Search results for "integral"
showing 10 items of 902 documents
Local correlation functional for electrons in two dimensions
2008
We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation for the pair density. Then, we introduce an ad-hoc modification which better accounts for both the long-range correlation, and the kinetic-energy contribution to the correlation energy. The resulting functional is local, and depends parametrically on the number of electrons in the system. We apply this functional to the homogeneous electron gas and to a set of two-dimensional quantum dots covering a wide range of electron densities and thus various amount…
The master two-loop two-point function. The general case
1991
Abstract We present a new calculation of the two-loop two-point function. Avoiding standard techniques such as Feynman parametrization and Wick rotation we end up with a simple double integral representation valid for arbitrary mass-cases. Numerical and analytical checks confirm our result.
Feynman graph polynomials
2010
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.
SYSTEMATICAL MULTIPARTICLE THEORY AND ITS APPLICATION TO THE FOUR-NUCLEON PROBLEM
1972
Publisher Summary This chapter discusses the systematical multiparticle theory and its application in the four-nucleon problem. The chapter describes the structure of the 2- body and 3-body equations and shows that the generalization to n particles can be accomplished in a natural way. It is a characteristic feature of this approach that the kernel of the occurring integral equations is built up by all subsystem transition operators in an explicit way. One of the important features of the 3-body theory is also achieved in the n-body formalism. This enables the application of the quasiparticle concept in a direct way. The 2-body problem is completely determined by the solution of the Lippman…
On-axis diffractional behavior of two-dimensional pupils
2010
We show that, at any Fresnel number, a suitable one-dimensional Fourier transform relates the complex-amplitude distribution along the optical axis with the zero-order circular harmonic of the amplitude transmittance of a two-dimensional diffracting screen. First, our general result is applied to recognize that any rationally nonsymmetric screen generates an axial-irradiance distribution that exhibits focal shift. In this way we identify a wide set of two-dimensional screens that produce the same focal shift as that produced by the clear circular aperture. Second, we identify several apodizers for shaping the axial-amplitude distribution. We discuss some examples for achieving high-precisio…
The Fučík spectrum for nonlocal BVP with Sturm–Liouville boundary condition
2014
Boundary value problem of the form x''=-μx++λx-, αx(0)+(1-α)x'(0)=0, ∫01 x(s)ds=0 is considered, where μ,λ∈ R and α∈ [0,1]. The explicit formulas for the spectrum of this problem are given and the spectra for some α values are constructed. Special attention is paid to the spectrum behavior at the points close to the coordinate origin.
Shapes of a gas bubble rising in the vertical Hele–Shaw cell with magnetic liquid
2005
Abstract Dynamics of the bubble rising in the vertical Hele–Shaw cell with magnetic liquid in the normal magnetic field is studied. Linear stability analysis of the circular shape is carried out. Development of the instability with respect to the lowest symmetric mode is simulated by the boundary integral equation technique.
Rotational Motion of Linear Molecules in Three Dimensions. A Path-Integral Monte Carlo Approach
1994
Abstract A path-integral Monte Carlo (PIMC) simulation method for the rotational motion of linear molecules in three dimensions is presented. The technique is applied to an H2 impurity in a static crystal-field. The resulting orientational distributions from quantum and classical simulations are obtained and discussed. The algorithm suffers from the “sign problem” of quantum simulations. However, as can be seen by comparing the low temperature simulation result to the variational solution of the Schrodinger equation, the PIMC method captures the quantum fluctuations.
On weak solutions of linear coercive integral equations in spacesL 2(X; ℋ k )
1989
Пусть (X,A, μ) - полное про странство с σ-конечно й мерой, и пусть\(\overline {\mu \times \mu } \). - замык ание меры μ×μ. Пусть далееg: X×X→C - квадратично интегрируемая функц ия по мере\(\overline {\mu \times \mu } \). Рассматривается лин ейное интегральное у равнение (слабого) типа (1) $$u(t) + A(\mathop \smallint \limits_x g(t,s)u(s)d\mu ) = f(t)\Pi .B.B\,X,$$ (1) гдеА - максимальное р асширение L k ′ (в простр анстве ХeрмандераH 1=B2к) соотв ествующего линейного (псевдодиф ференциального) опер атораL: S→S; иS обозначает класс Щварца функций Rn→-C. Уст анавливается сущест вование (слабых) решений (1) при н екотором условии коэрпитивно сти на оператор (2) $$(L\Psi )(t) = \Psi (t) + \int\…
Simplicial Wheeler-DeWitt equation in 2+1 spacetime dimensions.
1993
We introduce an equation which rue suggest to be a simplicial counterpart to the Wheeler-DeWitt equation in 2 + 1 spacetime dimensions. Our approach is based on the use of the Ashtekar variables