1,721,015 research outputs found
Identities and exponential inequalities for transfer matrices
Full text linkRigorous results are presented for the decay of eigenvalues of transfer matrices, based on the theorem by Demko Moss and Smit on the decay of matrix elements for the inverse of a band matrix
An introduction to functional methods for many-body Green functions
Full text linkThis is an introduction to the coherent-state representation of the generating functional of correlators for fermions. Ward's identities, Dyson's equations, and the effective potential are discussed for systems of electrons with Coulomb interaction
Determinants of block tridiagonal matrices
Full text linkAbstractAn identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it)
On conformally recurrent manifolds of dimension greater than 4
No full textConformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni–Nomizu product. If the square of the Weyl tensor is non-zero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak’s theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If the square of the Weyl tensor is non-zero, the manifold is decomposable. A null recurrence vector makes the Weyl tensor of algebraic type IId or higher in the Bel–Debever–Ortaggio classification, while a time-like recurrence vector makes the Weyl tensor purely electric
Riemann compatible tensors
Full text linkDerdzinski and Shen's theorem on the restrictions on the Riemann tensor imposed by the existence of a Codazzi tensor holds more generally when a Riemann compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity for a new "Codazzi deviation tensor" with a geometric significance, The above general properties are studied, with their implications on Pontryagin forms. Examples are given of manifolds with Riemann compatible tensors, in particular those generated by geodesic mappings. Compatibility is extended to generalized curvature tensors, with an application to Weyl's tensor and general relativity
Weyl compatible tensors
Full text linkWe introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications. In particular, it is shown that the existence of a Weyl compatible vector implies that the Weyl tensor is alge- braically special, and it is a necessary and sufficient condition for the magnetic part to vanish. Some theorems (Derdzin ́ski and Shen [11], Hall [15]) are extended to the broader hypothesis of Weyl or Riemann compatibility. Weyl compatibility includes con- ditions that were investigated in the literature of general relativity (as in McIntosh et al. [16, 17]). A simple example of Weyl compatible tensor is the Ricci tensor of an hypersurface in a manifold with constant curvature
Random antagonistic matrices
Full text linkThe ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries A(ij) and A(ji) i are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology
Enumeration of many-body skeleton diagrams
No full textThe many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for self-energy, polarization, propagator, effective potential, and vertex function, dressed (skeleton) Feynman diagrams are enumerated. Such diagram counts provide useful simple checks for extensions of the theory for future realistic simulations
Many-body method for infinite nonperiodic systems
Full text linkA method to implement the many-body Green function formalism in the GW approximation for infinite nonperiodic systems is presented. It is suitable to treat systems of known "asymptotic" properties which enter as boundary conditions, while the effects of the lower symmetry are restricted to regions of finite volume. For example, it can be applied to surfaces or localized impurities. We illustrate the method with a study of the surface of semi-infinite jellium. We report the dielectric function, the effective potential, and the electronic self-energy discussing the effects produced by the screening and by the charge density profile near the surface
Simple conformally recurrent space-times are conformally recurrent pp-waves
No full textWe show that in dimension n >3 the class of simple conformally recurrent space-times coincides with the class of conformally recurrent pp-waves
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