Hello, bonjour, ahn nyeong, salvete,
Welcome to the seventh homework session of
Statistical Mechanics: Algorithms and Computations
from the Physics Department of Ecole Normale Supérieure.
This week has given rise to a providential Quantum Monte Carlo algorithm for ideal bosons.
It was by this algorithm, implemented in a few lines in Python,
that we studied the fascinating subject of Bose-Einstein condensation
for many hundreds and even thousands of particles in a three-dimensional harmonic trap.
So it 's now up to you to thoroughly investigate this algorithm
and to study some of the physical properties of the Bose gas.
At low temperature
there are spectacular effects that you will study in detail
Surprisingly, also at high temperature there are effects of the bosonic statistics
and our, your Quantum Monte Carlo algorithm is powerful enough to see them.
We left out the treatment of Bosons interacting with each other via a pair potential.
But remember: this is not a serious restriction:
because in an ideal Bose gas the main effect
is the curious statistical interaction
that comes from the indiscernability
of the particles in the trap.
So good luck, and have fun with homework session 7.