ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs
10.1007/s10955-009-9697-1
Crossref journal-article
Springer Science and Business Media LLC
Journal of Statistical Physics (297)
Bibliography

Jacquet, P. A. (2009). ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs. Journal of Statistical Physics, 134(4), 709–748.

Authors 1
  1. Philippe A. Jacquet (first)
References 59 Referenced 34
  1. Jackson, E.A.: Nonlinearity and irreversibility in lattice dynamics. Rocky Mt. J. Math. 8, 127–196 (1978) (10.1216/RMJ-1978-8-1-127) / Rocky Mt. J. Math. by E.A. Jackson (1978)
  2. Bonetto, F., Lebowitz, J.L., Rey-Bellet, L.: Fourier’s law: a challenge to theorists. In: Mathematical Physics 2000, pp. 128–150. Imp. Coll. Press, London (2000) (10.1142/9781848160224_0008) / Mathematical Physics 2000 by F. Bonetto (2000)
  3. Lepri, S., Livi, R., Politi, A.: Thermal conduction in classical low-dimensional lattices. Phys. Rep. 377(1), 1–80 (2003) (10.1016/S0370-1573(02)00558-6) / Phys. Rep. by S. Lepri (2003)
  4. Lorentz, H.A.: Le mouvement des électrons dans les métaux. Arch. Neerl. 10, 336–371 (1905) / Arch. Neerl. by H.A. Lorentz (1905)
  5. Lebowitz, J.L., Spohn, H.: Transport properties of the Lorentz gas: Fourier’s law. J. Stat. Phys. 19(6), 633–654 (1978) (10.1007/BF01011774) / J. Stat. Phys. by J.L. Lebowitz (1978)
  6. Lebowitz, J.L., Spohn, H.: Microscopic basis for Fick’s law for self-diffusion. J. Stat. Phys. 28(3), 539–556 (1982) (10.1007/BF01008323) / J. Stat. Phys. by J.L. Lebowitz (1982)
  7. Wagner, C., Klages, R., Nicolis, G.: Thermostating by deterministic scattering: Heat and shear flow. Phys. Rev. E 60(2), 1401–1411 (1999) (10.1103/PhysRevE.60.1401) / Phys. Rev. E by C. Wagner (1999)
  8. Klages, R., Rateitschak, K., Nicolis, G.: Thermostating by deterministic scattering: Construction of nonequilibrium steady states. Phys. Rev. Lett. 84(19), 4268–4271 (2000) (10.1103/PhysRevLett.84.4268) / Phys. Rev. Lett. by R. Klages (2000)
  9. Rateitschak, K., Klages, R., Nicolis, G.: Thermostating by deterministic scattering: the periodic Lorentz gas. J. Stat. Phys. 99(5–6), 1339–1364 (2000) (10.1023/A:1018645007533) / J. Stat. Phys. by K. Rateitschak (2000)
  10. Mejía-Monasterio, C., Larralde, H., Leyvraz, F.: Coupled normal heat and matter transport in a simple model system. Phys. Rev. Lett. 86(24), 5417–5420 (2001) (10.1103/PhysRevLett.86.5417) / Phys. Rev. Lett. by C. Mejía-Monasterio (2001)
  11. Larralde, H., Leyvraz, F., Mejía-Monasterio, C.: Transport properties of a modified Lorentz gas. J. Stat. Phys. 113(1–2), 197–231 (2003) (10.1023/A:1025726905782) / J. Stat. Phys. by H. Larralde (2003)
  12. Eckmann, J.-P., Young, L.-S.: Nonequilibrium energy profiles for a class of 1-D models. Commun. Math. Phys. 262(1), 237–267 (2006) (10.1007/s00220-005-1462-y) / Commun. Math. Phys. by J.-P. Eckmann (2006)
  13. Landauer, R.: Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Develop. 1, 223–231 (1957) (10.1147/rd.13.0223) / IBM J. Res. Develop. by R. Landauer (1957)
  14. Landauer, R.: Electrical resistance of disordered one-dimensional lattices. Philos. Mag. 21(172), 863–867 (1970) (10.1080/14786437008238472) / Philos. Mag. by R. Landauer (1970)
  15. Büttiker, M.: Four-terminal phase-coherent conductance. Phys. Rev. Lett. 57(14), 1761–1764 (1986) (10.1103/PhysRevLett.57.1761) / Phys. Rev. Lett. by M. Büttiker (1986)
