The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged. (Wikipedia).

Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger

The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon

From playlist Math Foundations

What is the max and min of a horizontal line on a closed interval

đź‘‰ Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points

From playlist Extreme Value Theorem of Functions

Calculus - The Fundamental Theorem, Part 3

The Fundamental Theorem of Calculus. Specific examples of simple functions, and how the antiderivative of these functions relates to the area under the graph.

From playlist Calculus - The Fundamental Theorem of Calculus

Calculus - The Fundamental Theorem, Part 2

The Fundamental Theorem of Calculus. A discussion of the antiderivative function and how it relates to the area under a graph.

From playlist Calculus - The Fundamental Theorem of Calculus

What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217

Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understandin

From playlist Math Foundations

Dominic Berry - Optimal scaling quantum linear systems solver via discrete adiabatic theorem

Recorded 25 January 2022. Dominic Berry of Macquarie University presents "Optimal scaling quantum linear systems solver via discrete adiabatic theorem" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Recently, several approaches to solving linear systems on a quantum compute

Determine the extrema using EVT of a rational function

đź‘‰ Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points

From playlist Extreme Value Theorem of Functions

Stefan Tuefel - Local response in bulk-gapped interacting systems - IPAM at UCLA

Recorded 12 April 2022. Stefan Teufel of Eberhard-Karls-UniversitĂ¤t TĂĽbingen, Mathematics, presents "Local response in bulk-gapped interacting systems" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: In my talk, I will first discuss effective descriptions from physics fo

From playlist 2022 Model Reduction in Quantum Mechanics Workshop

Calculus - The Fundamental Theorem, Part 5

The Fundamental Theorem of Calculus. How an understanding of an incremental change in area helps lead to the fundamental theorem

From playlist Calculus - The Fundamental Theorem of Calculus

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L16.1 Quantum adiabatic theorem stated License: Creative Commons BY-NC-SA

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Dong An - Improved complexity estimation for Hamiltonian simulation with Trotter formula

Recorded 25 January 2022. Dong An of the University of Maryland presents "Improved complexity estimation for Hamiltonian simulation with Trotter formula" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Trotter formula is one of the most widely used methods for time-dependent

AQC 2016 - Quantum Monte Carlo vs Tunneling vs. Adiabatic Optimization

A Google TechTalk, June 27, 2016, presented by Aram Harrow (MIT) ABSTRACT: Can quantum adiabatic evolution solve optimization problems much faster than classical computers? One piece of evidence for this has been their apparent advantage in "tunneling" through barriers to escape local mi

From playlist Adiabatic Quantum Computing Conference 2016

L16.3 Error in the adiabatic approximation

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L16.3 Error in the adiabatic approximation License: Creative Commons BY-N

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Lecture 4 | Modern Physics: Statistical Mechanics

April 20, 2009 - Leonard Susskind explains how to calculate and define pressure, explores the formulas some of applications of Helm-Holtz free energy, and discusses the importance of the partition function. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies P

Universal quantum noise in adiabatic pumping by Kyrylo Snizhko

DISCUSSION MEETING : EDGE DYNAMICS IN TOPOLOGICAL PHASES ORGANIZERS : Subhro Bhattacharjee, Yuval Gefen, Ganpathy Murthy and Sumathi Rao DATE & TIME : 10 June 2019 to 14 June 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore Topological phases of matter have been at the forefront of r

From playlist Edge dynamics in topological phases 2019

Determine the extrema using the end points of a closed interval

đź‘‰ Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points

From playlist Extreme Value Theorem of Functions

Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

Statistical Mechanics Lecture 5

(April 29, 2013) Leonard Susskind presents the mathematical definition of pressure using the Helmholtz free energy, and then derives the famous equation of state for an ideal gas: pV = NkT. Originally presented in the Stanford Continuing Studies Program. Stanford University: http://www.s

From playlist Course | Statistical Mechanics

Determine the extrema of a function on a closed interval

đź‘‰ Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points

From playlist Extreme Value Theorem of Functions

AQC 2016 - Adiabatic Quantum Computer vs. Diffusion Monte Carlo

A Google TechTalk, June 29, 2016, presented by Stephen Jordan (NIST) ABSTRACT: While adiabatic quantum computation using general Hamiltonians has been proven to be universal for quantum computation, the vast majority of research so far, both experimental and theoretical, focuses on stoquas

From playlist Adiabatic Quantum Computing Conference 2016