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1.
We construct a natural L2-metric on the perturbed Seiberg–Witten moduli spaces Mμ+ of a compact 4-manifold M, and we study the resulting Riemannian geometry of Mμ+. We derive a formula which expresses the sectional curvature of Mμ+ in terms of the Green operators of the deformation complex of the Seiberg–Witten equations. In case M is simply connected, we construct a Riemannian metric on the Seiberg–Witten principal U(1) bundle P→Mμ+ such that the bundle projection becomes a Riemannian submersion. On a Kähler surface M, the L2-metric on Mμ+ coincides with the natural Kähler metric on moduli spaces of vortices. 相似文献
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We consider a Schrödinger-type differential expression HV=∇∗∇+V, where ∇ is a Hermitian connection on a Hermitian vector bundle E over a complete Riemannian manifold (M,g) with metric g and positive smooth measure dμ, and V is a locally integrable section of the bundle of endomorphisms of E. We give a sufficient condition for m-accretivity of a realization of HV in L2(E). 相似文献
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Bi doped lanthanum manganites with the chemical composition of La0.67−xBixCa0.33MnO3 (x=0, 0.05, 0.1, 0.2) were prepared by the standard solid-state process. The Curie temperatures were measured to be 267 K for x=0, 248 K for x=0.05, 244 K for x=0.1 and 229 K for x=0.2 samples. It was found that the maximum value of the magnetic entropy change ∣ΔSm∣ has reached the highest value of 6.08 J/kg K at 3 T for the composition with x=0.05. Nearly the same maximum entropy change was observed for the x=0 sample. A large decrease in the magnitude of the entropy change was observed for the x=0.2 sample. 相似文献
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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
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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
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For a simply connected, compact, simple Lie group G, the moduli space of flat G-bundles over a closed surface Σ is known to be pre-quantizable at integer levels. For non-simply connected G, however, integrality of the level is not sufficient for pre-quantization, and this paper determines the obstruction–namely a certain cohomology class in H3(G2;Z)–that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups G. 相似文献
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Suppose that the sphere Sn has initially a homogeneous distribution of mass and let G be the Lie group of orientation preserving projective diffeomorphisms of Sn. A projective motion of the sphere, that is, a smooth curve in G, is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of Sn and, more generally, examples of subgroups H of G such that a force free motion initially tangent to H remains in H for all time (in contrast with the previously studied case for conformal motions, this property does not hold for H=SOn+1). The main tool is a Riemannian metric on G, which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy. 相似文献
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We discuss space-time symmetric Hamiltonian operators of the form H=H0+igH′, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc, where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. 相似文献
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In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as a†b=Λ(N) or N=Λ−1(a†b), where N, a†, and b denote the number, creation, and annihilation operators, i.e., N is a function of quadratic product of the creation and annihilation operators, the corresponding statistical distribution is the Gentile distribution, a statistical distribution in which the maximum occupation number is an arbitrary integer. As examples, we discuss the statistical distributions corresponding to various operator relations. In particular, besides the Bose–Einstein and Fermi–Dirac cases, we discuss the statistical distributions for various schemes of intermediate statistics, especially various q-deformation schemes. Our result shows that the statistical distributions corresponding to various q-deformation schemes are various Gentile distributions with different maximum occupation numbers which are determined by the deformation parameter q. This result shows that the results given in much literature on the q-deformation distribution are inaccurate or incomplete. 相似文献
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Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z) in He-like atomic ions for the range of (fractional) nuclear charges Z lying between the known critical value Zc=0.911 at which I(Z) tends to zero and Z=2. They showed that it is possible to fit I(Z) to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of Zc for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z) for these series. 相似文献
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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
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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
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The setting is an ergodic dynamical system (X,μ) whose points are themselves uniformly discrete point sets Λ in some space Rd and whose group action is that of translation of these point sets by the vectors of Rd. Steven Dworkin’s argument relates the diffraction of the typical point sets comprising X to the dynamical spectrum of X. In this paper we look more deeply at this relationship, particularly in the context of point processes. 相似文献
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First principles calculations based on density functional theory have been employed to study the electronic, magnetic and optical properties of Co3O4 in a cubic normal spinel structure. Exchange and correlation effects between electrons were treated by a B3PW91 hybrid functional, which produced better results than others scheme, such as GGA+U or PBE0 hybrid functionals or mBJ semilocal potential. The work focuses on clarifying the nature of the optical absorption bands, which have motivated various theoretical and experimental works in the literature. The calculated optical absorption spectrum was compared with available experimental data. On the basis of this calculated electronic and magnetic structure, the optical absorption peaks (theoretical and experimental) could be satisfactorily explained in terms of d3d charge transfer transitions between both CO2+→CO2+ and CO3+→CO3+ ions. The calculations also predicted that the crystal field splittings at both octahedral and tetrahedral sites in the Co3O4 compound are of the same magnitude. 相似文献
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We discuss three Hamiltonians, each with a central-field part H0 and a PT-symmetric perturbation igz. When H0 is the isotropic Harmonic oscillator the spectrum is real for all g because H is isospectral to H0+g2/2. When H0 is the Hydrogen atom then infinitely many eigenvalues are complex for all g. If the potential in H0 is linear in the radial variable r then the spectrum of H exhibits real eigenvalues for 0<g<gc and a PT phase transition at gc. 相似文献
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