficial foreign phase to be dissolved.

Stability and bandwidth enhancement of differencefrequency generation (DFG)-based wavelength conversion by pump detuning

The authors report on a method for enhancing the operating stability and signal bandwidth of difference-frequency-generation-based wavelength conversion by detuning the pump from the degenerate phase matching wavelength; both can be further enhanced by using nonuniform quasi-phase-matching structures.

Raman phase conjugate resonator for intracavity aero-optic turbulence aberration correction

A cw degenerate phase conjugate resonator (PCR) with intracavity aero-optic turbulent flow is demonstrated using sodium vapor pumped with a low intensity cw laser. A turbulent helium jet at a high flow velocity of 250 m/s and forcing frequency of 18 kHz generated the spatio-temporal aberrations. The intracavity normalized peak-to-peak intensity fluctuations at 18 kHz measured with a pinhole-detector are ten times smaller in the corrected beam than in the aberrated beam. The threshold pump intensity for the resonator is ∼4.5 W/cm 2 in the absence of the turbulent flow. The pump frequency is tuned well within the Doppler width of the Na D 1 transition. Evidence of a degenerate (laboratory frame) double-Λ mechanism involving Zeeman sublevels is also shown.

Causal structure and degenerate phase boundaries

Timelike and null hypersurfaces in degenerate space-times in Ashtekar theory are defined in the light of the degenerate causal structure proposed by Matschull. Using the new definition of null hypersurfaces, the conjecture that the ``phase boundary'' separating the degenerate space-time region from the nondegenerate one in Ashtekar's gravity is always null is proved under certain circumstances.

The Effect of Habitat Changes on the Endangered Ground Beetle Carabus Nitens (Coleoptera: Carabidae)

Carabus nitens, one of the most endangered ground beetles in Central Europe, was investigated with pitfall traps at 30 sampling sites in 17 heath fragments of the largest German heath landscape under nature conservation (nature reserve 'Luneburger Heide'). The preference for damp Erica heaths and dry Calluna heaths in the building phase was thereby evident. Calluna heaths in the mature and degenerate phase, with and without extensive coverage by Avenella flexuosa, are either not inhabited or are avoided. The results of ovary dissections indicate that the populations in two successive spring seasons consisted mainly of animals which had already reproduced and were therefore older than one and a half years. Allozyme electrophoreses revealed variation for three of the nine investigated enzyme loci, and large differences in the allele frequency at one of these loci indicated genetic drift and fluctuations in the size of local populations. According to these results and statements in the literature, the loss of heathland areas and habitat quality are both responsible for the decline of the species. Suitable measures for preserving the species are (1) restoration of building phases of the Calluna heaths and (2) interconnection of at least the smaller heath fragments. Finally, recommendations are given for reintroductions.

The Four Phases of Philosophy and Its Present Condition

Translator's Preface This lecture on the four phases of philosophy, originally addressed to a literary society rather than to an academic audience, is perhaps the most accessible of Brentano's work. Nevertheless, it can be seen from Brentano's own words that he did not achieve accessibility at the price of watering his thoughts down, and, although the lecture is on the face of it a commentary on a now forgotten book that the society published, Brentano uses the opportunity of the lecture to speak on the entire history of philosophy and to express several of his characteristic views. Among the latter are the views that Kant, speculative metaphysicians (such as German Idealists), and mystics fall into the lowest and most degenerate phase of philosophy, while thinkers such as Aristotle, Aquinas, and the early modems (especially Bacon, Descartes, and Locke), whose thought is grounded in experience, are on the highest level. It would be too grand a claim-and incorrect anyway-to say that this lecture alone influenced Meinong, Husserl, and the future course of Austrian and world philosophy. But Brentano's influence did reach that far. And this lecture expresses long-held and characteristic views of Brentano in a brief and forceful way. The following translation is based on the German text of Brentano's lecture, vier Phasen der Philosophie und ihr augenblicklicher Stand, edited, with introduction and notes by Oskar Kraus, published in his one-volume collection of Brentano's lectures and shorter works entitled Die Vier Phasen der Philosophie und ihr Augenblicklicher Stand (Leipzig, 1926). Kraus's was the second publication of the text of the lecture. The text was first published by Brentano himself in Stuttgart in 1895. The translation that follows below is the first English translation. The endnotes are Brentano's. Footnotes to Brentano's text (marked with asterisks) and bracketed material (mainly in his endnotes) have been added by the translator. These generally provide references or English translations of Brentano's references. (Some of the information in Brentano's notes, e.g., dates of birth and death of individual philosophers, has been superseded by more recent research.) The translator has benefitted from the assistance of many people and wishes especially to thank Helene Riley for assistance both in matters of translation details and in matters of Austrian culture and history. Additional gratitude is owed to Steven Grosby, Ralf Kruger, Todd May, Judy Melton, Ron Moran, Lucy Rollin, and Dan Wueste for their help. Errors that remain are of course entirely the responsibility of the translator. The first edition of this work bore the dedication: Dedicated from the heart to the academic youth of Austria-Hungary in expression of my gratitude for so many manifestations of the warmest concern Forward What I offer here is a lecture that was delivered to the Literary Society of Vienna on November 28, 1894. I had been requested to speak at the meeting about a work that the society had edited; and, in fact, anyone who has read Der grundlose Optimismus [Groundless Optimism]' by H. Lorm will find all of its essential points to be critically treated. But those who are unacquainted with this book will find the lecture no less comprehensible on that account. Its content stands on its own. The principal philosophical interests of the present are addressed in the lecture. Although, its conception of the history of philosophy might strike many as unusual, I have believed in it for years; and, for more than two decades, several scholars and I have taken it as a basis for academic lectures on the history of philosophy. I have not deluded myself into believing that my approach will not meet with prejudices, and that some of these may indeed be too strong to yield on initial impact. Still, I hope that those who thoughtfully follow the facts and considerations that are presented here will not fail to be impressed by them. …

