Quantum jitter vs thermal jitter

[naima]

In this book Susskind writes that if thermal jitter can burn our nerves, quantum jitter cannot. He explains why:
"Even though quantum jitters can be incredibly energetic, they cause no pain. Why? there is no way to borrow energy from the ground state. And quantum jitter is what is left over when the system is in its absolute minimum ground state."

I used to think that quantum fluctuations exist for all states. Could anyone elaborate this point?
Thanks

 

[Demystifier]

I used to think that quantum fluctuations exist for all states. Could anyone elaborate this point?

You are right, quantum fluctuations exist for all states. But for non-ground states there may be additional (e.g. thermal) fluctuations as well.

 

[naima]

Can a quantum jitter be partly thermal? Is it a yes/no property and how to define when a quantum jitter is thermal?

 

[Demystifier]

Can a quantum jitter be partly thermal? Is it a yes/no property and how to define when a quantum jitter is thermal?

Yes, a quantum jitter can be partly thermal. In this case the state of the system is a mixed thermal state proportional to $e^{-\beta H}$,
where $H$ is the Hamiltonian.

 

[naima]

So with a complex $\beta$ we should factorize the state in a thermal and a non thermal part?

 

[naima]

Is there a textbook in which a state is described with its two parts (thermal and non thermal)? Is there a generalized Schrödinger equation?

 

[naima]

I found this link it gives a good mathematical definiftion of your thermal density matrix.

 

[Demystifier]

So with a complex $\beta$ we should factorize the state in a thermal and a non thermal part?

No.

 

[Demystifier]

Is there a textbook in which a state is described with its two parts (thermal and non thermal)? Is there a generalized Schrödinger equation?

I would not talk about thermal and non-thermal fluctuations. I would talk about mixed-state and pure-state fluctuations. Thermal fluctuations are nothing but a very special case of mixed-state fluctuations. Evolution of pure states is described by Schrödinger equation. A generalization to mixed states is not so simple, so let me just say that one approximate approach is based on the Lindblad equation.