Equivalence of topological and scattering approaches to quantum pumping

Communications in Mathematical Physics

Volumn 295, Issue 1, 2010, Pages 243-259

  Braunlich G ^a   Graf, G M ^a   Ortelli, G ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 76349109235     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-009-0983-1     Document Type: Article

References (19)

1. Avron J. E., Elgart A., Graf G. M., Sadun L.: Transport and dissipation in quantum pumps. J. Stat. Phys. 116, 425-473 (2004).
2. Avron J. E., Elgart A., Graf G. M., Sadun L., Schnee K.: Adiabatic charge pumping in open quantum systems. Comm. Pure Appl. Math. 57, 528-561 (2004).
3. Avron J. E., Seiler R., Yaffe L. G.: Adiabatic theorems and applications to the quantum Hall effect. Commun. Math. Phys. 110, 33-49 (1987).
4. Avron J. E., Seiler R., Yaffe L. G.: Erratum: "Adiabatic theorems and applications to the quantum Hall effect". Commun. Math. Phys. 156, 649-650 (1993).
5. Blumenthal M. D., Kaestner B., Li L., Giblin S., Janssen T. J. B. M., Pepper M., Anderson D., Jones G., Ritchie D. A.: Gigahertz quantized charge pumping. Nat. Phys. 3, 343-347 (2007).
6. Brouwer P. W.: Scattering approach to parametric pumping. Phys. Rev. B 58, R10135 (1998).
7. Büttiker M., Thomas H., Prêtre A.: Current partition in multiprobe conductors in the presence of slowly oscillating external potentials. Z. Phys. B 94, 133-137 (1994).
8. Chern C. H., Onoda S., Murakami S., Nagaosa N.: Quantum charge pumping and electric polarization in Anderson insulators. Phys. Rev B 76, 035334 (2007).
9. Clark S., Gesztesy F.: On Povzner-Wienholtz-type self-adjointness results for matrix-valued Sturm-Liouville operators. Proc. Roy. Soc. Edinburgh Sect. A 133, 747-758 (2003).
10. Graf G. M., Ortelli G.: Comparison of quantization of charge transport in periodic and open pumps. Phys. Rev. B 77, 033304 (2008).
11. Ivanov D. A., Lee H. W., Levitov L. S.: Coherent states of alternating current. Phys. Rev. B 56, 6839-6850 (1997).
12. Leek P. J., Buitelaar M. R., Talyanskii V. I., Smith C. G., Anderson D., Jones G. A. C., Wei J., Cobden D. H.: Phys. Rev. Lett. 95, 256802 (2005).
13. Lesch M., Malamud M.: On the deficiency indices and self-adjointness of symmetric Hamiltonian systems. J. Diff. Eqs. 189, 556-615 (2003).
14. Lidskii V. B.: On the number of solutions with integrable square of differential equations. Dokl. Akad. Nauk SSSR 95, 217-220 (1954) (in Russian).
15. Nenciu G.: Linear adiabatic theory. Exponential estimates. Commun. Math. Phys. 152, 479-496 (1993).
16. Niu Q., Thouless D. J.: Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction. J. Phys. A 17, 2453-2462 (1984).
17. Shilton J. M., Talyanskii V. I., Pepper M., Ritchie D. A., Frost J. E. F., Ford C. J. B., Smith C. G., Jones G. A. C.: J. Phys. C 8, L531-L539 (1996).
18. Simon, B.: Trace Ideals and Their Applications. 2nd edition, Providence, RI: Amer. Math. Soc., 2005.
19. Thouless D. J.: Quantisation of particle transport. Phys. Rev. B 27, 6083-6087 (1983).