共查询到20条相似文献,搜索用时 46 毫秒
1.
We consider a Schrödinger differential expression L=ΔA+q on a complete Riemannian manifold (M,g) with metric g, where ΔA is the magnetic Laplacian on M and q≥0 is a locally square integrable function on M. In the terminology of W.N. Everitt and M. Giertz, the differential expression L is said to be separated in L2(M) if for all u∈L2(M) such that Lu∈L2(M), we have qu∈L2(M). We give sufficient conditions for L to be separated in L2(M). 相似文献
3.
In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle Vk to a decreasing family of k foliations Fi on a manifold M. We have shown that there exists a (1,1) tensor J of Vk such that Jk≠0, Jk+1=0 and we defined by LJ(Vk) the Lie Algebra of vector fields X on Vk such that, for each vector field Y on Vk, [X,JY]=J[X,Y]. 相似文献
4.
A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
5.
Let u be a function of n independent variables x1,…,xn, and let U=(uij) be the Hessian matrix of u. The symplectic Monge–Ampère equation is defined as a linear relation among all possible minors of U. Particular examples include the equation detU=1 governing improper affine spheres and the so-called heavenly equation, u13u24−u23u14=1, describing self-dual Ricci-flat 4-manifolds. In this paper we classify integrable symplectic Monge–Ampère equations in four dimensions (for n=3 the integrability of such equations is known to be equivalent to their linearisability). This problem can be reformulated geometrically as the classification of ‘maximally singular’ hyperplane sections of the Plücker embedding of the Lagrangian Grassmannian. We formulate a conjecture that any integrable equation of the form F(uij)=0 in more than three dimensions is necessarily of the symplectic Monge–Ampère type. 相似文献
6.
We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Zp) gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n dimensional vector space which we call Hn. The Zp gauge particles act on the vertex particles and thus Hn can be thought of as a C(Zp) module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n and p, though we believe this feature holds for all n>p. We will see that non-Abelian anyons of the quantum double of C(S3) are obtained as part of the vertex excitations of the model with n=6 and p=3. Ising anyons are obtained in the model with n=4 and p=2. The n=3 and p=2 case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Zp. This makes them possible candidates for realizing quantum computation. 相似文献
7.
Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0 1D insulator the charge stiffness D(T) vanishes for T>0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0 and vanishes for U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0 for all finite temperatures T>0. (At T=0 such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model. 相似文献
8.
Let (M,g) be a noncompact complete Bach-flat manifold with positive Yamabe constant. We prove that (M,g) is flat if (M,g) has zero scalar curvature and sufficiently small L2 bound of curvature tensor. When (M,g) has nonconstant scalar curvature, we prove that (M,g) is conformal to the flat space if (M,g) has sufficiently small L2 bound of curvature tensor and L4/3 bound of scalar curvature. 相似文献
9.
J. Lehmann-Lejeune in [J. Lehmann-Lejeune, Cohomologies sur le fibré transverse à un feuilletage, C.R.A.S. Paris 295 (1982), 495–498] defined on the transverse bundle V to a foliation on a manifold M, a zero-deformable structure J such that J2=0 and for every pair of vector fieldsX,Y on M: [JX,JY]−J[JX,Y]−J[X,JY]+J2[X,Y]=0. For every open set Ω of V, J. Lehmann-Lejeune studied the Lie Algebra LJ(Ω) of vector fields X defined on Ω such that the Lie derivative L(X)J is equal to zero i.e., for each vector field Yon Ω: [X,JY]=J[X,Y] and showed that for every vector field X on Ω such thatX∈KerJ, we can write X=∑[Y,Z] where ∑is a finite sum and Y,Z belongs to LJ(Ω)∩(KerJ|Ω). 相似文献
10.
11.
Let M be a connected complex projective manifold such that c1(T(1,0)M)=0. If M admits a holomorphic Cartan geometry, then we show that M is holomorphically covered by an abelian variety. 相似文献
12.
