Page 237 - Principles and Applications of NanoMEMS Physics

Appendix B

BOSONIZATION

B.1 Introduction

The method of bosonization consists in modeling a fermionic system by
an equivalent bosonic system, with the advantage that the diagonalization of
the bosonized Hamiltonian of the fermionic system becomes easier [138].
This fact becomes more transparent upon comparing the 1D specific heats
for a solid with sound velocity c , obtained by Debye c Debye , and that for a
s L
Fermi gas of noninteracting electrons with Fermi velocity v , obtained by
F
Pauli c Pauli ,
L
π § k T ·
c Debye = k ¨ B ¸ , (B.1a)
L B ¨ ¸
3 © c = s ¹
π § k T ·
c Pauli = k ¨ B ¸ . (B.1b)
L B ¨ ¸
3 © v = F ¹
Clearly, replacing c ⇔ v one obtains identical results.
s F

B.2 Bosonization “Rules”

While many works attempting to explain bosonization have been
published, a particularly lucid and very pedagogical treatment was that
advanced by Delft and Schoeller [139]. They clearly expose, in a systematic