Theory of quantum noise and decoherence, Lecture 7

Here in lecture 7 I show how to derive the master equation for open quantum systems.

[garywpearson]

Big fan of your work. Thanx for sharing this and other videos on QM. I look forward to more, now that we live in a "post-quantum" world. One can not get enough clear and thoughtful explanations of such a infinitely complex field. ;-)


cheers!

[leonardogoller]

Good morning,
I cannot understand why in the master equation derived at 48:00 there is no dependence by V_s in the integral part. Can you please explain me why this is the case?

Thank you

[Shashankx]

Is it possible to extend Born-Markov master equation for higher order interactions? For example, in Four wave mixing, to calculate the output signal of electric field we go till 3rd order ( this calculation is very similar to power series you wrote in the lecture ). If I want to model a master equation for interaction in such system, can I take the 3rd order term in the power series of the above master equation? Your comment on this will be very helpful. Thank you for such a great lecture.

[jungyunhan]

Dear Professor Osborne,

It just trivial thing but,

In 26:00, You wrote Potential in interaction picture as

V(int) = E^(-iHt)VE^(+iHt)

But I think and textbook assures that(e.g. K.Gottfried's QM) potential in interaction picture is

V(int) = E^(iHt)VE^(-iHt)

Also, Can you explain How we can make

[V_(se)(t), rho(0)] = 0

by redefining H_0? (Or example)

Thank you:)

Robert

[ariisaac]

I seem to recall in a prior lecture where a needed simplifying assumption was made that the harmonic resonators had finite dimension and energy. So, are there practical situations where we need to make such contradicting assumptions (i.e., that the harmonic resonators are finite while making the conflicting Born approximation and continuous spectrum assumptions), and the system/environment product 'master' equation approximation fails to be valid?

[ariisaac]

I also have difficulty understanding how can the environment be modeled as an infinite number of harmonic resonators when each one has an infinite dimensional Hilbert space, which implies each as infinite energy. Yet, even ‘empty’ space cannot have infinite energy (black hole?).