The
Hubbard model is an approximate model used to describe the transition between
conducting and insulating systems. The Hubbard model, named after John Hubbard
1963, is the simplest model of interacting particles in lattices, with the only
two tennis in the Hamiltonian; a kinetic term allowing for hopping of particles
between soles of the lattice and a potential term consisting of an on sites
interaction. The particles can either be fermions or bosons.
The
Hubbard model is a good approximate for particles in a periodic potential at
sufficiently low temperature that all the particles are in the lowest Bloch
band, as long as any long-range interactions between the particles can be
ignored. If interaction between particles on different sites of the lattice are
included, the model is often referred to as the extended Hubbard model .The
model was originally proposed to describe electrons in solids and has since
been the focus of particular interest as a model for high temperature super
conductivity. Read more>>>>>>>>>>>>>>>
The
Lorentz transformation (LT) is the centerpiece of Einstein’s special theory of
relativity (STR). It satisfies the two postulates of relativity: the relativity
principle (RP) and the assumption of the constancy of the speed of light in
free space (LSP). It was pointed out as early as 1898 by Lorentz that there is
a degree of freedom in the definition of a space-time transformation that
satisfies the LSP and/or leaves Maxwell’s equations invariant. He introduced a
series of four equations that can be referred to as the General Lorentz
transformation (GLT) in which a common normalization function appears on the
right-hand side of each relation.
It therefore follows that there are an
infinite number of such transformations that satisfy the LSP. However, the RP
puts another constraint on the definition of a fully relativistic space-time
transformation. In addition, there is the obvious criterion that the equations
must be in agreement with all relevant experimental data In the following it
will be shown that, although the LT satisfies both of the relativity
postulates, it fails to predict the results of a number of experiments that
were carried out in the latter half of the 20th century. Read more>>>>>>>>>
