Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

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22 R. Shankar broken critical fan u∗ symmetric Fig. 6. The generic phase diagram for a second-order quantum phase transition. The horizontal axis represents the coupling constant which can be tuned to take one across the transition. The vertical axis is usually the temperature in bulk quantum systems, but is 1/g here, since in our system one of the roles played by g is that of the inverse temperature without actually traversing it. As we move further to the left, we reach the strongly-coupled symmetry-broken phase, with a non-zero order parameter. It can be shown that in our problem, 1/g plays the role of T . One way to see is this that in any large N theory N stands in front of the action when written in terms of the collective variable. That is true in this case well for g. (Hereg also enters at a subdominant level inside the action, which makes it hard to predict the exact shape of the critical fan. The bottom line is that we can see the critical point at finite 1/g. In addition one can also raise temperature or bias voltage to see the critical fan. Subsequent work has shown, in more familiar examples that Landau interactions, that the general picture depicted here is true in the large g limit: upon adding sufficiently strong interactions the Universal Hamiltonian gives way to other descriptions with broken symmetry [33, 34]. 3 Acknowledgement It is a pleasure to thank the organizers of this school especially Professors Dieter Heiss, Nithaya Chetty and Hendrik Geyer for their stupendous hospitality that made all of decide to revisit South Africa as soon as possible. 3 The only result that is not exact in the large g limit is the critical value u ∗ m since the input value of um at ET is related in a non-universal way to the Landau parameter. In other words, the Landau coupling um settles down to its fixed point value at an energy scale that is much larger than ET .Wedonotknowhowit flows as we reach energies inside ET wherein our RMT assumptions are valid. 1/g u
References RG for Interacting Fermions 23 1. M. E. Fisher Critical Phenomena, F.W.J.Hahne,Editor,LectureNotesNumber 186, Springer-Verlag, Berlin, (1983). These notes are from the Engelbrecht Summer School of 1983! 4 2. R. Shankar, Physica A177, 530 (1991); R.Shankar, Rev. Mod. Phys. 66, 129 (1994). 5, 6, 11, 12, 14 3. L. D. Landau, Sov. Phys. JETP 3, 920 (1956); Sov. Phys. JETP 5, 101 (1957). 8 4. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Dover Publications, New York, 1963. 8 5. D. J. Gross and A. Neveu, Phys. Rev.D10, 3235 (1974). 10 6. P. Polchinski In: TASI Elementary Particle Physics, edbyJ.Polchinskiand J.Harvey (World Scientific, 1992.) 12 7. For recent reviews, see, T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Phys. Rep. 299, 189 (1998); Y. Alhassid, Rev. Mod. Phys. 72, 895 (2000); A. D. Mirlin, Phys. Rep. 326, 259 (2000). 12, 13 8. M. L. Mehta, Random Matrices, Academic Press, San Diego, 1991. K. B. Efetov, Adv. Phys. 32, 53 (1983); B. L. Al’tshuler ad B. I. Shklovskii, Sov. Phys. JETP 64, 127 (1986). 13 9. I. L. Aleiner, P. W. Brouwer, and L. I. Glazman, Phys. Rep. 358, 309 (2002), and references therein; Y. Oreg, P. W. Brouwer, X. Waintal, and B. I. Halperin, condmat/0109541, “Spin, spin-orbit, and electron-electron interactions in mesoscopic systems”. 12, 13, 14 10. R. A. Jalabert, A. D. Stone, and Y. Alhassid, Phys. Rev. Lett.68, 3468 (1992). 13 11. A. M. Chang, H. U. Baranger, L. N. Pfeiffer, K. W. West, and T. Y. Chang, Phys. Rev. Lett.76, 1695 (1996); J. A. Folk, S. R. Patel, S. F. Godjin, A. G. Huibers,S.M.Cronenwett,andC.M.Marcus,Phys.Rev.Lett.76, 1699 (1996). 13 12. S. R. Patel, D. R. Stewart, C. M. Marcus, M. Gokcedag, Y. Alhassid, A. D. Stone, C. I. Dururoz, and J. S. Harris, Phys. Rev. Lett.81, 5900 (1998). 13 13. D. V. Averin and K. K. Likharev, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. Webb (Elsevier, Amsterdam, 1991); C. W. J. Beenakker, Phys. Rev. B44, 1646 (1991). 13 14. A. V. Andreev and A. Kamenev, Phys. Rev. Lett.81, 3199 (1998), P. W. Brouwer, Y. Oreg, and B. I. Halperin, Phys. Rev. B60, R13977 (1999), H. U. Baranger, D. Ullmo, and L. I. Glazman, Phys. Rev. B61, R2425 (2000). 13, 14 15. I. L. Kurland, I. L. Aleiner, and B. L. Al’tshuler, Phys. Rev. B62, 14886 (2000). 13, 14 16. O. Prus, A. Auerbach, Y. Aloni, U. Sivan, and R. Berkovits, Phys. Rev. B54, R14289 (1996), R. Berkovits, Phys. Rev. Lett. 81, 2128 (1998), A. Cohen, K. Richter, and R. Berkovits, Phys. Rev. B60, 2536 (1999), P. N. Walker, G. Montambaux, and Y. Gefen, ibid, 2541 (1999), S. Levit and D. Orgad, Phys. Rev. B60, 5549 (1999), D. Ullmo and H. U. Baranger, Phys. