Chapter 9: Wave turbulence theory for capillary water waves

This post is based on my joint paper with Toan Nguyen. Although many studies have been carried on to understand the Hasselmann-Zakharov weak turbulence equation for capillary waves since its derivation in the 60’s, the question about the existence and uniqueness of solutions to the equation still remains unanswered, due to the complexity of the…… Continue reading Chapter 9: Wave turbulence theory for capillary water waves

Chapter 8: Quantum hydrodynamic approximations to finite temperature trapped Bose gases

This post is based on my joint paper with Shi Jin. At temperature $latex  T$, bosons of mass $latex  m$ can be regarded as quantum-mechanical wavepackets which have an extent on the order of a thermal de Broglie wavelength $latex  \lambda_{dB} = \left(\frac{2 \pi \hbar^2}{m k_B T}\right)^\frac12$, where $latex  k_B$ is the Boltzmann constant. The…… Continue reading Chapter 8: Quantum hydrodynamic approximations to finite temperature trapped Bose gases

Chapter 7: Coupling kinetic and Schrodinger equations – A simplified model by Soffer and Tran.

This post is based on my joint paper with Avy Soffer. When a bose gas is cooled below the Bose-Einstein critical temperature, the Bose-Einstein condensate is formed, consisting of a macroscopic number of particles, all in the ground state of the system. As we have already known from previous chapters (Chapters 1 &3), a finite…… Continue reading Chapter 7: Coupling kinetic and Schrodinger equations – A simplified model by Soffer and Tran.

Chapter 6: Derivation of quantum kinetic equations

This post is based on my joint work with Linda Reichl. Let us recall from the previous chapters 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: $latex…… Continue reading Chapter 6: Derivation of quantum kinetic equations

Extra Chapter 1: iHDG – Iterative Hybridized Discontinuous Galerkin method

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

Chapter 5: Chemical reaction network and quantum kinetic theories. The key of a successful marriage.

This post is based on my joint work with Gheorghe Craciun. So… what is the key for a successful marriage? This is a very tough question for me since I am still single. However, let me apply the trick that scientists usually do, whenever they encounter a difficult scientific question: to simplify it. In this chapter, I…… Continue reading Chapter 5: Chemical reaction network and quantum kinetic theories. The key of a successful marriage.

Chapter 4: A result on the convergence to equilibrium and some meditation

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