  16. Büttiker, M.: Scattering theory of thermal and excess noise in open conductors. Phys. Rev. Lett. 65(23), 2901–2904 (1990) (10.1103/PhysRevLett.65.2901) / Phys. Rev. Lett. by M. Büttiker (1990)
  17. Büttiker, M.: Scattering theory of current and intensity noise correlations in conductors and wave guides. Phys. Rev. B 46(19), 12485–12507 (1992) (10.1103/PhysRevB.46.12485) / Phys. Rev. B by M. Büttiker (1992)
  18. Bolsterli, M., Rich, M., Visscher, W.M.: Simulation of nonharmonic interactions in a crystal by self-consistent reservoirs. Phys. Rev. A 1(4), 1086–1088 (1970) (10.1103/PhysRevA.1.1086) / Phys. Rev. A by M. Bolsterli (1970)
  19. Rich, M., Visscher, W.M.: Disordered harmonic chain with self-consistent reservoirs. Phys. Rev. B 11(6), 2164–2170 (1975) (10.1103/PhysRevB.11.2164) / Phys. Rev. B by M. Rich (1975)
  20. Visscher, W.M., Rich, M.: Stationary nonequilibrium properties of a quantum-mechanical lattice with self-consistent reservoirs. Phys. Rev. A 12(2), 675–680 (1975) (10.1103/PhysRevA.12.675) / Phys. Rev. A by W.M. Visscher (1975)
  21. Davies, E.B.: A model of heat conduction. J. Stat. Phys. 18(2), 161–170 (1978) (10.1007/BF01014307) / J. Stat. Phys. by E.B. Davies (1978)
  22. Bonetto, F., Lebowitz, J.L., Lukkarinen, J.: Fourier’s law for a harmonic crystal with self-consistent stochastic reservoirs. J. Stat. Phys. 116(1–4), 783–813 (2004) (10.1023/B:JOSS.0000037232.14365.10) / J. Stat. Phys. by F. Bonetto (2004)
  23. Roy, D., Dhar, A.: Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs. Phys. Rev. B 75(19), 195110(9) (2007) / Phys. Rev. B by D. Roy (2007)
  24. Büttiker, M.: Small normal-metal loop coupled to an electron reservoir. Phys. Rev. B 32(3), 1846–1849 (1985) (10.1103/PhysRevB.32.1846) / Phys. Rev. B by M. Büttiker (1985)
  25. Büttiker, M.: Role of quantum coherence in series resistors. Phys. Rev. B 33(5), 3020–3026 (1986) (10.1103/PhysRevB.33.3020) / Phys. Rev. B by M. Büttiker (1986)
  26. Büttiker, M.: Coherent and sequential tunneling in series barriers. IBM J. Res. Develop. 32(1), 63–75 (1988) (10.1147/rd.321.0063) / IBM J. Res. Develop. by M. Büttiker (1988)
  27. D’Amato, J.L., Pastawski, H.M.: Conductance of a disordered linear chain including inelastic scattering events. Phys. Rev. B 41(11), 7411–7420 (1990) (10.1103/PhysRevB.41.7411) / Phys. Rev. B by J.L. D’Amato (1990)
  28. Büttiker, M.: Quantum coherence and phase randomization in series resistors. Resonant Tunneling in Semiconductors, pp. 213–227 (1991) (10.1007/978-1-4615-3846-2_21)
  29. Blanter, Ya.M., Büttiker, M.: Shot noise in mesoscopic conductors. Phys. Rep. 336(1–2), 1–166 (2000) (10.1016/S0370-1573(99)00123-4) / Phys. Rep. by Ya.M. Blanter (2000)
  30. Ando, T.: Crossover between quantum and classical transport: quantum hall effect and carbon nanotubes. Physica E 20, 24–32 (2003) (10.1016/j.physe.2003.09.018) / Physica E by T. Ando (2003)
  31. Pilgram, S., Samuelsson, P., Forster, H., Büttiker, M.: Full-counting statistics for voltage and dephasing probes. Phys. Rev. Lett. 97(6), 066801(4) (2006) (10.1103/PhysRevLett.97.066801) / Phys. Rev. Lett. by S. Pilgram (2006)
  32. Forster, H., Samuelsson, P., Pilgram, S., Büttiker, M.: Voltage and dephasing probes in mesoscopic conductors: A study of full-counting statistics. Phys. Rev. B 75(3), 035340(17) (2007) (10.1103/PhysRevB.75.035340) / Phys. Rev. B by H. Forster (2007)
