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

This post is based on my paper. 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 temperature trapped Bose gas … Continue reading Chapter 7: Coupling kinetic and Schrodinger equations – A simplified model.

Chapter 6: Derivation of quantum kinetic equations

This post is based on my work  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: $latex  C_{22}$ (Uehling-Ulenbeck term), … Continue reading Chapter 6: Derivation of quantum kinetic equations

Extra Chapter 1: iHDG – Iterative Hybridized Discontinuous Galerkin method

This post is based on my work   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 Tan Bui-Thanh and Sriramkrishnan Muralikrishnan, at the CEO group, Department of Aerospace … 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 paper.. 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 differential equations (ODEs). … 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. 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 we discussing about … Continue reading Chapter 4: A result on the convergence to equilibrium and some meditation

Chapter 3: What else besides the condensate growth term?

This post is based on my paper. 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 - excited atoms. … Continue reading Chapter 3: What else besides the condensate growth term?

Chapter 2: Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons

This post is based on my paper. 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. Our question in this … Continue reading Chapter 2: Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons