This post is based on my joint work with Tan Bui-Thanh and Sriramkrishnan Muralikrishnan. Congratulations, Prof Tan Bui-Thanh for the great achievement! Although the blog is about Quantum Kinetic Theory, I would like to, sometimes, take advantage of it to introduce some other aspects of my work. In this extra chapter, I will discuss my joint work with … Continue reading Extra Chapter 1: iHDG – Iterative Hybridized Discontinuous Galerkin method
This post is based on my joint work with Gheorghe Craciun. In this chapter, I will try to answer the following conjecture: ''What is the key for the marriage of chemical reaction network and quantum kinetic theories to be successful?'' The behavior of reactor vessels used in chemical engineering are often based on systems of nonlinear ordinary … Continue reading Chapter 5: Chemical reaction network and quantum kinetic theories. The key of a successful marriage.
This post is based on my paper with Miguel Escobedo. I googled ''relaxation to equilibrium'' and found these pictures: What is the meaning of ``relaxation to equilibrium'' in meditation? By meditation, we recreate an inner space that allows us to relax our mind from the external circumstances. That helps us develop the mental equilibrium. But, are … Continue reading Chapter 4: A result on the convergence to equilibrium and some meditation
This post is based on my paper with Avy Soffer. Let us recall from Chapter 1 that the BEC occupies the lowest quantum state, at that point macroscopic quantum phenomena become apparent. Above the BEC are excited atoms, which occupy higher quantum states. The are two types of interactions: excited atoms - excited atoms, condensate atoms … Continue reading Chapter 3: What else besides the condensate growth term?
This post is based on my joint work with Toan Nguyen. Milady de Winter is a spy for Cardinal Richelieu and the most beautiful female fictional character in the classic ''The Three Musketeers'' by Alexandre Dumas (father). Being twenty-two, uncommonly beautiful, with brilliant blue eyes and a bewitching voice, Milady can seduce any men she wants. … Continue reading Chapter 2: Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons
This post is based on my joint work with Ricardo Alonso and Irene M. Gamba. If a dilute gas of bosons, about one-hundred-thousandth the density of normal air, is cooled to a temperature very close to absolute zero (0 K or -273.15C), the gas will be changed into a new state of matter, called Bose-Einstein condensate (BEC). … Continue reading Chapter 1. Condensate growth term: existence, uniqueness, propagations of moments
Please have a look at the About and Table of Contents also. There have been very few rigorous mathematical results on Boltzmann equations arising in wave turbulence and quantum kinetic theories, despite their central roles in several aspects of sciences and engineering. One of my research interests is to understand the mathematical properties of these Boltzmann equations. … Continue reading Chapter 0. Introduction