  33. Engquist, H.-L., Anderson, P.W.: Definition and measurement of the electrical and thermal resistances. Phys. Rev. B 24(2), 1151–1154 (1981) (10.1103/PhysRevB.24.1151) / Phys. Rev. B by H.-L. Engquist (1981)
  34. Sivan, U., Imry, Y.: Multichannel Landauer formula for thermoelectric transport with application to thermopower near the mobility edge. Phys. Rev. B 33(1), 551–558 (1986) (10.1103/PhysRevB.33.551) / Phys. Rev. B by U. Sivan (1986)
  35. Büttiker, M.: Symmetry of electrical conduction. IBM J. Res. Develop. 32(3), 317–334 (1988) (10.1147/rd.323.0317) / IBM J. Res. Develop. by M. Büttiker (1988)
  36. Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge Univ. Press, Cambridge (1995) (10.1017/CBO9780511805776) / Electronic Transport in Mesoscopic Systems by S. Datta (1995)
  37. Aschbacher, W., Jakšić, V., Pautrat, Y., Pillet, C.-A.: Transport properties of quasi-free fermions. J. Math. Phys. 48(3), 032101–032128 (2007) (10.1063/1.2709849) / J. Math. Phys. by W. Aschbacher (2007)
  38. Butcher, P.N.: Thermal and electrical transport formalism for electronic microstructures with many terminals. J. Phys., Condens. Matter 2(22), 4869–4878 (1990) (10.1088/0953-8984/2/22/008) / J. Phys., Condens. Matter by P.N. Butcher (1990)
  39. Streda, P.: Quantised thermopower of a channel in the ballistic regime. J. Phys., Condens. Matter 1(5), 1025–1027 (1989) (10.1088/0953-8984/1/5/021) / J. Phys., Condens. Matter by P. Streda (1989)
  40. Beenakker, C.W.J., Staring, A.A.M.: Theory of the thermopower of a quantum dot. Phys. Rev. B 46(15), 9667–9676 (1992) (10.1103/PhysRevB.46.9667) / Phys. Rev. B by C.W.J. Beenakker (1992)
  41. Staring, A.A.M., Molenkamp, L.W., Alphenaar, B.W., van Houten, H., Buyk, O.J.A., Mabesoone, M.A.A., Beenakker, C.W.J., Foxon, C.T.: Coulomb-blockade oscillations in the thermopower of a quantum dot. Europhys. Lett. 22(1), 57–62 (1993) (10.1209/0295-5075/22/1/011) / Europhys. Lett. by A.A.M. Staring (1993)
  42. Molenkamp, L., Staring, A.A.M., Alphenaar, B.W., van Houten, H., Beenakker, C.W.J.: Sawtooth-like thermopower oscillations of a quantum dot in the coulomb blockade regime. Semicond. Sci. Technol. 9(5S), 903–906 (1994) (10.1088/0268-1242/9/5S/136) / Semicond. Sci. Technol. by L. Molenkamp (1994)
  43. Godijn, S.F., Möller, S., Buhmann, H., Molenkamp, L.W., van Langen, S.A.: Thermopower of a chaotic quantum dot. Phys. Rev. Lett. 82(14), 2927–2930 (1999) (10.1103/PhysRevLett.82.2927) / Phys. Rev. Lett. by S.F. Godijn (1999)
  44. Lunde, A.M., Flensberg, K.: On the mott formula for the thermopower of non-interacting electrons in quantum point contacts. J. Phys., Condens. Matter 17(25), 3879–3884 (2005) (10.1088/0953-8984/17/25/014) / J. Phys., Condens. Matter by A.M. Lunde (2005)
  45. Nakanishi, T., Kato, T.: Thermopower of a quantum dot in a coherent regime. J. Phys. Soc. Jpn. 76(3), 034715(6) (2007) (10.1143/JPSJ.76.034715) / J. Phys. Soc. Jpn. by T. Nakanishi (2007)
  46. Saito, K., Takesue, S., Miyashita, S.: Energy transport in the integrable system in contact with various types of phonon reservoirs. Phys. Rev. E 61(3), 2397–2409 (2000) (10.1103/PhysRevE.61.2397) / Phys. Rev. E by K. Saito (2000)
