**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Quantum Chaos and Scrambling

Description

This lecture delves into the concept of scrambling in quantum chaotic systems, where small perturbations can lead to large effects over time. The discussion connects classical chaos to quantum chaos, emphasizing sensitivity to initial conditions. The instructor explores the quantum mechanical counterpart of this phenomenon, known as scrambling, and its implications in spectral statistics. The lecture also touches upon the implications of chaos in black holes and the behavior of out-of-time-ordered correlators. Various concepts such as Lyapunov exponents, conformal field theory, and the bound on chaos are discussed, shedding light on the intricate interplay between chaos and quantum mechanics.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (373)

2

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method.

1

1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0.

−1

In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0. Multiplying a number by −1 is equivalent to changing the sign of the number – that is, for any x we have (−1) ⋅ x = −x. This can be proved using the distributive law and the axiom that 1 is the multiplicative identity: x + (−1) ⋅ x = 1 ⋅ x + (−1) ⋅ x = (1 + (−1)) ⋅ x = 0 ⋅ x = 0.

Exact solutions in general relativity

In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field.

Metric system

The metric system is a system of measurement that succeeded the decimalised system based on the metre, which had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body. Adopting the metric system is known as metrication. The historical evolution of metric systems has resulted in the recognition of several principles.

Related lectures (1,000)

Understanding Chaos in Quantum Field Theories

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Partons and Hadrons: Strong Force and Deep Inelastic Scattering

Explores partons, hadrons, strong force, deep inelastic scattering, elastic and inelastic scattering, and Bjorken scaling.

Brown-York Stress TensorPHYS-739: Conformal Field theory and Gravity

Covers the Brown-York stress tensor and its relation to AdS/CFT correspondence.

Holography in Classical GravityPHYS-739: Conformal Field theory and Gravity

Covers the concept of holography in classical gravity and its relation to string theory.

Conformal Transformations: Theory and ApplicationsPHYS-739: Conformal Field theory and Gravity

Explores the theory and applications of conformal transformations, covering special conformal transformations and isomorphic transformations.