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1.
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
2.
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
3.
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
4.
The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m -axial Lifshitz points. We derive the leading non-trivial 1/n correction for the perpendicular correlation-length exponent νL2 and hence several related thermal exponents to order O(1/n). The results are consistent with known large-n expansions for d -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d?=4+m/2 for generic m∈[0,d]. Analytical results are given for the special case d=4, m=1. For uniaxial Lifshitz points in three dimensions, 1/n coefficients are calculated numerically. The estimates of critical exponents at d=3, m=1 and n=3 are discussed. 相似文献
5.
We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order q, we first provide a generalized monogamy inequality of multi-qubit entanglement for q=2 or 3. This generalization encapsulates the multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-q entropy for 1≤q≤2 or 3≤q≤4, which also contains the multi-qubit polygamy inequality as a special case. 相似文献
6.
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
7.
The β-expansion of the Helmholtz free energy (HFE) up to order β12 of the classical XYZ model with a single-ion anisotropy term and external magnetic field is calculated and compared to the numerical solution of Joyce's [Phys. Rev. Lett. 19 (1967) 581] for the XXZ classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as kT/Jx≈0.5. The specific heat and magnetic susceptibility of the S=2 antiferromagnetic chain can be approximated by their respective classical results, within an error of 2.5%, up to kT/J≈0.8. For a vanishing external magnetic field the ferromagnetic and antiferromagnetic chains are shown to have the same classical HFE; their behaviour in a non-vanishing external magnetic field is also described. 相似文献
8.
Geometrical characterizations are given for the tensor R⋅S, where S is the Ricci tensor of a (semi-)Riemannian manifold (M,g) and R denotes the curvature operator acting on S as a derivation, and of the Ricci Tachibana tensor ∧g⋅S, where the natural metrical operator ∧g also acts as a derivation on S. As a combination, the Ricci curvatures associated with directions on M, of which the isotropy determines that M is Einstein, are extended to the Ricci curvatures of Deszcz associated with directions and planes on M, and of which the isotropy determines that M is Ricci pseudo-symmetric in the sense of Deszcz. 相似文献
9.
The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused R-matrices and K-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T−Q relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix. 相似文献
11.
Discrete nonlinear Schrödinger (DNLS) equation describes a chain of oscillators with nearest-neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to 1/l1+α with fractional α<2 and l as a distance between oscillators. This model is called αDNLS. It exhibits competition between the nonlinearity and a level of correlation between interacting far-distanced oscillators, that is defined by the value of α. We consider transition to chaos in this system as a function of α and nonlinearity. It is shown that decreasing of α with respect to nonlinearity stabilize the system. Connection of the model to the fractional generalization of the NLS (called FNLS) in the long-wave approximation is also discussed and some of the results obtained for αDNLS can be correspondingly extended to the FNLS. 相似文献
12.
Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ? and −?−1 are constructed using the technique of intertwining vectors for elliptic L-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W-operators) serve as building blocks for the elliptic R-matrix which intertwines tensor product of two L-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang–Baxter equation for this R-matrix follows from simpler equations of the star–triangle type for the W-operators. A natural graphic representation of the objects and equations involved in the construction is used. 相似文献
13.
We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with λ≥0) in a Euclidean space EN. Assume that the immersion is proper , that is, the preimage of every compact set in EN is also compact in M. Then, we prove that M is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ<0, we construct examples of biminimal submanifolds and curves. 相似文献
14.
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
15.
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
16.
The grand partition functions Z(T,B) of the Ising model on L×L triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B , are evaluated exactly for L<12 (using microcanonical transfer matrix) and approximately for L?12 (using Wang–Landau Monte Carlo algorithm). From Z(T,B), the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0 are obtained and discussed for the first time. The critical points aN(x) and the thermal scaling exponents yt(x) of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB, are estimated using the partition function zeros. 相似文献
17.
Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V are almost the right triangles with α≈90°. We highlight a very suggestive parametrization of V and show that its CP-violating phase ? is nearly equal to α (i.e., ?−α≈1.1°). Both ? and α are stable against the renormalizaton-group evolution from the electroweak scale MZ to a superhigh energy scale MX or vice versa, and thus it is impossible to obtain α=90° at MZ from ?=90° at MX. We conjecture that there might also exist a maximal CP-violating phase φ≈90° in the MNS lepton mixing matrix U. The approximate quark–lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U simply due to the smallness of |Vub| and |Ve3|. 相似文献
18.
We employ chaotic (?2 and ?4) inflation to illustrate the important role radiative corrections can play during the inflationary phase. Yukawa interactions of ? , in particular, lead to corrections of the form −κ?4ln(?/μ), where κ>0 and μ is a renormalization scale. For instance, ?4 chaotic inflation with radiative corrections looks compatible with the most recent WMAP (5 year) analysis, in sharp contrast to the tree level case. We obtain the 95% confidence limits 2.4×10−14?κ?5.7×10−14, 0.931?ns?0.958 and 0.038?r?0.205, where ns and r respectively denote the scalar spectral index and scalar to tensor ratio. The limits for ?2 inflation are κ?7.7×10−15, 0.929?ns?0.966 and 0.023?r?0.135. The next round of precision experiments should provide a more stringent test of realistic chaotic ?2 and ?4 inflation. 相似文献
19.
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