Theoretical Nanophysics 2023/1

The scattering matrix describing the scattering region of a ballistic conductor is ...

• a hermitian matrix.

• an antilinear matrix.

• a unitary matrix.

• an anti-hermitian matrix.

Scattering in this system can be described by the Circular Unitary Ensemble.

• Spinless electrons in the absence of magnetic field

• Spinful electrons in the presence of spin-orbit interaction

• Spinless electrons in the presence of a magnetic field

• Spinful electrons in the presence of an electric field

What is the resistance of a 1D perfect, ballistic conductor?

• cca. 13 kOhm

• cca. 6.5 kOhm

• cca. 26 kOhm

• cca. 1.3 kOhm

If I double the length of a classical copper wire, then its resistance...

• increases by a factor of 2

• decreases by a factor of 2

• does not change

• increases by a factor of 4

If I double the length of a 1D perfect, ballistic conductor, then its resistance...

• increases by a factor of 2

• decreases by a factor of 2

• does not change

• increases by a factor of 4

If I double the cross section of a classical copper wire, then its resistance...

• increases by a factor of 2

• decreases by a factor of 2

• does not change

• increases by a factor of 4

If I double the cross section of a quasi-1D ballistic conductor, then its resistance...

• does not change

• might increase

• might decrease

• must decrease

The three symmetry classes covered in the lecture are labelled by three integers. Which integer does not appear as a symmetry class label?

• 1

• 2

• 3

• 4

Sum up N Independent and identically distributed random variables. The expectation value of this sum is proportional to...