Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics

We establish new existence results for the Einstein constraint equations for mean extrinsic curvature arbitrarily far from constant. The results hold for rescaled background metric in the positive Yamabe class, with freely specifiable parts of the data sufficiently small, and with matter energy density not identically zero. Two technical advances make these results possible: A new topological fixed-point argument without smallness conditions on spatial derivatives of the mean extrinsic curvature, and a new global supersolution construction for the Hamiltonian constraint that is similarly free of such conditions. The results are presented for strong solutions on closed manifolds, but also hold for weak solutions and for compact manifolds with boundary. These results are apparently the first that do not require smallness conditions on spatial derivatives of the mean extrinsic curvature.     

Chiral Nonlinear sigma models as models for topological superconductivity

We study the mechanism of topological superconductivity in a hierarchical chain of chiral nonlinear sigma models (models of current algebra) in one, two, and three spatial dimensions. The models illustrate how the 1D Fr?hlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a pointlike topological soliton carries an electric charge. We discuss a flux quantization mechanism and show that it is essentially a generalization of the persistent current phenomenon, known in quantum wires. We also discuss why the superconducting state is stable in the presence of a weak disorder.     

A Damped Oscillator with a <Emphasis Type="Italic">δ</Emphasis>-Kicked Frequency in the Probability Representation of Quantum Mechanics

We obtain the tomogram of squeezed correlated states of a quantum parametric damped oscillator in an explicit form. We study the damping within the framework of the Caldirola–Kanai model and chose the parametric excitation in the form of a very short pulse simulated by a δ-kick of frequency; the squeezing phenomenon is reviewed for both models. The cases of strong and weak damping are investigated.     

Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.     

Bounds on isocurvature perturbations from cosmic microwave background and large scale structure data

We obtain very stringent bounds on the possible cold dark matter, baryon, and neutrino isocurvature contributions to the primordial fluctuations in the Universe, using recent cosmic microwave background and large scale structure data. Neglecting the possible effects of spatial curvature, tensor perturbations, and reionization, we perform a Bayesian likelihood analysis with nine free parameters, and find that the amplitude of the isocurvature component cannot be larger than about 31% for the cold dark matter mode, 91% for the baryon mode, 76% for the neutrino density mode, and 60% for the neutrino velocity mode, at 2sigma, for uncorrelated models. For correlated adiabatic and isocurvature components, the fraction could be slightly larger. However, the cross-correlation coefficient is strongly constrained, and maximally correlated/anticorrelated models are disfavored. This puts strong bounds on the curvaton model.     

GLSMs for partial flag manifolds

In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to realizations of tangent bundles and other aspects pertinent to (0, 2) models. Second, we review constructions of Calabi–Yau complete intersections within such flag manifolds, and properties of the gauged linear sigma models. We discuss a number of examples of nonabelian GLSMs in which the Kähler phases are not birational, and in which at least one phase is realized in some fashion other than as a complete intersection, extending previous work of Hori–Tong. We also review an example of an abelian GLSM exhibiting the same phenomenon. We tentatively identify the mathematical relationship between such non-birational phases, as examples of Kuznetsov’s homological projective duality. Finally, we discuss linear sigma model moduli spaces in these gauged linear sigma models. We argue that the moduli spaces being realized physically by these GLSMs are precisely Quot and hyperquot schemes, as one would expect mathematically.     

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.     

Classical integrability of two-dimensional non-linear sigma models

The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature relation. Some new integrable two-dimensional sigma models are then presented.     

A note on a local effect at the Schwarzschild sphere

Passage of the Schwarzschild radius is shown to be locally measurable by a sign change in a certain scalar. In the Kerr solution this scalar changes sign at the stationary limit. This is an example of the use of a coordinate-invariant method, based on the curvature tensor and a finite number of its covariant derivatives, for investigating gravitational fields.     

Singularity formation on a fluid interface during the Kelvin-Helmholtz instability development

The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small interface angle approximation (gravity and capillary forces are neglected) admit exact solutions in the implicit form. The analysis of these solutions shows that, in the general case, weak root singularities are formed on the interface in a finite time for which the curvature becomes infinite, while the slope angles remain small. For Atwood numbers close to unity in absolute values, the surface curvature has a definite sign correlated with the boundary deformation directed towards the light fluid. For the fluids with comparable densities, the curvature changes its sign in a singular point. In the particular case of the fluids with equal densities, the obtained results are consistent with those obtained by Moore based on the Birkhoff-Rott equation analysis.     

