A new model for quantum dot light emitting-absorbing devices: proofs and supplements
https://doi.org/10.17586/2220-8054-2015-6-1-6-45
Аннотация
Motivated by the Jaynes-Cummings (JC) model, we consider here a quantum dot coupled simultaneously to a reservoir of photons and to two electric leads (free-fermion reservoirs). This new Jaynes-Cummings-Leads (JCL) model permits a fermion current through the dot to create a photon flux, which describes a light-emitting device. The same model is also used to describe the transformation of a photon flux into a current of fermions, i.e. a quantum dot light-absorbing device. The key tool to obtain these results is the abstract Landauer-Büttiker formula.
Ключевые слова
Об авторах
H. Neidhardt
WIAS Berlin; 3Institut de Mathématiques de Marseille - UMR 7373 CMI - Technopôle Château-Gombert
Германия
Германия
L. Wilhelm
Institut de Mathématiques de Marseille - UMR 7373 CMI - Technopôle Château-Gombert
Франция
Франция
V. Zagrebnov
Institut de Mathématiques de Marseille - UMR 7373 CMI - Technopôle Château-Gombert
Франция
Франция
Список литературы
1. W. Aschbacher, V. Jakši´c, Y. Pautrat, and C.-A. Pillet. Transport properties of quasi-free fermions. J. Math. Phys., 48(3), P. 032101, 28 (2007).
2. S. Attal, A. Joye, and C.-A. Pillet, editors. Open quantum systems. I, volume 1880 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (2006).
3. S. Attal, A. Joye, and C.-A. Pillet, editors. Open quantum systems. II, volume 1881 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2006. The Markovian approach, Lecture notes from the Summer School held in Grenoble, June 16–July 4, 2003.
4. S. Attal, A. Joye, and C.-A. Pillet, editors. Open quantum systems. III, volume 1882 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2006. Recent developments, Lecture notes from the Summer School held in Grenoble, June 16–July 4, 2003.
5. M. Baro, H.-Chr. Kaiser, H. Neidhardt, and J. Rehberg. A quantum transmitting Schrödinger-Poisson system. Rev. Math. Phys., 16(3), P. 281–330 (2004).
6. H. Baumgärtel and M. Wollenberg. Mathematical scattering theory. Akademie-Verlag, Berlin (1983).
7. M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas. Generalized many-channel conductance formula with application to small rings. Phys. Rev. B, 31(10), P. 6207–6215 (May 1985).
8. H. D. Cornean, P. Duclos, G. Nenciu, and R. Purice. Adiabatically switched-on electrical bias and the Landauer- Büttiker formula. J. Math. Phys., 49(10), P. 102106, 20 (2008).
9. H. D. Cornean, P. Duclos, and R. Purice. Adiabatic non-equilibrium steady states in the partition free approach. Ann. Henri Poincaré, 13(4), P. 827–856 (2012).
10. H. D. Cornean, C. Gianesello, and V. A. Zagrebnov. A partition-free approach to transient and steady-state charge currents. J. Phys. A, 43(47), P. 474011, 15 (2010).
11. H. D. Cornean, A. Jensen, and V. Moldoveanu. A rigorous proof of the Landauer-Büttiker formula. J. Math. Phys., 46(4), P. 042106, 28 (2005).
12. H. D. Cornean, A. Jensen, and V. Moldoveanu. The Landauer-Büttiker formula and resonant quantum transport. Lecture Notes in Phys., 690, pages 45–53. Springer, Berlin (2006).
13. H. D. Cornean, H. Neidhardt, L.Wilhelm, and V. A. Zagrebnov. The Cayley transform applied to non-interacting quantum transport. J. Funct. Anal., 266(3), P. 1421–1475 (2014).
14. H. D. Cornean, H. Neidhardt, and V. A. Zagrebnov. The effect of time-dependent coupling on non-equilibrium steady states. Ann. Henri Poincaré, 10(1), P. 61–93 (2009).
15. M. Damak. On the spectral theory of tensor product Hamiltonians. J. Operator Theory, 55(2), P. 253–268 (2006).
16. C. Gerry and P. Knight. Introductory Quantum Optics. Cambridge University Press, Cambridge (2005).
17. T. Kato. Perturbation theory for linear operators. Classics in Mathematics. Springer-Verlag, Berlin (1995). Reprint of the 1980 edition.
18. R. Landauer. Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction. IBM J. Res. Develop., 1(3), P. 223–231 (1957).
19. H. Neidhardt, L.Wilhelm, and V. A. Zagrebnov. A new model for quantum dot light emitting-absorbing devices. J. Math. Phys., Anal., Geom., 10(3), P. 350–385 (2014).
20. G. Nenciu. Independent electron model for open quantum systems: Landauer-Büttiker formula and strict positivity of the entropy production. J. Math. Phys., 48(3), P. 033302, 8 (2007).
Рецензия
Для цитирования:
, , . Наносистемы: физика, химия, математика. 2015;6(1):6-45. https://doi.org/10.17586/2220-8054-2015-6-1-6-45
For citation:
Neidhardt H., Wilhelm L., Zagrebnov V.A. A new model for quantum dot light emitting-absorbing devices: proofs and supplements. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(1):6-45. https://doi.org/10.17586/2220-8054-2015-6-1-6-45
Просмотров:
5
Послать статью по эл. почте 