Bose-Einstein condensation of excitons in Cu2_2O

We present a parameter-free model which estimates the density of excitons in Cu$_2$O, related to experiments that have tried to create an excitonic Bose-Einstein condensate. Our study demonstrates that the triplet-state excitons move along adiabats and obey classical statistics, while the singlet-state excitons are a possible candidate for forming a Bose-Einstein condensate. Finally we show that the results of this study do not change qualitatively in a two-dimensional exciton gas, which can be realized in a quantum well.Comment: 6 pages, RevTex, 1 ps figur

Constrained Willmore Surfaces

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the critical points of arbitrary geometric functionals on the space of immersions under the constraint that the admissible variations infinitesimally preserve the conformal structure. Besides constrained Willmore surfaces we discuss in some detail examples of constrained minimal and volume critical surfaces, the critical points of the area and enclosed volume functional under the conformal constraint.Comment: 17 pages, 8 figures; v2: Hopf tori added as an example, minor changes in presentation, numbering changed; v3: new abstract and appendix, several changes in presentatio

Molecular vibration in cold collision theory

Cold collisions of ground state oxygen molecules with Helium have been investigated in a wide range of cold collision energies (from 1 $\mu$K up to 10 K) treating the oxygen molecule first as a rigid rotor and then introducing the vibrational degree of freedom. The comparison between the two models shows that at low energies the rigid rotor approximation is very accurate and able to describe all the dynamical features of the system. The comparison between the two models has also been extended to cases where the interaction potential He - O$_2$ is made artificially stronger. In this case vibration can perturb rate constants, but fine-tuning the rigid rotor potential can alleviate the discrepancies between the two models.Comment: 11 pages, 3 figure

Probing semiclassical analogue gravity in Bose--Einstein condensates with widely tunable interactions

Bose-Einstein condensates (BEC) have recently been the subject of considerable study as possible analogue models of general relativity. In particular it was shown that the propagation of phase perturbations in a BEC can, under certain conditions, closely mimic the dynamics of scalar quantum fields in curved spacetimes. In two previous articles [gr-qc/0110036, gr-qc/0305061] we noted that a varying scattering length in the BEC corresponds to a varying speed of light in the ``effective metric''. Recent experiments have indeed achieved a controlled tuning of the scattering length in Rubidium 85. In this article we shall discuss the prospects for the use of this particular experimental effect to test some of the predictions of semiclassical quantum gravity, for instance, particle production in an expanding universe. We stress that these effects are generally much larger than the Hawking radiation expected from causal horizons, and so there are much better chances for their detection in the near future.Comment: 18 pages; uses revtex4. V2: Added brief discussion of "Bose-Nova" phenomenon, and appropriate reference

Photoassociation spectroscopy of cold calcium atoms

Photoassociation spectroscopy experiments on 40Ca atoms close to the dissociation limit 4s4s 1S0 - 4s4p 1P1 are presented. The vibronic spectrum was measured for detunings of the photoassociation laser ranging from 0.6 GHz to 68 GHz with respect to the atomic resonance. In contrast to previous measurements the rotational splitting of the vibrational lines was fully resolved. Full quantum mechanical numerical simulations of the photoassociation spectrum were performed which allowed us to put constraints on the possible range of the calcium scattering length to between 50 a_0 and 300 a_0

Interactions between arbuscular mycorrhizal fungi and intraspecific competition affect size and size inequality of Plantago lanceolata L.

Intraspecific competition causes decreases in plant size and increases in size inequality. Arbuscular mycorrhizas usually increase the size and inequality of non-competing plants, but mycorrhizal effects often disappear when plants begin competing. We hypothesized that mycorrhizal effects on size inequality would be determined by the experimental conditions, and conducted simultaneous field and glasshouse experiments to investigate how AM fungi and intraspecific competition determine size inequality in Plantago lanceolata. 2 As predicted, plant size was reduced when plants were competing, in both field and controlled conditions. However, size inequality was unexpectedly reduced by competition. Plants may have competed in a symmetric fashion, probably for nutrients, rather than the more common situation, in which plant competition is strongly asymmetric. 3 Mycorrhizas had no effect on plant size or size inequality in competing plants in either field or controlled conditions, possibly because competition for nutrients was intense and negated any benefit the fungi could provide. 4 The effects of mycorrhizas on non-competing plants were also unexpected. In field-grown plants, AM fungi increased plant size, but decreased size inequality: mycorrhizal plants were more even in size, with few very small individuals. In glasshouse conditions, mycorrhizal colonization was extremely high, and was generally antagonistic, causing a reduction in plant size. Here, however, mycorrhizas caused an increase in size inequality, supporting our original hypothesis. This was because most plants were heavily colonized and small, but a few had low levels of colonization and grew relatively large. 5 This study has important implications for understanding the forces that structure plant communities. AM fungi can have a variety of effects on size inequality and thus potentially important influences on long-term plant population dynamics, by affecting the genetic contribution of individuals to the next generation. However, these effects differ, depending on whether plants are competing or not, the degree of mycorrhizal colonization and the responsiveness of the plant to different colonization densities

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps

We consider the problem of cold atomic collisions in tight traps, where the absolute scattering length may be larger than the trap size. As long as the size of the trap ground state is larger than a characteristic length of the van der Waals potential, the energy eigenvalues can be computed self-consistently from the scattering amplitude for untrapped atoms. By comparing with the exact numerical eigenvalues of the trapping plus interatomic potentials, we verify that our model gives accurate eigenvalues up to milliKelvin energies for single channel s-wave scattering of $^{23}$Na atoms in an isotropic harmonic trap, even when outside the Wigner threshold regime. Our model works also for multi-channel scattering, where the scattering length can be made large due to a magnetically tunable Feshbach resonance.Comment: 7 pages, 4 figures (PostScript), submitted to Physical Review

Model study on the photoassociation of a pair of trapped atoms into an ultralong-range molecule

Using the method of quantum-defect theory, we calculate the ultralong-range molecular vibrational states near the dissociation threshold of a diatomic molecular potential which asymptotically varies as $-1/R^3$. The properties of these states are of considerable interest as they can be formed by photoassociation (PA) of two ground state atoms. The Franck-Condon overlap integrals between the harmonically trapped atom-pair states and the ultralong-range molecular vibrational states are estimated and compared with their values for a pair of untrapped free atoms in the low-energy scattering state. We find that the binding between a pair of ground-state atoms by a harmonic trap has significant effect on the Franck-Condon integrals and thus can be used to influence PA. Trap-induced binding between two ground-state atoms may facilitate coherent PA dynamics between the two atoms and the photoassociated diatomic molecule.Comment: 11 pages, 4 figures, to appear in Phys. Rev. A (September, 2003