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1.
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
2.
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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T. Rożek D. Grzonka H.-H. Adam A. Budzanowski R. Czyżykiewicz M. Janusz L. Jarczyk B. Kamys A. Khoukaz K. Kilian P. Klaja P. Kowina P. Moskal W. Oelert C. Piskor-Ignatowicz J. Przerwa J. Ritman T. Sefzick M. Siemaszko J. Smyrski A. Täschner P. Winter M. Wolke P. Wüstner Z. Zhang W. Zipper 《Physics letters. [Part B]》2006
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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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An exact incompressible quantum liquid is constructed at the filling factor 1/m2 in the square lattice. It supports deconfined fractionally charged excitation. At the filling factor 1/m2, the excitation has fractional charge e/m2, where e is the electric charge. This model can be easily generalized to the n-dimensional square lattice (integer lattice), where the charge of excitations becomes e/mn. 相似文献
8.
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
9.
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
10.
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
11.
The deviation δQW of the weak charge from its standard model prediction due to the mixing of the W boson with the charged bilepton Y as well as of the Z boson with the neutral Z′ and the real part of the non-Hermitian neutral bilepton X in the economical 3–3–1 model is established. Additional contributions to the usual δQW expression in the extra U(1) models and the left–right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3–3–1 models and give the limit on mass of the Z′ boson, the Z–Z′ and W–Y mixing angles with the more appropriate values: MZ′>564 GeV, −0.018<sinφ<0 and |sinθ|<0.043. 相似文献
12.
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
13.
C.R. Hoffman T. Baumann D. Bazin J. Brown G. Christian D.H. Denby P.A. DeYoung J.E. Finck N. Frank J. Hinnefeld S. Mosby W.A. Peters W.F. Rogers A. Schiller A. Spyrou M.J. Scott S.L. Tabor M. Thoennessen P. Voss 《Physics letters. [Part B]》2009
The decay energy spectrum for neutron unbound states in 24O (Z=8, N=16) has been observed for the first time. The resonance energy of the lowest lying state, interpreted as the 2+ level, has been observed at a decay energy above 600 keV. The resulting excitation energy of the 2+ level above 4.7 MeV, supplies strong evidence that 24O is a doubly magic nucleus. The data is also consistent with the presence of a second excited state around 5.33 MeV which can be interpreted as the 1+ level. 相似文献
14.
The hadron spectrum of SU(2) lattice gauge theory with two flavours of Wilson quark is studied on an 83×16 lattice using all-to-all propagators, with particular emphasis on the dependence on quark chemical potential μ. As μ is increased from zero the diquark states with non-zero baryon number B respond as expected, while states with B=0 remain unaffected, until the onset of non-zero baryon density at μ=mπ/2. Post onset the pi-meson mass increases in accordance with chiral perturbation theory while the rho becomes lighter. In the diquark sector a Goldstone state associated with a superfluid ground state can be identified. A further consequence of superfluidity is an approximate degeneracy between mesons and baryons with the same spacetime and isospin quantum numbers. Finally we find tentative evidence for the binding of states with kaon quantum numbers within the baryonic medium. 相似文献
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M. Teresa Blázquez Marta Anguiano Fernando Arias de Saavedra Antonio M. Lallena Pedro Carpena 《Physica A》2012
The effects associated to the length of stabilograms, a measure of the time dependence of the center of pressure of an individual standing up, are analyzed. The fractal characteristics of 27 signals with a length of 214 points, each one corresponding to a different individual, are studied by using the Detrended Fluctuation Analysis technique. The properties of the complete signals are compared to those of various subsignals extracted from them. No differences have been found between the characteristic exponents found for x and y signals. The relation between the exponents of the position and velocity signals is accomplished by the 214 point signals, while subsignals with up to 212 points do not verify it. Using artificial signals with 214 points, generated for α values given, it has been demonstrated that the exponents obtained from these signals take values larger than expected for α<0.3, while the exponents of the accumulated series are smaller than expected for 0.7<α. For CoP trajectories this indicates that DFA-1 provides feasible exponents for the short τ-end region of the velocity signal and the large τ-end region of the accumulated (position) one. It has been found that the characteristic exponents vary along the series. A slightly larger persistence is found in the last part of the signal for large frequencies in the x direction. 相似文献
17.
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
18.
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
19.
To complement existing knowledge of the density matrix γF(x,y) of independent fermions for N particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y) for impenetrable bosons is given for N=2 and 3 (with the N=4 form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10. The boson momentum density is studied analytically at high momentum p , the coefficients of the p−4 and p−6 terms being tabulated for N=2–5 inclusive. Their dependence on powers of N is exhibited numerically. Finally, the functional relationship between γIB(x,y) and γF(x,y) is formally set out and illustrated. 相似文献
20.
The question of whether BPS invariants are protected in maximally supersymmetric Yang–Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants (F4) are indeed protected while the double-trace one-quarter BPS invariant (d2F4) is not protected at two loops in D=7, but is protected at three loops in D=6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected. 相似文献