共查询到20条相似文献,搜索用时 31 毫秒
1.
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
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In this paper we show that for a compact minimal hypersurface M of constant scalar curvature in the unit sphere S6 with the shape operator A satisfying ‖A‖2>5, there exists an eigenvalue λ>10 of the Laplace operator of the hypersurface M such that ‖A‖2=λ−5. This gives the next discrete value of ‖A‖2 greater than 0 and 5. 相似文献
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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
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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
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We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is controlled through a probability p. These systems present a crossover, for small values of p, from random to correlated (KPZ) growth of surface roughness, which is studied through scaling arguments and Monte Carlo simulations on one- and two-dimensional substrates. We show that the crossover characteristic time t× scales with p according to t×∼p−y with y=(n+1) and that the interface width at saturation Wsat scales as Wsat∼p−δ with δ=(n+1)/2, where n is either the maximal number of broken bonds or of dislodged suspended particles. This result shows that the sets of exponents y=1 and δ=1/2 or y=2 and δ=1 found in all previous works focusing on systems with this same type of crossover are not universal. Using scaling arguments, we show that the bulk porosity P of the deposits scales as P∼py−δ for small values of p. This general scaling relation is confirmed by our numerical simulations and explains previous results present in literature. 相似文献
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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
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We investigate the geometry of the moduli space of N vortices on line bundles over a closed Riemann surface Σ of genus g>1, in the little explored situation where 1≤N<g. In the regime where the area of the surface is just large enough to accommodate N vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ. For N=1, we show that the metric on the moduli space converges to a natural Bergman metric on Σ. When N>1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics. 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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A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞ and infinite equation of state parameter, w→∞. During evolution it subsequently passes through the stiff fluid era, q=2, w=1, the radiation dominated era, q=1, w=1/3 and the matter dominated era, q=1/2, w=0. Finally, deceleration halts, q=0, w=−1/3, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1, w→−1. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1) the model. 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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We study the oil displacement and production behavior in an isothermal thin layered reservoir model subjected to water flooding. We use the CMG’s (Computer Modelling Group ) numerical simulators to solve mass balance equations. The influences of the viscosity ratio (m≡μoil/μwater) and the inter-well (injector-producer) distance r on the oil production rate C(t) and the breakthrough time tbr are investigated. Two types of reservoir configuration are used, namely one with random porosities and another with a percolation cluster structure. We observe that the breakthrough time follows a power-law of m and r, tbr∝rαmβ, with α=1.8 and β=−0.25 for the random porosity type, and α=1.0 and β=−0.2 for the percolation cluster type. Moreover, our results indicate that the oil production rate is a power law of time. In the percolation cluster type of reservoir, we observe that P(t)∝tγ, with γ=−1.81, where P(t) is the time derivative of C(t). The curves related to different values of m and r may be collapsed suggesting a universal behavior for the oil production rate. 相似文献
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We develop a variational approximation to the entanglement entropy for scalar ?4 theory in 1+1, 2+1, and 3+1 dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+1 and 2+1 dimensions, the entanglement entropy of ?4 theory as a function of coupling is monotonically decreasing and convex. While ?4 theory with positive bare coupling in 3+1 dimensions is thought to lead to a trivial free theory, we analyze a version of ?4 with infinitesimal negative bare coupling, an asymptotically free theory known as precarious ?4 theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious ?4 theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling. 相似文献
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A curve α immersed in the three-dimensional sphere S3 is said to be a Bertrand curve if there exists another curve β and a one-to-one correspondence between α and β such that both curves have common principal normal geodesics at corresponding points. The curves α and β are said to be a pair of Bertrand curves in S3. One of our main results is a sort of theorem for Bertrand curves in S3 which formally agrees with the classical one: “Bertrand curves in S3 correspond to curves for which there exist two constants λ≠0 and μ such that λκ+μτ=1”, where κ and τ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S3 as the only twisted curves in S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3 and (1,3)-Bertrand curves in R4. 相似文献
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In this paper, we try to propose a toy model, which follows the majority rule with the Fermi function, to uncover the role of the heterogeneous interaction between individuals in opinion formation. In order to do this, we define the impact factor IFi, says individual i, as the exponential function of its connectivity ki with the tunable parameter β. β also shows the public information that can be collected by individuals in the system. We realize our model in scale-free networks with mean connectivity 〈k〉. We find that much more public information (β>β2) and less public information (β<β1) cannot let either of the two opinions be the majority during the opinion formation. Furthermore, β1 is a constant and equal to −0.76(±0.04), and β2 decreases as a power-law function of the mean connectivity 〈k〉 of the network. Our work can provide some perspectives and tools to understand the diversity of opinion in social networks. 相似文献
18.
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
19.
Let M be a connected compact quantizable Kähler manifold equipped with a Hamiltonian action of a connected compact Lie group G. Let M//G=?−1(0)/G=M0 be the symplectic quotient at value 0 of the moment map ?. The space M0 may in general not be smooth. It is known that, as vector spaces, there is a natural isomorphism between the quantum Hilbert space over M0 and the G-invariant subspace of the quantum Hilbert space over M. In this paper, without any regularity assumption on the quotient M0, we discuss the relation between the inner products of these two quantum Hilbert spaces under the above natural isomorphism; we establish asymptotic unitarity to leading order in Planck’s constant of a modified map of the above isomorphism under a “metaplectic correction” of the two quantum Hilbert spaces. 相似文献