Riemann–Hilbert problem on a torus and a vortex patch in a wedge

2021 ◽  
pp. 1-29
Author(s):  
Y. A. Antipov ◽  
A. Y. Zemlyanova
Keyword(s):  
Hilbert Problem ◽  
Vortex Patch ◽  
Riemann Hilbert Problem

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa II: Riemann–Hilbert Problem

2015 ◽  
Vol 336 (1) ◽  
pp. 337-380 ◽  
Author(s):  
Martin A. Guest ◽  
Alexander R. Its ◽  
Chang-Shou Lin
Keyword(s):  
Hilbert Problem ◽  
Riemann Hilbert Problem

MONODROMY APPROACH TO QUANTUM COMPUTING

2002 ◽  
Vol 16 (30) ◽  
pp. 4593-4605 ◽  
Author(s):  
G. GIORGADZE
Keyword(s):  
Quantum Computing ◽  
Hilbert Problem ◽  
Holomorphic Vector Bundle ◽  
Classical System ◽  
Unitary Operators ◽  
Unitary Matrices ◽  
Classical Procedure ◽  
Logarithmic Singularities ◽  
The Given ◽  
Riemann Hilbert Problem

In this work, a gauge approach to quantum computing is considered. It is assumed that there exists a classical procedure for placing certain classical system in a state described by a holomorphic vector bundle with connection with logarithmic singularities. This bundle and its connection are constructed with the aid of unitary operators realizing the given algorithm using methods of the monodromic Riemann–Hilbert problem. Universality is understood in the sense that for any collection of unitary matrices there exists a connection with logarithmic singularities whose monodromy representation involves these matrices.

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