Elements of Mechanics

Elements of Quantum Mechanics

Non-relativistic quantum mechanics is necessarily an approximation to relativistic quantum mechanics. It is valid in the regime where kinetic energies and potential energies (more generally field energies) are much less than the rest mass energies of particles. Following philosophy of Laughlin (2005), I prefer to think of non-relativistic quantum mechanics as an emergent theory: one that is exa...

Elements of Vascular Mechanics

Between half and two thirds of human mortality in developed countries can be attributed to vascular diseases. Financial losses, human sufferings are increasing with aging of the population. Vascular diseases develop when some or many vessels in the body are unable to fulfill their functions. The main function of blood vessels is essentially a mechanical one: to conduct blood. Vessels are functi...

Elements of Nonequilibrium Statistical Mechanics

Elements of Nonlinear Quantum Mechanics (II): Triple bracket generalization of quantum mechanics

An extension of quantum mechanics to a generalized Nambu dynamics leads to a new version of nonlinear quantum mechanics. The time evolution of states is given in here by a triple bracket generalization of the Liouville-von Neumann equation, where one of the generators is an average energy, and the other is a measure of entropy. A nonlinear evolution can occur only for mixed states, and for syst...

Elements of the Mathematical Formulation of Quantum Mechanics

In this paper, we will explore some of the basic elements of the mathematical formulation of quantum mechanics. In the first section, I will list the motivations for introducing a probability model that is quite different from that of the classical probability theory, but still shares quite a few significant commonalities. Later in the paper, I will discuss the quantum probability theory in det...