scholarly journals Asymptotic Behavior of the Green Function in a Solvable Field Theory

1974 ◽  
Vol 52 (2) ◽  
pp. 647-658
Author(s):  
J. Sakamoto
Keyword(s):  
Field Theory ◽  
Asymptotic Behavior ◽  
Green Function ◽  
The Green Function

Existence and global asymptotic behavior of positive solutions for superlinear fractional dirichlet problems on the half-line

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Imed Bachar ◽  
Habib Mâagli
Keyword(s):  
Asymptotic Behavior ◽  
Green Function ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Half Line ◽  
Dirichlet Problems ◽  
The Green Function

AbstractUsing estimates on the Green function and a perturbation argument, we prove the existence and uniqueness of a positive continuous solution to problem:

scholarly journals Spectra of Collective Excitations and Low-Frequency Asymptotics of Green’s Functions in Uniaxial and Biaxial Ferrimagnetics

2019 ◽  
Keyword(s):  
Asymptotic Behavior ◽  
Green Function ◽  
Wave Vector ◽  
Easy Axis ◽  
Green’S Functions ◽  
Low Frequency ◽  
Easy Plane ◽  
Collective Excitations ◽  
Green Functions ◽  
The Green Function

The paper studies the dynamic description of uniaxial and biaxial ferrimagnetics with spin s=1/2 in alternative external field. The nonlinear dynamic equations with sources are obtained, on basis on which low-frequency asymptotics of two-time Green functions in the uniaxial and biaxial cases of the ferrimagnet are obtained. Energy models are constructed that are specific functions of Casimir invariants of the algebra of Poisson brackets for magnetic degrees of freedom. On their basis, the question of the stable magnetic states has been solved for the considered systems. These equations were linearized, an explicit form of the collective excitations spectra was found, and their character was analyzed. The article studies the uniaxial case of a ferrimagnet, as well as biaxial cases of an antiferromagnet, easy-axis and easy-plane ferrimagnets. It is shown that for a uniaxial antiferromagnet the spectrum of magnetic excitations has a Goldstone character. For biaxial ferrimagnetic materials, it was found that the spectrum has either a quadratic character or a more complex dependence on the wave vector. It is shown that in the uniaxial case of an antiferromagnet the Green function of the type Gsα,sβ(k,0), Gsα,nβ(k,0) and Gsα,sβ(0,ω) have regular asymptotic behavior, and the Green function of type Gnα,nβ(k,0)≈1/k2 and Gsα,nβ(0,ω)≈1/ω, Gnα,nβ(0,ω)≈1/ω2 have a pole feature in the wave vector and frequency. Biaxial ferrimagnetic states have another type of the features of low-frequency asymptotics of the Green's functions. In the case of a ferrimagnet, the “easy-axis” of the asymptotic behavior of the Green functions Gsα,sβ(0,ω), Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,sβ(k,0), Gsα,nβ(k,0), Gnα,nβ(k,0) have a pole character. For the case of the “easy-plane” type ferrimagnet, the asymptotics of the Green functions Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,nβ(k,0), Gnα,nβ(k,0), have a pole character, and the Green function Gsα,sβ(k,ω) contains both the pole component and the regular part. A comparative analysis of the low-frequency asymptotics of Green functions shows that the nature of magnetic anisotropy significantly effects the structure of low-frequency asymptotics for uniaxial and biaxial cases of ferrimagnet. Separately, we note the non-Bogolyubov character of the Green function asymptotics for ferrimagnet with biaxial anisotropy Gnα,nβ(k,0)≈1/k4.

scholarly journals ASYMPTOTIC BEHAVIOR OF MULTIDIMENSIONAL SCALAR RELAXATION SHOCKS

2009 ◽  
Vol 06 (04) ◽  
pp. 663-708 ◽  
Author(s):  
BONGSUK KWON ◽  
KEVIN ZUMBRUN
Keyword(s):  
Asymptotic Behavior ◽  
Green Function ◽  
Equilibrium Model ◽  
Normal Direction ◽  
Linearized Stability ◽  
Relaxation Systems ◽  
The Green Function ◽  
Scalar Relaxation ◽  
First Moment ◽  
Weak Shocks

We establish pointwise bounds for the Green function and consequent linearized stability for multidimensional planar relaxation shocks of general relaxation systems whose equilibrium model is scalar, under the necessary assumption of spectral stability. Moreover, we obtain nonlinear L2asymptotic behavior/sharp decay rate of perturbed weak shocks of general simultaneously-symmetrizable relaxation systems, under small L1∩ H[d/2]+3perturbations with first moment in the normal direction to the front.

QUANTIZATION OF SUPERPARTICLES BY MEANS OF A PATH INTEGRAL

1988 ◽  
Vol 03 (17) ◽  
pp. 1669-1671
Author(s):  
I.K. KOSTOV ◽  
A.G. SEDRAKYAN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Green Function ◽  
Path Integral ◽  
Relativistic Particle ◽  
World Line ◽  
Quantum Field ◽  
The World ◽  
The Green Function

The path integral is calculated that describes the dynamics of the supersymmetric relativistic particle with an action proportional to the world line superlength. The kernel of the superparticle propagation is shown to coincide with the Green function of the quantum-field theory with the same supersymmetry.

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

The Green function method for the two-surface problem

1970 ◽  
Vol 8 (13) ◽  
pp. 1069-1071 ◽  
Author(s):  
F. Flores ◽  
F. Garcia-Moliner ◽  
J. Rubio
Keyword(s):  
Green Function ◽  
Function Method ◽  
Green Function Method ◽  
The Green Function
Sign in / Sign up

Export Citation Format

Share Document