On the degenerate phase boundaries

The structure of the phase boundary between degenerate and non-degenerate regions in Ashtekar's gravity has been studied recently by Bengtsson and Jacobson who conjectured that the phase boundary should always be null. In this paper, we reformulate the reparametrization procedure in the mapping language and distinguish a phase boundary from its image . It is shown that has to be null, while the nullness of requires some more suitable criterion.

Summary

Summary

On the effect of spatial dispersion on the degeneracies of acoustic-wave branches in crystals

The effect of spatial dispersion on the phase-speed degeneracies of acoustic waves in noncentrosymmetric crystals is explored in the framework of continuum elasticity. It is shown that the degeneracies, which in the nondispersive limit occur in directions neither lying in a symmetry plane nor parallel to a rotation inversion axis, are lifted on account of spatial dispersion. The degeneracies lying in symmetry planes change their in-plane orientation depending on the frequency, unless remaining fixed to a symmetry axis. Given that the degeneracy with regard for linear spatial dispersion occurs in some direction m, the value of degenerate phase speed coincides with the value of one of the speeds assigned to m in the nondispersive limit. Relations for the acoustic-wave parameters with dispersive corrections are derived and discussed for various particular cases.

Interference of a first-order transition with the formation of a spin-Peierls state inα′-NaV2O5

We present results of high-resolution thermal-expansion and specific-heat measurements on single crystalline ${\ensuremath{\alpha}}^{\ensuremath{'}}$-${\mathrm{NaV}}_{2}$O${}_{5}$. We find clear evidence for two almost degenerate phase transitions associated with the formation of the dimerized state around 33 K: A sharp first-order transition at ${T}_{1}=(33\ifmmode\pm\else\textpm\fi{}0.1)$ K slightly below the onset of a second-order transition at ${T}_{2}^{\mathrm{onset}}\ensuremath{\approx}(34\ifmmode\pm\else\textpm\fi{}0.1)$ K. The latter is accompanied by pronounced spontaneous strains. Our results are consistent with a structural transformation at ${T}_{1}$ induced by the incipient spin-Peierls order parameter above ${T}_{2}{=T}_{\mathrm{SP}}.$

Brillouin enhanced four-wave mixing and phase conjugation in weakly collisional plasmas

Brillouin enhanced four-wave mixing and phase conjugation of electromagnetic waves in weakly collisional fully ionized plasmas are considered. It is found that the nonlinearity associated with the nonlocal electron heat transport may dominate over the ponderomotive force and consequently there might appear an enhanced degenerate four-wave mixing and phase conjugation reflectivity.

Degenerate metric phase boundaries

The structure of boundaries between degenerate and non-degenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such `phase boundaries' in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of flat space, Schwarzschild and plane-wave solutions joined to degenerate regions. In the last case, the wave collides with a planar phase boundary and continues on with the same curvature but degenerate triad, while the phase boundary continues in the opposite direction. We conjecture that degenerate phase boundaries are always null.