As an analogue of the previous post dealing with the classical particles, in this post, I shall formally discuss how similar models for quantum particles arrive. These particles behave like a wave and their dynamics is governed by the Schrödinger equation. We start the chapter with some basic quantum mechanics.

## Archive for the ‘Kinetic theory’ Category

## Kinetic Theory, chapter 2: quantum models

Posted in Kinetic theory, Math 597C: Graduate topics course on Kinetic Theory, Quantum kinetic theory, tagged Gross-Pitaevskii equations, Hartree equations, quantum Boltzmann, Schrodinger on October 4, 2017| Leave a Comment »

## Kinetic theory: global solution to 3D Vlasov-Poisson

Posted in Kinetic theory, Math 597C: Graduate topics course on Kinetic Theory, tagged Vlasov-Poisson on September 6, 2017| Leave a Comment »

One of the beautiful results in kinetic theory is to construct the global classical solution to the 3D Vlasov-Poisson system. The result is now classical; see, for instance, chapter 4 of Glassey‘s book. However, I feel the result is a bit non-trivial to convey to students and beginners. Would you agree? Anyway, this post is to try to present this classical result, aiming to be as pedagogical as possible, with the original the good, the bad, and the ugly proof of J. Schaeffer ’91.

## Kinetic Theory, chapter 1: classical kinetic models.

Posted in Kinetic theory, Math 597C: Graduate topics course on Kinetic Theory, tagged BBGKY hierarchy, Boltzmann equations, Liouville's equations, Mean field equations, Vlasov on August 16, 2017| 2 Comments »

This fall of 2017, I teach a graduate topics course on Kinetic Theory of Gases. The idea is to introduce the foundation of kinetic theory starting from classical mechanics (and also, basic quantum mechanics!), to survey some classical results on both collisional and collisionless kinetic models, and to detail a few selected mathematical topics in the field. The materials are based on several books, papers, and online resources, which I shall mention in the text. Periodically, I shall post my lecture notes for the course here on this blog (email me for a full pdf copy, with figures and precise references).

## On the Zakharov’s weak turbulence theory for capillary waves

Posted in Kinetic theory, New papers on February 11, 2017| Leave a Comment »

In this paper with M.-B. Tran, we construct solutions to the following weak turbulence kinetic equation for capillary waves (cf. Hasselmann ’62, Zakharov ’67):

## Graduate student seminar: Kinetic theory of gases

Posted in Kinetic theory, Uncategorized on January 28, 2017| Leave a Comment »

Lat week, I gave a graduate student seminar, whose purpose is to introduce to first and second year graduate students (at Penn State) an active and beautiful topics of research, and suggest a few possible ideas for students’ presentation later in the semester. Here are slides of my talk, which focuses on Kinetic Theory of Gases, a topics that I will teach as a graduate topics course, next fall (2017).

## Stability of a collisionless plasma

Posted in Kinetic theory, Plasma Physics, tagged Stability theory, Vlasov-Maxwell on September 10, 2015| Leave a Comment »

What is a plasma? A plasma is an ionized gas that consists of charged particles: positive ions and negative electrons. To describe the dynamics of a plasma, let be the (nonnegative) density distribution of ions and electrons, respectively, at time , position , and particle velocity (or momentum) . The dynamics of a plasma is commonly modeled by the Vlasov equations