  47. Shapiro, B.: Classical transport within the scattering formalism. Phys. Rev. B 35(15), 8256–8259 (1987) (10.1103/PhysRevB.35.8256) / Phys. Rev. B by B. Shapiro (1987)
  48. Cahay, M., McLennan, M., Datta, S.: Conductance of an array of elastic scatterers: A scattering-matrix approach. Phys. Rev. B 37(17), 10125–10136 (1988) (10.1103/PhysRevB.37.10125) / Phys. Rev. B by M. Cahay (1988)
  49. Beenakker, C.W.J.: Random-matrix theory of quantum transport. Rev. Mod. Phys. 69(3), 731–808 (1997) (10.1103/RevModPhys.69.731) / Rev. Mod. Phys. by C.W.J. Beenakker (1997)
  50. Mezzadri, F.: How to generate random matrices from the classical compact groups. AMS 54(5), 592–604 (2007) / AMS by F. Mezzadri (2007)
  51. Büttiker, M.: Negative resistance fluctuations at resistance minima in narrow quantum hall conductors. Phys. Rev. B 38(17), 12724–12727 (1988) (10.1103/PhysRevB.38.12724) / Phys. Rev. B by M. Büttiker (1988)
  52. Büttiker, M.: Chemical potential oscillations near a barrier in the presence of transport. Phys. Rev. B 40(5), 3409–3412 (1989) (10.1103/PhysRevB.40.3409) / Phys. Rev. B by M. Büttiker (1989)
  53. Levitov, L.S., Lesovik, G.B.: Charge distribution in quantum shot noise. JETP Lett. 58, 230–235 (1993) / JETP Lett. by L.S. Levitov (1993)
  54. Levitov, L.S., Lee, H., Lesovik, G.B.: Electron counting statistics and coherent states of electric current. J. Math. Phys. 37(10), 4845–4866 (1996) (10.1063/1.531672) / J. Math. Phys. by L.S. Levitov (1996)
  55. Bagrets, D.A., Nazarov, Yu.V.: Full counting statistics of charge transfer in coulomb blockade systems. Phys. Rev. B 67(8), 085316(16) (2003) (10.1103/PhysRevB.67.085316) / Phys. Rev. B by D.A. Bagrets (2003)
  56. Pilgram, S., Jordan, A.N., Sukhorukov, E.V., Büttiker, M.: Stochastic path integral formulation of full counting statistics. Phys. Rev. Lett. 90(20), 206801(4) (2003) (10.1103/PhysRevLett.90.206801) / Phys. Rev. Lett. by S. Pilgram (2003)
  57. Pilgram, S.: Electron-electron scattering effects on the full counting statistics of mesoscopic conductors. Phys. Rev. B 69(11), 115315(8) (2004) (10.1103/PhysRevB.69.115315) / Phys. Rev. B by S. Pilgram (2004)
  58. Kindermann, M., Pilgram, S.: Statistics of heat transfer in mesoscopic circuits. Phys. Rev. B 69(15), 155334(8) (2004) (10.1103/PhysRevB.69.155334) / Phys. Rev. B by M. Kindermann (2004)
  59. Saito, K., Dhar, A.: Fluctuation theorem in quantum heat conduction. Phys. Rev. Lett. 99(18), 180601(4) (2007) (10.1103/PhysRevLett.99.180601) / Phys. Rev. Lett. by K. Saito (2007)
Dates
Type When
Created 16 years, 5 months ago (March 4, 2009, 9:34 a.m.)
Deposited 6 years, 2 months ago (June 2, 2019, 1:51 a.m.)
Indexed 1 year, 11 months ago (Sept. 12, 2023, 6:45 p.m.)
Issued 16 years, 6 months ago (Feb. 1, 2009)
Published 16 years, 6 months ago (Feb. 1, 2009)
Published Online 16 years, 5 months ago (March 5, 2009)
Published Print 16 years, 6 months ago (Feb. 1, 2009)
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@article{Jacquet_2009, title={ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs}, volume={134}, ISSN={1572-9613}, url={http://dx.doi.org/10.1007/s10955-009-9697-1}, DOI={10.1007/s10955-009-9697-1}, number={4}, journal={Journal of Statistical Physics}, publisher={Springer Science and Business Media LLC}, author={Jacquet, Philippe A.}, year={2009}, month=feb, pages={709–748} }