M3L14b.txt

#
# File:   content-mit-8-421-3x-subtitles/M3L14b.txt
#
# Captions for 8.421x module
#
# This file has 38 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------

Let's just summarize what we have done in a table.
We have seen two different regimes.
In one case, with the Rabi resonance,
we are discussing a single final state
of the atom, a single mode of the electromagnetic field.
All energy levels, all states are discrete.
We are talking about unitary reversible time evolution.
When we have rate equations, we are talking
about many final states.
We integrate over them and/or many modes
of the external field.
We are naturally dealing not with a discrete number,
but with a continuum of states.
The time evolution has becomes irreversible.
And it's therefore no longer a unitary evolution,
but it's a dissipative evolution.
And all of these came about not because we
have spontaneous emission here to put
in some-- I will tell you throughout this course
that spontaneous emission is not as spontaneous as everybody
assumes.
Spontaneous emission is actually unitary time evolution,
unless you discard information.
But a lot of people think rate equation,
irreversibility comes from something
which is genuinely spontaneous and irreproducible.
I don't know anything in physics which is
spontaneous and irreproducible.
But we come to that later.
And this is an example where we obtain rate equation
by simply driving a system.
And the irreversibility comes by performing the integral
over the spectral density.

So let me just write that down.
Due to integration since we integrate over
an infinite number of modes or states.