**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# Introduction to Quantum Chaos

Description

This lecture introduces the concepts of Quantum Chaos and Black Holes, covering topics such as classical chaos, sensitivity to initial conditions, ergodicity, Lyapunov exponents, quantum chaos, semi-classical methods, random matrix theory, thermalization, and scrambling. The lecture explores the bound on chaos, information paradox, randomness, and wormholes. It also delves into the logistic map, discrete time dynamics, and the exponential sensitivity to initial conditions. The presentation progresses to discuss the stability of fixed points, bifurcation diagrams, and the period doubling cascade, providing insights into the onset of chaos and the Feigenbaum constant.

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 (423)

X-ray generator

An X-ray generator is a device that produces X-rays. Together with an X-ray detector, it is commonly used in a variety of applications including medicine, X-ray fluorescence, electronic assembly inspection, and measurement of material thickness in manufacturing operations. In medical applications, X-ray generators are used by radiographers to acquire x-ray images of the internal structures (e.g., bones) of living organisms, and also in sterilization. An X-ray generator generally contains an X-ray tube to produce the X-rays.

X-ray tube

An X-ray tube is a vacuum tube that converts electrical input power into X-rays. The availability of this controllable source of X-rays created the field of radiography, the imaging of partly opaque objects with penetrating radiation. In contrast to other sources of ionizing radiation, X-rays are only produced as long as the X-ray tube is energized. X-ray tubes are also used in CT scanners, airport luggage scanners, X-ray crystallography, material and structure analysis, and for industrial inspection.

Mixing (mathematics)

In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: e.g. mixing paint, mixing drinks, industrial mixing. The concept appears in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including strong mixing, weak mixing and topological mixing, with the last not requiring a measure to be defined.

Measure-preserving dynamical system

In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.

Map

A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although most commonly used to depict geography, maps may represent any space, real or fictional, without regard to context or scale, such as in brain mapping, DNA mapping, or computer network topology mapping.

Related lectures (1,000)

Ergodicity & Mixing: Understanding Chaos

Explores ergodicity and mixing in dynamical systems to understand chaos and system behavior.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Dynamical Systems: Maps and StabilityPHYS-460: Nonlinear dynamics, chaos and complex systems

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Meromorphic Functions & DifferentialsMATH-410: Riemann surfaces

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.