Notes

Outline

Quantum Gears


	Angus MacKinnon
	14/11/01

Introduction


	Moore’s Law
	Mesoscopics
	Mechanical Devices
	Molecular Motors
	Simplest Components

Hamiltonian


	2 Gears:



	Simplified – 1 Driven Gear

Single Gear


	Simple Hamiltonian



	Rotating Frame

Nearly Free Gear


	Try
	Only coupled for
	Compare with
	No. of states in BZ = No. of teeth
	Angular Group Velocity

Nearly Free Electrons/Gears

Unexpected Result


	Finite V – Finite Angular Group Velocity
		Except at
	But this condition is almost certainly not fulfilled.
		Why should be an integer?

2 Gears








	Let

Selection Rules


	But



	1^st Brillouin Zone:

	Tunnelling except:

Identical Gears

Different Gears