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1.
A complex symplectic structure on a Lie algebra hh is an integrable complex structure JJ with a closed non-degenerate (2,0)(2,0)-form. It is determined by JJ and the real part ΩΩ of the (2,0)(2,0)-form. Suppose that hh is a semi-direct product g?Vg?V, and both gg and VV are Lagrangian with respect to ΩΩ and totally real with respect to JJ. This note shows that g?Vg?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of ΩΩ and JJ are isomorphic.  相似文献   

2.
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/n1/n correction for the perpendicular correlation-length exponent νL2νL2 and hence several related thermal exponents to order O(1/n)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/2d?=4+m/2 for generic m∈[0,d]m[0,d]. Analytical results are given for the special case d=4d=4, m=1m=1. For uniaxial Lifshitz points in three dimensions, 1/n1/n coefficients are calculated numerically. The estimates of critical exponents at d=3d=3, m=1m=1 and n=3n=3 are discussed.  相似文献   

3.
Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V   are almost the right triangles with α≈90°α90°. 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°?α1.1°). Both ? and α   are stable against the renormalizaton-group evolution from the electroweak scale MZMZ to a superhigh energy scale MXMX or vice versa, and thus it is impossible to obtain α=90°α=90° at MZMZ from ?=90°?=90° at MXMX. We conjecture that there might also exist a maximal CP-violating phase φ≈90°φ90° 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||Vub| and |Ve3||Ve3|.  相似文献   

4.
5.
We discuss three Hamiltonians, each with a central-field part H0H0 and a PT-symmetric perturbation igzigz. When H0H0 is the isotropic Harmonic oscillator the spectrum is real for all gg because HH is isospectral to H0+g2/2H0+g2/2. When H0H0 is the Hydrogen atom then infinitely many eigenvalues are complex for all gg. If the potential in H0H0 is linear in the radial variable rr then the spectrum of HH exhibits real eigenvalues for 0<g<gc0<g<gc and a PT phase transition at gcgc.  相似文献   

6.
Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0T=0 1D insulator the charge stiffness D(T)D(T) vanishes for T>0T>0 and finite values of the on-site repulsion UU 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 TT and U>0U>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=0U=0 and vanishes for U>0U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0U=Uc=0 for all finite temperatures T>0T>0. (At T=0T=0 such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the ηη-spin SU(2)SU(2) symmetry with the hidden U(1)U(1) symmetry beyond SO(4)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   

7.
We develop a variational approximation to the entanglement entropy for scalar ?4?4 theory in 1+11+1, 2+12+1, and 3+13+1 dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+11+1 and 2+12+1 dimensions, the entanglement entropy of ?4?4 theory as a function of coupling is monotonically decreasing and convex. While ?4?4 theory with positive bare coupling in 3+13+1 dimensions is thought to lead to a trivial free theory, we analyze a version of ?4?4 with infinitesimal negative bare coupling, an asymptotically free theory known as precarious  ?4?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?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   

8.
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)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 nn dimensional vector space which we call HnHn. The ZpZp gauge particles act on the vertex particles and thus HnHn can be thought of as a C(Zp)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 nn and pp, though we believe this feature holds for all n>pn>p. We will see that non-Abelian anyons of the quantum double of C(S3)C(S3) are obtained as part of the vertex excitations of the model with n=6n=6 and p=3p=3. Ising anyons are obtained in the model with n=4n=4 and p=2p=2. The n=3n=3 and p=2p=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 ZpZp. This makes them possible candidates for realizing quantum computation.  相似文献   

9.
We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field HH and transverse magnetic field ΩΩ. Using the effective-field theory (EFT) with correlation in cluster with N=1N=1 spin we calculate the thermodynamic properties as a function of temperature with values HH and ΩΩ fixed. The model consists of ferromagnetic interaction JxJx in the xx direction and antiferromagnetic interaction JyJy in the yy direction, and it is found that for H/Jy∈[0,2]H/Jy[0,2] the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=Jx/Jy=1λ=Jx/Jy=1 (isotropic square lattice).  相似文献   

10.
The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (TT), frequency (ww), Onsager coefficient (γγ) and external magnetic field (HH) near the second-order (Tc)(Tc) and first-order (Tt)(Tt) phase transition temperatures are examined for given coordination numbers qq on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)(α). Our investigations revealed that only one peak is obtained near TtTt and three peaks are found near TcTc when the Onsager coefficient is varied at a given constant frequency for q=3q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4q=3,4 and 6 near TcTc. The sound attenuation peaks are observed near TtTt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.  相似文献   

11.
We discuss space-time symmetric Hamiltonian operators of the form H=H0+igHH=H0+igH, where H0H0 is Hermitian and gg real. H0H0 is invariant under the unitary operations of a point group GG while HH is invariant under transformation by elements of a subgroup GG of GG. If GG exhibits irreducible representations of dimension greater than unity, then it is possible that HH has complex eigenvalues for sufficiently small nonzero values of gg. In the particular case that HH is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc0<g<gc, where gcgc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether HH may exhibit real or complex eigenvalues for g>0g>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   

