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1
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D. V. Averin and K. K. Likharev, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb, Vol. 30 of Modern Problem in Condensed Matter Sciences (Elsevier Science, Amsterdam, 1991), Chap. 6
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D. V. Averin and K. K. Likharev, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb, Vol. 30 of Modern Problem in Condensed Matter Sciences (Elsevier Science, Amsterdam, 1991), Chap. 6.
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2
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85038283921
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G.-L. Ingold and Yu. V. Nazarov, in Ref. 55, Chap. 2, p. 21
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G.-L. Ingold and Yu. V. Nazarov, in Ref. 55, Chap. 2, p. 21.
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3
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85038309822
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G. Schön, in Quantum Transport and Dissipation, edited by T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, and W. Zwerger (Wiley-VCH, Weinheim, 1998), p. 149
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G. Schön, in Quantum Transport and Dissipation, edited by T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, and W. Zwerger (Wiley-VCH, Weinheim, 1998), p. 149.
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J. K. König, H. Schoeller, G. Schön, and R. Fazio, in Quantum Dynamics of Submicron Structures, Vol. 291 of NATO Advanced Study Institute, Series E, edited by H. A. Cerdeira, B. Kramer, and G. Schön (Kluwer Academic, Dordrecht, 1995), p. 221, and references therein
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J. K. König, H. Schoeller, G. Schön, and R. Fazio, in Quantum Dynamics of Submicron Structures, Vol. 291 of NATO Advanced Study Institute, Series E, edited by H. A. Cerdeira, B. Kramer, and G. Schön (Kluwer Academic, Dordrecht, 1995), p. 221, and references therein.
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H. Schoeller, in Mesoscopic Electron Transport, Vol. 345 of NATO Advanced Study Institute, Series E, edited by L. L. Sohn, L. P. Kouwenhoven, and G. Schön (Kluwer Academic, Dordrecht, 1997), p. 291
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H. Schoeller, in Mesoscopic Electron Transport, Vol. 345 of NATO Advanced Study Institute, Series E, edited by L. L. Sohn, L. P. Kouwenhoven, and G. Schön (Kluwer Academic, Dordrecht, 1997), p. 291.
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A. N. Korotkov, D. V. Averin, K. K. Likharev, and S. A. Vasenko, in Single-Electron Tunneling and Mesoscopic Devices, edited by H. Koch and H. Lübbig, Vol. 31 of Springer Series in Electronics and Photonics (Springer-Verlag, Berlin, 1992), pp. 45–59
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A. N. Korotkov, D. V. Averin, K. K. Likharev, and S. A. Vasenko, in Single-Electron Tunneling and Mesoscopic Devices, edited by H. Koch and H. Lübbig, Vol. 31 of Springer Series in Electronics and Photonics (Springer-Verlag, Berlin, 1992), pp. 45–59.
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D. V. Averin, in Macroscopic Quantum Coherence and Quantum Computing, edited by D. V. Averin, R. Ruggiero, and P. Silvestrini (Kluwer Academic/Plenum, New York, 2001), pp. 399–407
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D. V. Averin, in Macroscopic Quantum Coherence and Quantum Computing, edited by D. V. Averin, R. Ruggiero, and P. Silvestrini (Kluwer Academic/Plenum, New York, 2001), pp. 399–407.
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17
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22
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85038317411
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D. V. Averin and Yu. V. Nazarov, in Ref. 55, Chap. 6, p. 217
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D. V. Averin and Yu. V. Nazarov, in Ref. 55, Chap. 6, p. 217.
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23
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D. C. Langreth, in Linear and Nonlinear Transport in Solids, Vol. 17 of NATO Advanced Study Institute, Series B: Physics, edited by J. T. Devreese and V. E. van Doren (Plenum Press, New York, 1976)
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D. C. Langreth, in Linear and Nonlinear Transport in Solids, Vol. 17 of NATO Advanced Study Institute, Series B: Physics, edited by J. T. Devreese and V. E. van Doren (Plenum Press, New York, 1976).
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25
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33646878355
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K.-C. Chou, Z.-B. Su, B.-L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985)
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K.-C. Chou, Z.-B. Su, B.-L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985).
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J. König, J. Schmid, H. Schoeller, and G. Schön, Phys. Rev. B 54, 16 820 (1996).
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König, J.1
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31
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85038339810
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We adopt the time-path C used in Ref. 56, rather than the Keldysh contour (Formula presented) in Ref. 25, because the path C makes the formulation compact in the case where the initial state is in equilibrium
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We adopt the time-path C used in Ref. 56, rather than the Keldysh contour (Formula presented) in Ref. 25, because the path C makes the formulation compact in the case where the initial state is in equilibrium.
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32
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85038279211
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In Ref. 25, the normalization condition of the generating functional is (Formula presented) viz., Z is normalized by (Formula presented) in advance
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In Ref. 25, the normalization condition of the generating functional is (Formula presented) viz., Z is normalized by (Formula presented) in advance.
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33
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85038307992
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D. C. Mattis, The Theory of Magnetism, 2nd ed., Vol. 17 of Springer Series in Solid-State Sciences (Springer-Verlag, Berlin, 1988), p. 90
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D. C. Mattis, The Theory of Magnetism, 2nd ed., Vol. 17 of Springer Series in Solid-State Sciences (Springer-Verlag, Berlin, 1988), p. 90.
