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Anderson localization

Publication

Exploiting Long-Range Disorder in Slow-Light Photonic Crystal Waveguides: Anderson Localization and Ultrahigh Q/V Cavities

Juan Pablo Vasco Cano

The interplay between order and disorder in photonic lattices opens up a wide range of novel optical scattering mechanisms, cavity-mode resonances, and applications that can be obscured by typical ordered design approaches to photonics. Striking examples i ...

2019

Concept

Random matrix

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice. In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms.

Concept

Quantum Hall effect

The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is Planck's constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,.

Concept

Kondo effect

In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature. The cause of the effect was first explained by Jun Kondo, who applied third-order perturbation theory to the problem to account for scattering of s-orbital conduction electrons off d-orbital electrons localized at impurities (Kondo model).

Lecture

Coherent Transport: Resonant Tunneling and Anderson Localization

Covers coherent transport, resonant tunneling, and Anderson localization in solid-state physics.

Lecture

Data Compression and Entropy: Illustrating Entropy Properties

Explores entropy as a measure of disorder and how it can be increased.

Lecture

Probability and Statistics: Basics and Applications

Covers fundamental concepts of probability and statistics, focusing on data analysis, graphical representation, and practical applications.

Lecture

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Lecture

Probability and Statistics

Introduces key concepts in probability and statistics, such as events, Venn diagrams, and conditional probability.

Lecture

Probability and Statistics

Covers fundamental concepts in probability and statistics, emphasizing data analysis techniques and statistical modeling.

Lecture

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Lecture

Probability and Statistics

Explores joint random variables, conditional density, and independence in probability and statistics.

Lecture

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Lecture

Conditional Density and Expectation

Explores conditional density, expectations, and independence of random variables with practical examples.

Lecture

Quantum Mechanics: Probability and Measurement

Explores probability in Quantum Mechanics, focusing on measurement outcomes and the role of consciousness in determining perceptions.

Lecture

Conditional Probability: Prediction Decomposition

Explores conditional probability, Bayes' theorem, and prediction decomposition for informed decision-making.

Lecture

Probability and Statistics

Introduces key concepts in probability and statistics, covering random experiments, events, intersections, unions, and more.

Lecture

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

Lecture

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Lecture

Quantum Theory of Electronic Transport

Explores the quantum theory of electronic transport, including Drude theory, Ohm's law, and Anderson localization.