12.
Bi doped lanthanum manganites with the chemical composition of La0.67−xBixCa0.33MnO3 (x=0x=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=0x=0, 248 K for x=0.05x=0.05, 244 K for x=0.1x=0.1 and 229 K for x=0.2x=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=0.05x=0.05. Nearly the same maximum entropy change was observed for the x=0x=0 sample. A large decrease in the magnitude of the entropy change was observed for the x=0.2x=0.2 sample.  相似文献   

13.
A curve αα immersed in the three-dimensional sphere S3S3 is said to be a Bertrand curve if there exists another curve ββ and a one-to-one correspondence between αα and ββ such that both curves have common principal normal geodesics at corresponding points. The curves αα and ββ are said to be a pair of Bertrand curves in S3S3. One of our main results is a sort of theorem for Bertrand curves in S3S3 which formally agrees with the classical one: “Bertrand curves in S3S3 correspond to curves for which there exist two constants λ≠0λ0 and μμ such that λκ+μτ=1λκ+μτ=1”, where κκ and ττ 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 S3S3 as the only twisted curves in S3S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3S3 and (1,3)-Bertrand curves in R4R4.  相似文献   

14.
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 VkVk to a decreasing family of kk foliations FiFi on a manifold MM. We have shown that there exists a (1,1)(1,1) tensor JJ of VkVk such that Jk≠0Jk0, Jk+1=0Jk+1=0 and we defined by LJ(Vk)LJ(Vk) the Lie Algebra of vector fields XX on VkVk such that, for each vector field YY on VkVk, [X,JY]=J[X,Y][X,JY]=J[X,Y].  相似文献   

15.
We consider a Schrödinger differential expression L=ΔA+qL=ΔA+q on a complete Riemannian manifold (M,g)(M,g) with metric gg, where ΔAΔA is the magnetic Laplacian on MM and q≥0q0 is a locally square integrable function on MM. In the terminology of W.N. Everitt and M. Giertz, the differential expression LL is said to be separated in L2(M)L2(M) if for all u∈L2(M)uL2(M) such that Lu∈L2(M)LuL2(M), we have qu∈L2(M)quL2(M). We give sufficient conditions for LL to be separated in L2(M)L2(M).  相似文献   

16.
We present new axially symmetric half-monopole configuration of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge 2π/e2π/e which is half the magnetic charge of a Cho–Maison monopole. The electromagnetic gauge potential is singular along the negative zz-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant λ1/2λ1/2 at sin2θW=0.2312sin2θW=0.2312. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin r=0r=0 and lying along the negative zz-axis. In the SU(2) ’t Hooft magnetic field, it is a point magnetic charge located at r=0r=0. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant λ1/2λ1/2 at sin2θW=0.2312sin2θW=0.2312.  相似文献   

17.
We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes mm “ambassador” nodes and ll of each ambassador’s descendants where mm and ll are random variables selected from any choice of distributions plpl and qmqm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant mm and the number of selected descendants from each ambassador is the constant ll, the power-law exponent is (2l+1)/l(2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of ll and mm. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically.  相似文献   

18.
In this paper we show that for a compact minimal hypersurface MM of constant scalar curvature in the unit sphere S6S6 with the shape operator AA satisfying ‖A‖2>5A2>5, there exists an eigenvalue λ>10λ>10 of the Laplace operator of the hypersurface MM such that ‖A‖2=λ−5A2=λ5. This gives the next discrete value of ‖A‖2A2 greater than 0 and 5.  相似文献   

19.
We show that pQCD factorization incorporated with pre-hadronization energy-loss effect naturally leads to flatness of the nuclear modification factor RAARAA for produced hadrons at high transverse momentum pTpT. We consider two possible scenarios for the pre-hadronization: In scenario 1, the produced gluon propagates through dense QCD medium and loses energy. In scenario 2, all gluons first decay to quark–antiquark pairs and then each pair loses energy as propagating through the medium. We show that the estimates of the energy-loss in these two different models lead to very close values and is able to explain the suppression of high-pTpT hadrons in nucleus–nucleus collisions at RHIC. We show that the onset of the flatness of RAARAA for the produced hadron in central collisions at midrapidity is about pT≈15pT15 and 25 GeV at RHIC and the LHC energies, respectively. We show that the smallness (RAA<0.5RAA<0.5 ) and the high-pTpT flatness of RAARAA obtained from the kTkT factorization supplemented with the Balitsky–Kovchegov (BK) equation is rather generic and it does not strongly depend on the details of the BK solutions. We show that energy-loss effect reduces the nuclear modification factor obtained from the kTkT factorization about 30–50% at moderate pTpT.  相似文献   

20.
We analyse the phase diagram of a quantum mean spherical model in terms of the temperature TT, a quantum parameter gg, and the ratio p=−J2/J1p=J2/J1, where J1>0J1>0 refers to ferromagnetic interactions between first-neighbour sites along the dd directions of a hypercubic lattice, and J2<0J2<0 is associated with competing antiferromagnetic interactions between second neighbours along m≤dmd 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=0g=0 space, with a Lifshitz point at p=1/4p=1/4, for d>2d>2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0T=0 phase diagram, there is a critical border, gc=gc(p)gc=gc(p) for d≥2d2, with a singularity at the Lifshitz point if d<(m+4)/2d<(m+4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4p=1/4.  相似文献   

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