The Density Matrix Concept

Abstract

One naturally asks a question what is this density matrix and why do we need it. The answer is that the density matrix (DM) is a physical representation of an ensemble of atoms, molecules in a matrix format, whose elements tell us at any point in space and time what is the status of the spins and the spin system as a whole. In the absence of any external field the spins distribute themselves in a random manner in the brain. The net magnetism is thus zero. The magnitude of the magnetization (magnetic moment per unit volume) at any point in space and time is not constant in an ensemble like the brain. It is measured through the number of spins per unit volume N₀. One basically measures the susceptibility variation which is the same thing as the magnetization variation in space and time in the MRI mapping of the brain. The spin distribution overall can be assumed to be in equilibrium (though not uniform in space) in an ensemble like our brain. The equilibrium is due to the internal fields e.g. the magnetic fields of the nuclei, various metabolic activities etc.