In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from quantum Monte Carlo simulations, which often compute Green function values only at imaginary-times or Matsubara frequencies. Mathematically, the problem reduces to solving a Fredholm integral equation of the first kind with an ill-conditioned kernel. As a result, it is an ill-posed inverse problem with no unique solution and where a small noise on the input leads to large errors in the unregularized solution. There are different methods for solving this problem including the maximum entropy method, the average spectrum method and Pade approximation methods. (Wikipedia).
Math 135 Complex Analysis Lecture 24 042315: Analytic Continuation
Analytic continuation: function element; direct analytic continuation; global analytic function; analytic continuation. Analytic continuation along a curve is essentially unique; statement of Monodromy theorem.
From playlist Course 8: Complex Analysis
Thoughts on the 1-1+1-1+... Series - A Gentle Discussion About Analytic Continuation
We're going to mess around with some divergent series in this video, namely the Grandi Series, 1-1+1-1+... and the related series 1-2+3-4+... and I'll hopefully convince you that the sums that are associated with these divergent series make some sense when seen through the lens of calculus
From playlist Math
Number Theory 1.4 : Analytic Continuation of the Zeta Function
In this video, I prove an analytic continuation of the Riemann Zeta function for all positive Re(z). Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Number Theory
Analytic Continuation and the Zeta Function
Where do complex functions come from? In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for co
From playlist Analytic Number Theory
Analytic Continuation I The Identity Theorem I Complex Analysis #26
Analytic Continuation and the Identity theorem in Complex Analysis explained. Analytic continuation is a method to expand the domain of an analytic function and the Identity theorem tells us everything we need to know about analytic functions. The Identity Theorem is lowkey the greatest t
From playlist Summer of Math Exposition Youtube Videos
Number Theory 3.1: Analytic Continuation of the Xi/Zeta Function (ACZ 1/2)
In this video, I will prove the analytic continuation of the xi function, which will lead into the continuation of the Riemann Zeta Function. Translate This Video : http://www.youtube.com/timedtext_video?v=epnPu9mx738&ref=share Notes : None yet Patreon : https://www.patreon.com/user?u=164
From playlist Number Theory
Mod-01 Lec-03 Interpolating Polynomials
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Complex analysis: Analytic continuation
This lecture is part of an online undergraduate course on complex analysis. We discuss analytic continuation, which is the extraordinary property that the values of a holomorphic function near one point determine its values at point far away. We give two examples of this: the gamma functi
From playlist Complex analysis
Closed loop discrete controller Lecture 2019-04-08
Evaluating the response of a continuous system controlled by a discrete controller using several methods
From playlist Discrete
Numerically Solving Partial Differential Equations
In this video we show how to numerically solve partial differential equations by numerically approximating partial derivatives using the finite difference method. We develop an algorithm that will allow direct numerical simulation of a partial differential equation. Topics and Timestamps
From playlist Partial Differential Equations
Antoine Levitt - Numerical methods for scattering and resonance properties in molecules and solids
Recorded 03 May 2022. Antoine Levitt of the Institut National de Recherche en Informatique Automatique presents "Numerical methods for scattering and resonance properties in molecules and solids" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: The
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
The Analytic S-matrix Bootstrap (Lecture - 01) by Alexander Zhiboedov
STRING THEORY LECTURES THE ANALYTIC S-MATRIX BOOTSTRAP SPEAKER: Alexander Zhiboedov (Theory Division, CERN, Geneva) DATE: 29 January 2019 to 31 January 2019 VENUE: Emmy Noether Seminar Room, ICTS Bangalore Lecture 1: Jan 29, 2019 at 11:00 am Lecture 2: Jan 30, 2019 at 11:00 am Lecture
From playlist Infosys-ICTS String Theory Lectures
Business Analytics Full Course
Business analytics (BA) is a set of disciplines and technologies for solving business problems using data analysis, statistical models and other quantitative methods. It involves an iterative, methodical exploration of an organization's data, with an emphasis on statistical analysis, to dr
From playlist Business Analytics
What Math Classes do Engineers (and Physics Majors) Take? (Part 3)
Support the Channel: https://www.patreon.com/zachstar PayPal(one time donation): https://www.paypal.me/ZachStarYT This video completes the series on math classes that engineers (and physics majors) take. It covers the last of the math classes you could see including... Numerical Methods D
From playlist What You Need To Know About Engineering
Engineering CEE 20: Engineering Problem Solving. Lecture 9
UCI CIvil & Environmental Engineering 20 Engineering Problem Solving (Spring 2013) Lec 09. Engineering Problem Solving -- View the complete course: http://ocw.uci.edu/courses/cee_20_introduction_to_computational_engineering_problem_solving.html Instructor: Jasper Alexander Vrugt, Ph.D.
From playlist Engineering CEE 20: Engineering Problem Solving
Numerical Aperture in Fourier Optics
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video
From playlist Fourier Optics
The Analytic S-matrix Bootstrap (Lecture - 02) by Alexander Zhiboedov
STRING THEORY LECTURES THE ANALYTIC S-MATRIX BOOTSTRAP SPEAKER: Alexander Zhiboedov (Theory Division, CERN, Geneva) DATE: 29 January 2019 to 31 January 2019 VENUE: Emmy Noether Seminar Room, ICTS Bangalore Lecture 1: Jan 29, 2019 at 11:00 am Lecture 2: Jan 30, 2019 at 11:00 am Lecture
From playlist Infosys-ICTS String Theory Lectures
The computational theory of Riemann–Hilbert problems (Lecture 1) by Thomas Trogdon
ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This program aims to address various aspects of integrability and its role in
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Introduction to Resurgence, Trans-series and Non-perturbative Physics - I by Gerald Dunne
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Understanding and computing the Riemann zeta function
In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f
From playlist Programming