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35
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85038270152
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The method to perform the path integral directly on C is demonstrated in an appendix of Refs. 36, and 57., A solution of differential equations defined on C is shown in an appendix of Ref. 36,
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The method to perform the path integral directly on C is demonstrated in an appendix of Refs. 36, and 57., A solution of differential equations defined on C is shown in an appendix of Ref. 36.
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36
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4244133724
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Y. Utsumi, H. Imamura, M. Hayashi, and H. Ebisawa, Phys. Rev. B 66, 024513 (2002).
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(2002)
Phys. Rev. B
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Utsumi, Y.1
Imamura, H.2
Hayashi, M.3
Ebisawa, H.4
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37
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85038333133
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A. M. Zagoskin, Quantum Theory of Many-Body Systems (Springer-Verlag, New York, 1998)
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A. M. Zagoskin, Quantum Theory of Many-Body Systems (Springer-Verlag, New York, 1998).
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38
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85038265777
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Our treatment of the finite transport voltage is equivalent to the widely used one (Refs. 58, 59, 60, 61, 62, 63,), where the voltage difference between two leads is included in the initial distribution function. Two treatments are related each other by a gauge transformation
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Our treatment of the finite transport voltage is equivalent to the widely used one (Refs. 58, 59, 60, 61, 62, 63,), where the voltage difference between two leads is included in the initial distribution function. Two treatments are related each other by a gauge transformation.
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39
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85038297898
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There are two differences between our definition and that in Ref. 30., First, we use the generating functional for connected Green function W rather than Z, because we are interested in the correlation function of the current (or charge) fluctuation operator. Second, we propose the modified expression for the noise: Besides the standard definition, the first term of Eq. (29) or Eq. (30), we introduce the additional second term. It circumvents the uncertainty related to the order of operators (Appendix A)
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There are two differences between our definition and that in Ref. 30., First, we use the generating functional for connected Green function W rather than Z, because we are interested in the correlation function of the current (or charge) fluctuation operator. Second, we propose the modified expression for the noise: Besides the standard definition, the first term of Eq. (29) or Eq. (30), we introduce the additional second term. It circumvents the uncertainty related to the order of operators (Appendix A).
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42
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85038268811
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Our notation (Formula presented) and (Formula presented) corresponds to (Formula presented) and (Formula presented) in Ref. 6, respectively
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Our notation (Formula presented) and (Formula presented) corresponds to (Formula presented) and (Formula presented) in Ref. 6, respectively.
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43
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0037082804
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Y. Utsumi, H. Imamura, M. Hayashi, and H. Ebisawa, Physica C 367, 237 (2002).
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(2002)
Physica C
, vol.367
, pp. 237
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Utsumi, Y.1
Imamura, H.2
Hayashi, M.3
Ebisawa, H.4
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45
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85038336979
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Equation (42) in Ref. 18, is the corresponding result (for (Formula presented) We adopt different notation and definitions: (Formula presented) corresponds to (Formula presented) (Formula presented) and (Formula presented) correspond to (Formula presented) and (Formula presented) respectively
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Equation (42) in Ref. 18, is the corresponding result (for (Formula presented) We adopt different notation and definitions: (Formula presented) corresponds to (Formula presented) (Formula presented) and (Formula presented) correspond to (Formula presented) and (Formula presented) respectively.
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46
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85038289623
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We confirmed that following numerical calculations achieve the spectral sum rule for the c-field GF, (Formula presented) up to (Formula presented)
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We confirmed that following numerical calculations achieve the spectral sum rule for the c-field GF, (Formula presented) up to (Formula presented)
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51
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85038337867
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cond-mat/0211036, Physica E (to be published)
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Y. Utsumi, H. Imamura, M. Hayashi, and H. Ebisawa, cond-mat/0211036, Physica E (to be published).
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Utsumi, Y.1
Imamura, H.2
Hayashi, M.3
Ebisawa, H.4
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53
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85038323419
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cond-mat/0207624 (unpublished)
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D. A. Bagrets and Yu. V. Nazarov, cond-mat/0207624 (unpublished).
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Bagrets, D.A.1
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54
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85038276295
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We can confirm that the term (Formula presented) is 0 from the analytic properties of the step function (Formula presented) viz., (Formula presented) The standard definition for noise, the first term of Eq. (29) or Eq. (30), includes such terms, and thus one must remove them carefully. Our definition does not include such terms, which simplifies practical calculations for the second moment
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We can confirm that the term (Formula presented) is 0 from the analytic properties of the step function (Formula presented) viz., (Formula presented) The standard definition for noise, the first term of Eq. (29) or Eq. (30), includes such terms, and thus one must remove them carefully. Our definition does not include such terms, which simplifies practical calculations for the second moment.
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55
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85038328072
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Single Charge Tunneling, Vol. 294 of NATO Advanced Study Institute, Series B: Physics, edited by H. Grabert and M. H. Devoret (Plenum Press, New York, 1992)
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Single Charge Tunneling, Vol. 294 of NATO Advanced Study Institute, Series B: Physics, edited by H. Grabert and M. H. Devoret (Plenum Press, New York, 1992).
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58
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0001415608
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C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, J. Phys. C 4, 916 (1971).
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J. Phys. C
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Caroli, C.1
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59
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33748465079
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J. Phys. C
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Caroli, C.1
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61
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0002527748
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C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, J. Phys. C 5, 21 (1972).
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J. Phys. C
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Caroli, C.1
Combescot, R.2
Nozieres, P.3
Saint-James, D.4
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