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

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
	1st Brillouin Zone:
	Tunnelling except:

Identical Gears

Different Gears

Summary

	Quantisation of angular momentum not generally consistent with
		Driving frequency
		Other gears
	Finite Temperature
		Need

The End