Effect of thermal undulations on the bending elasticity and spontaneous curvature of fluid membranes

We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its fluctuations, recently derived for spherical shapes, is recovered for cylindrical curvature. Employing curvilinear coordinates, we then discuss stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian curvature is not renormalized in the presence of fluctuations, and show for the first time that any spontaneous curvature also remains unchanged. Received 19 April 1999 and in Received in final form 7 January 2000     

Weak Gravity Conjecture and Holographic Dark Energy Model with Interaction and Spatial Curvature

In the paper, we apply the weak gravity conjecture to the holographic quintessence model of dark energy. Three different holographic dark energy models are considered: without the interaction in the non-flat universe; with interaction in the flat universe; with interaction in the non-flat universe. We find that
only in the models with the spatial curvature and interaction term proportional to the energy density of matter, it is possible for the weak gravity conjecture to be satisfied. And it seems that the weak gravity conjecture favors an open universe and the decaying of matter into dark energy.     

Coherent control of light shifts in an atomic system: modulation of the medium gain

A sequence of two femtosecond coherent pulses--a strong pi-polarized pulse and a weak sigma-polarized pulse--excite the S1/2-P1/2 transition of atomic rubidium in an optically dense vapor. The sigma pulse induces transitions between the adiabatic states with a coupling strength that is different for identically and oppositely light-shifted coupled states, and that can be modified by tuning the relative phase between the pulses. An efficient control of the medium gain for the sigma pulse is experimentally demonstrated. It is shown to be the result of interference between the absorption and the stimulated emission paths for sigma photons.     

Notes on holographic superconductor models with the nonlinear electrodynamics

We investigate systematically the effect of the nonlinear correction to the usual Maxwell electrodynamics on the holographic dual models in the backgrounds of AdS black hole and AdS soliton. Considering three types of typical nonlinear electrodynamics, we observe that in the black hole background the higher nonlinear electrodynamics correction makes the condensation harder to form and changes the expected relation in the gap frequency, which is similar to that caused by the curvature correction. However, in strong contrast to the influence of the curvature correction, we find that in the AdS soliton background the nonlinear electrodynamics correction will not affect the properties of the holographic superconductor and insulator phase transitions, which may be a quite general feature for the s-wave holographic superconductor/insulator system.     

Cosmological classicalization: maintaining unitarity under relevant deformations of the Einstein-Hilbert action

Generic relevant deformations of Einstein's gravity theory contain additional degrees of freedom that have a multifaceted stabilization dynamics on curved spacetimes. We show that these relevant degrees of freedom are self-protected against unitarity violations by the formation of classical field lumps that eventually merge to a new background geometry. The transition is heralded by the massive decay of the original vacuum and evolves through a strong coupling regime. This process fits in the recently proposed classicalization mechanism and extends it further to free field dynamics on curved backgrounds.     

Small 51V chemical shift anisotropy for LaVO4 from MQMAS and MAS NMR spectroscopy

51V MQMAS NMR of the triple-quantum transitions is shown to be particularly useful in the determination of the sign and magnitude of the chemical shift anisotropy (CSA) parameter delta(sigma)(= delta(iso)-delta(zz)) along with the asymmetry parameter (eta(sigma)) for a vanadium environment with a small CSA and a rather strong quadrupole coupling. This is demonstrated for the orthovanadate LaVO(4) for which 51V magic-angle spinning (MAS) NMR of the central and satellite transitions at 14.1T gives precise values for the quadrupole coupling parameters, however, an ambiguous sign for delta(sigma). The CSA parameters are reliably obtained from analysis of the spinning sidebands observed in a 51V triple-quantum MAS experiment. Combining these data with least-squares analysis of the manifold of spinning sidebands in the single-pulse MAS NMR spectrum results in a precise determination of the magnitudes and relative orientation of the 51V quadrupole coupling and CSA tensors for LaVO(4).     

On the geometry of classically integrable two-dimensional non-linear sigma models

A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

规范场静态解的稳定性

对有规范条件或约束的非线性理论,研究了其驻点的Hessian形式.指出了规范场的经典解的稳定性由包含拉格朗日乘子贡献的有效拉氏量的二阶变分决定.