1
00:00:03,220 --> 00:00:06,820
Hello, bonjour, ahn nyeong, salvete,

2
00:00:07,350 --> 00:00:09,890
Welcome to the seventh homework session of

3
00:00:09,890 --> 00:00:13,550
Statistical Mechanics: Algorithms and Computations

4
00:00:13,550 --> 00:00:16,610
from the Physics Department of Ecole Normale Supérieure.

5
00:00:17,090 --> 00:00:23,160
This week has given rise to a providential Quantum Monte Carlo algorithm for ideal bosons.

6
00:00:23,850 --> 00:00:27,720
It was by this algorithm, implemented in a few lines in Python,

7
00:00:27,720 --> 00:00:32,290
that we studied the fascinating subject of Bose-Einstein condensation

8
00:00:32,290 --> 00:00:38,430
for many hundreds and even thousands of particles in a three-dimensional harmonic trap.

9
00:00:38,430 --> 00:00:43,000
So it 's now up to you to thoroughly investigate this algorithm

10
00:00:43,000 --> 00:00:47,000
and to study some of the physical properties of the Bose gas.

11
00:00:47,470 --> 00:00:49,560
At low temperature

12
00:00:49,560 --> 00:00:53,560
there are spectacular effects that you will study in detail

13
00:00:53,560 --> 00:00:59,620
Surprisingly, also at high temperature there are effects of the bosonic statistics

14
00:00:59,620 --> 00:01:06,170
and our, your Quantum Monte Carlo algorithm is powerful enough to see them.

15
00:01:07,830 --> 00:01:14,440
 We left out the treatment of Bosons interacting with each other via a pair potential.

16
00:01:14,980 --> 00:01:18,640
 But remember: this is not a serious restriction:

17
00:01:18,640 --> 00:01:22,640
because in an ideal Bose gas the main effect

18
00:01:22,640 --> 00:01:25,930
is the curious statistical interaction

19
00:01:25,930 --> 00:01:28,680
that comes from the indiscernability

20
00:01:28,680 --> 00:01:30,710
of the particles in the trap.

21
00:01:31,280 --> 00:01:34,710
So good luck, and have fun with homework session 7.