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Using geometrical and algebraic ideas, we study tunnel eigenvalue asymptotics and tunnel bilocalization of eigenstates for certain class of operators (quantum Hamiltonians) including the case of Penning traps, well known in physical literature. For general hyperbolic traps with geometric asymmetry, we study resonance regimes which produce hyperbolic type algebras of integrals of motion. Such algebras have polynomial (non-Lie) commutation relations with creation-annihilation structure. Over this algebra, the trap asymmetry (higher-order anharmonic terms near the equilibrium) determines a pendulum-like Hamiltonian in action-angle coordinates. The symmetry breaking term generates a tunneling pseudoparticle (closed instanton). We study the instanton action and the corresponding spectral splitting.  相似文献   

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We analyze the behavior of the high-energy scattering amplitude in the brane-world scenario in extra dimensions. We claim that in contrast to the popular opinion based on the Kaluza-Klein approach, the differential cross section does not increase with the energy but only changes slope near the compactification scale value and then decreases, as in the four-dimensional theory. As an example, we consider quark-antiquark scattering with a one-gluon exchange in the bulk. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 103–112, April, 2006.  相似文献   

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We analyze the radial symmetry of extremals for a class of interpolation inequalities known as Caffarelli?CKohn?CNirenberg inequalities, and for a class of weighted logarithmic Hardy inequalities which appear as limiting cases of the first ones. In both classes we show that there exists a continuous surface that splits the set of admissible parameters into a region where extremals are symmetric and a region where symmetry breaking occurs. In previous results, the symmetry breaking region was identified by showing the linear instability of the radial extremals. Here we prove that symmetry can be broken even within the set of parameters where radial extremals correspond to local minima for the variational problem associated with the inequality. For interpolation inequalities, such a symmetry breaking phenomenon is entirely new.  相似文献   

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We show that an algebra with a non-nilpotent Lie group of automorphisms or “symmetries” (e.g., smooth functions on a manifold with such a group of diffeomorphisms) may generally be deformed (in the function case, “quantized”) in such a way that only a proper subgroup of the original group acts. This symmetry breaking is a consequence of the existence of certain “universal deformation formulas” which are elements, independent of the original algebra, in the tensor algebra of the enveloping algebra of the Lie algebra of the group.  相似文献   

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A non-symmetric reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q and primitive central character twisted by the ?-th Hecke eigenvalue as a twisted mixed moment of automorphic L-functions of level ? and trivial central character. As an application, uniform subconvexity bounds for L-functions in the level and the eigenvalue aspect are derived.  相似文献   

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We consider the phenomenon of forced symmetry breaking in a symmetric Hamiltonian system on a symplectic manifold. In particular we study the persistence of an initial relative equilibrium subjected to this forced symmetry breaking. We see that, under certain nondegeneracy conditions, an estimate can be made on the number of bifurcating relative equilibria. To cite this article: F. Grabsi et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).  相似文献   

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On the Grushin operator and hyperbolic symmetry   总被引:3,自引:0,他引:3  

Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensions using hyperbolic symmetry and conformal geometry.

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In this article, we prove that there are three positive solutions of a semilinear elliptic equation in a bounded symmetric domain t for large t>0 in which one is axially symmetric and the other two are nonaxially symmetric. Main tools are the Palais-Smale theory.  相似文献   

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The phase structure of a three-dimensional four-fermion field theory is considered. It IS shown that forg < 0 both parity and the U(N) invariance of the model are spontaneously broken. For oddN, this leads to the generation of a Chern-Simons term if the fermions interact with a gauge field.Institute of High Energy Physics, Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 1, pp. 166–171, July, 1992.  相似文献   

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In this paper, we prove explicit formulas for all Willmore surfaces of revolution and demonstrate their use in the discussion of the associated Dirichlet boundary value problems. It is shown by an explicit example that symmetric Dirichlet boundary conditions do in general not entail the symmetry of the surface. In addition, we prove a symmetry result for a subclass of Willmore surfaces satisfying symmetric Dirichlet boundary data.  相似文献   

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Perm State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 74, No. 3, pp. 463–468, March, 1988.  相似文献   

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We prove nondegeneracy of extremals for some Hardy-Sobolev-Maz'ya inequalities and present applications to scalar curvature-type problems, including the Webster scalar curvature equation in a cylindrically symmetric setting. The main theme is hyperbolic symmetry.  相似文献   

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