scholarly journals Exact asymptotic behavior of correlation functions for disordered spin-1/2 XXZ chains

2012 ◽  
Vol 864 (2) ◽  
pp. 317-327 ◽  
Author(s):  
Zoran Ristivojevic ◽  
Aleksandra Petković ◽  
Thierry Giamarchi
Keyword(s):  
Asymptotic Behavior ◽  
Correlation Functions ◽  
Exact Asymptotic Behavior

scholarly journals Mocking the u-plane integral

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Georgios Korpas ◽  
Jan Manschot ◽  
Gregory W. Moore ◽  
Iurii Nidaiev
Keyword(s):  
Asymptotic Behavior ◽  
Gauge Theory ◽  
Entire Function ◽  
Gauge Group ◽  
Strong Coupling ◽  
Modular Forms ◽  
Correlation Functions ◽  
Coulomb Branch ◽  
Mock Modular Forms ◽  
Donaldson Invariants

AbstractThe u-plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

Exact asymptotic behavior near the boundary to the solution for singular nonlinear Dirichlet problems

2009 ◽  
Vol 71 (9) ◽  
pp. 4137-4150 ◽  
Author(s):  
Sonia Ben Othman ◽  
Habib Mâagli ◽  
Syrine Masmoudi ◽  
Malek Zribi
Keyword(s):  
Asymptotic Behavior ◽  
Dirichlet Problems ◽  
Exact Asymptotic Behavior

Asymptotic Behavior of The Unique Solution to a Singular Elliptic Problem With Nonlinear Convection Term And Singular Weight

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Zhijun Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Local Solution ◽  
Variation Theory ◽  
Convection Term ◽  
Unique Classical Solution ◽  
Nonlinear Convection ◽  
Comparison Functions ◽  
Exact Asymptotic Behavior ◽  
Nonlinear Convection Term ◽  
Singular Dirichlet Problem

AbstractBy Karamata regular variation theory, we first derived the exact asymptotic behavior of the local solution to the problem -φʹʹ(s) = g(φ(s)), φ(s) > 0, s ∈ (0, a) and φ(0) = 0. Then, by a perturbation method and constructing comparison functions, we derived the exact asymptotic behavior of the unique classical solution near the boundary to a singular Dirichlet problem -Δu = b(x)g(u) + λ|▽u|

scholarly journals FULLY DISCRETE ADAPTIVE METHODS FOR A BLOW-UP PROBLEM

2004 ◽  
Vol 14 (10) ◽  
pp. 1425-1450 ◽  
Author(s):  
CRISTINA BRÄNDLE ◽  
PABLO GROISMAN ◽  
JULIO D. ROSSI
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Blow Up ◽  
Numerical Study ◽  
Adaptive Methods ◽  
Fully Discrete ◽  
Adaptive Procedures ◽  
Exact Asymptotic Behavior ◽  
Blow Up Rate ◽  
Continuous Problem

We present adaptive procedures in space and time for the numerical study of positive solutions to the following problem: [Formula: see text] with p,m>0. We describe how to perform adaptive methods in order to reproduce the exact asymptotic behavior (the blow-up rate and the blow-up set) of the continuous problem.

scholarly journals ON THE QUANTUM INVARIANT FOR THE BRIESKORN HOMOLOGY SPHERES

2005 ◽  
Vol 16 (06) ◽  
pp. 661-685 ◽  
Author(s):  
KAZUHIRO HIKAMI
Keyword(s):  
Asymptotic Behavior ◽  
Irreducible Representation ◽  
Fundamental Group ◽  
Modular Form ◽  
Quantum Invariant ◽  
Exact Asymptotic Behavior ◽  
Chern Simons ◽  
Eichler Integrals ◽  
Limiting Value ◽  
Modular Property

We study an exact asymptotic behavior of the Witten–Reshetikhin–Turaev SU(2) invariant for the Brieskorn homology spheres Σ(p1, p2, p3) by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit τ → N ∈ ℤ. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern–Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function.

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