Theoretical Nanophysics 2023/3

What is the dimension of the electric current autocorrelation function?

What is the dimension of the electric current noise power spectrum?

What is the dimension of the position noise power spectrum of a harmonic oscillator?

Which feature of the position noise spectrum of a harmonic oscillator is controlled by temperature?

• peak heights

• peak widths

• distance of peaks

• none

For a harmonic oscillator with eigenfrequency f = 5 GHz, at which temperature is the average excitation number equal to 1?

• 346 mK

• 3.46 K

• 34.6 mK

• 3.46 mK

At the lecture, what was the practical motivation to calculate quantum noise of a quantum system?

• mathematical beauty

• no practical motivation, just an abstract quantity

• can characterize measurement back-action

• can characterize entanglement with the environment

The position autocorrelation function of a finite-temperature harmonic oscillator is proportional to the

• temperature

• mass

• eigenfrequency

• none of the others

The negative-frequency part of the position noise spectral density of a finite-temperature quantum system indicates its ability to

• emit energy to its environment

• absorb energy from its environment

• emit electrons to its environment

• absorb electrons from its environment

The Wiener-Kninchin theorem expresses the relation between the autocorrelation function of an observable and ...

• the average of the observable

• the autocorrelation time scale of the observable

• the variance of the observable

• the noise spectral density of the observable

The zero-frequency value of the current noise spectral density characterizes...

• the average current

• the current autocorrelation time

• the variance of the transmitted charge

• the thermal noise of the current