13.
14.
Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H2+ of the quantum numbers (n,m,Λ,±) with n=m=0 at Λ=0,1,2, with n=1, m=0 and n=0, m=1 at Λ=0 of both parities are explored for all interproton distances R. For all these states this approximation provides the relative accuracy ?10−5 (not less than 5 s.d.) locally, for any real coordinate x in eigenfunctions, when for total energy E(R) it gives 10-11 s.d. for R∈[0,50] a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1 is calculated with not less than 6 s.d. A dramatic dip in the E1 oscillator strength f1sσg−3pσu at R∼Req is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±) (or, equivalently, 1sσg and 2pσu states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσg and 2pσu potential curves is approximated with modified Pade Re−R[Pade(8/7)](R) with not less than 4-5 figures at R∈[0,40] a.u. Sum of potential curves E1sσg+E2pσu is approximated by Pade 1/R[Pade(5/8)](R) in R∈[0,40] a.u. with not less than 3-4 figures. 相似文献
15.
We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant mth mean curvature. By using Otsuki’s idea, we obtain the global classification result. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Lorentz–Minkowski (n+1)-spaces (n≥3) of nonzero constant mth mean curvature (m≤n−1) with two distinct principal curvatures λ and μ satisfying inf(λ−μ)2>0 are the hyperbolic cylinders. We also obtain a global characterization for hyperbolic cylinder Hn−1(c)×R in terms of square length of the second fundamental form. 相似文献
16.
The evolution of the scoring performance of Rugby Union players is investigated over the seven rugby world cups (RWC) that took place from 1987 to 2011, and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995. The distribution of the points scored by individual players, Ps, ranked in order of performance were well described by the simplified canonical law Ps∝(r+?)−α, where r is the rank, and ? and α are the parameters of the distribution. The parameter α did not significantly change from 1987 to 2007 (α=0.92±0.03), indicating a negligible effect of professionalism on players’ scoring performance. In contrast, the parameter ? significantly increased from ?=1.32 for 1987 RWC, ?=2.30 for 1999 to 2003 RWC and ?=5.60 for 2007 RWC, suggesting a progressive decrease in the relative performance of the best players. Finally, the sharp decreases observed in both α(α=0.38) and ?(?=0.70) in the 2011 RWC indicate a more even distribution of the performance of individuals among scorers, compared to the more heterogeneous distributions observed from 1987 to 2007, and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players. Note that neither α nor ? significantly correlate with traditional performance indicators such as the number of points scored by the best players, the number of games played by the best players, the number of points scored by the team of the best players or the total number of points scored over each RWC. This indicates that the dynamics of the scoring performance of Rugby Union players is influenced by hidden processes hitherto inaccessible through standard performance metrics; this suggests that players’ scoring performance is connected to ubiquitous phenomena such as anomalous diffusion. 相似文献
17.
We continue the study of U(1) vortices with cholesteric vacuum structure. A new class of solutions is found which represent global vortices of the internal spin field. These spin vortices are characterized by a non-vanishing angular dependence at spatial infinity, or winding. We show that despite the topological Z2 behavior of SO(3) windings, the topological charge of the spin vortices is of the Z type in the cholesteric. We find these solutions numerically and discuss the properties derived from their low energy effective field theory in 1+1 dimensions. 相似文献
18.
19.
We prove that if the fundamental 4-form Ω of an almost-quaternionic Hermitian manifold (M,Q,g) of dimension 4n≥8 satisfies the conformal-Killing equation, then (M,Q,g) is quaternionic-Kähler. 相似文献
20.
We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p=−J2/J1, where J1>0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J2<0 is associated with competing antiferromagnetic interactions between second neighbours along m≤d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0 space, with a Lifshitz point at p=1/4, for d>2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0 phase diagram, there is a critical border, gc=gc(p) for d≥2, with a singularity at the Lifshitz point if d<(m+4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4. 相似文献