Download Topological quantum numbers in nonrelativistic physics by David Thouless PDF

  • admin
  • March 29, 2017
  • Waves Wave Mechanics
  • Comments Off on Download Topological quantum numbers in nonrelativistic physics by David Thouless PDF

By David Thouless

Quantization of electrical and magnetic cost; stream and vortices in superfluid 4He; superconductivity and flux quantization; Josephson results; superfluid 3He; the quantum corridor results; solids and drinks; topological section transitions

Show description

Read Online or Download Topological quantum numbers in nonrelativistic physics PDF

Similar waves & wave mechanics books

Waves and Instabilities in Plasmas

This e-book offers the contents of a CISM direction on waves and instabilities in plasmas. For newcomers and for complex scientists a evaluate is given at the nation of data within the box. shoppers can receive a huge survey.

Excitons and Cooper Pairs : Two Composite Bosons in Many-Body Physics

This ebook bridges a spot among significant groups of Condensed subject Physics, Semiconductors and Superconductors, that experience thrived independently. utilizing an unique point of view that the most important debris of those fabrics, excitons and Cooper pairs, are composite bosons, the authors increase basic questions of present curiosity: how does the Pauli exclusion precept wield its strength at the fermionic parts of bosonic debris at a microscopic point and the way this impacts their macroscopic physics?

Additional info for Topological quantum numbers in nonrelativistic physics

Sample text

43) by Eq. 42), we get a ˆ À tanÀ1   er2 g1 ‡ q1 p er1 g2 …q1 ˆ 0; 1; 2; . †: …2:46† On the other hand, dividing Eq. 45) by Eq. 44), we get g2 W ˆ tan À1   er2 g3 À a ‡ q2 p er3 g2 …q2 ˆ 0; 1; 2; . †: …2:47† 20 ANALYTICAL METHODS Substitution of the variable a in Eq. 46) into Eq. 47) results in the following characteristic equation: À1 g2 W ˆ tan     er2 g1 À1 er2 g3 ‡ tan ‡ qp er1 g2 er3 g2 …q ˆ 0; 1; 2; . †: …2:48† Using Eq. 31), we also get g2 W ˆ À tan À1     er1 g2 À1 er3 g2 À tan er2 g1 er2 g3 ‡ …q ‡ 1†p …2:49† …q ˆ 0; 1; 2; .

25) by Eq. 24), we get   g1 a ˆ À tan ‡ q1 p g2 À1 …q1 ˆ 0; 1; 2; . †: …2:28† On the other hand, dividing Eq. 27) by Eq. 26), we get   g3 À a ‡ q2 p g2 W ˆ tan g2 À1 …q2 ˆ 0; 1; 2; . †: …2:29† Substitution of a in Eq. 28) into Eq. 29) results in the following characteristic equation:     g1 À1 g3 ‡ tan ‡ qp g2 W ˆ tan g2 g2 À1 …q ˆ 0; 1; 2; . †: …2:30† Or, using tan À1   p À1 x ˆ À tan ; x 2 y y …2:31† 18 ANALYTICAL METHODS we can rewrite this equation as g2 W ˆ À tanÀ1     g2 g À tanÀ1 2 ‡ …q ‡ 1†p g1 g3 …q ˆ 0; 1; 2; .

Applying the rotation formula       1 @Az @Ay @Ar @Az 1 @ 1 @Ar =3A ˆ …rAy † À À r‡ À u‡ z r @y r @r r @y @z @z @r …2:206† for a vector A ˆ Ar r ‡ Ay u ‡ Az z to the Maxwell equations =3E ˆ Àjom0 H; …2:207† =3H ˆ Àjoe0 er E ˆ ÀjoeE; …2:208† we get 1 @Ez ‡ jbEy ˆ Àjom0 Hr ; r @y …2:209† @Ez ˆ Àjom0 Hy ; @r …2:210† 1 @ 1 @Er …rEy † À ˆ Àjom0 Hz ; r @r r @y …2:211† 1 @Hz ‡ jbHy ˆ joeEr ; r @y …2:212† ÀjbEr À @Hz ˆ ÀjoeEy ; @r …2:213† 1 @ 1 @Hr …rHy † À ˆ ÀjoeEz : r @r r @y …2:214† ÀjbHr À 50 ANALYTICAL METHODS Expressing the tangential ®eld components (Er , Ey , Hr , and Hy ) as functions of the longitudinal ®eld components (Ez and Hz ), we get jbEy À jom0 Hr ˆ ÀjbEr ‡ jom0 Hy ˆ joeEr À jbHy ˆ 1 @Ez ; r @y …2:215† @Ez ; @r …2:216† 1 @Hz ; r @y …2:217† @Hz : @r …2:218† joeEy ‡ jbHr ˆ À The radial and azimuthal ®eld components are obtained as follows: Equation …2:216†  b ‡ Eq.

Download PDF sample

Rated 4.28 of 5 – based on 35 votes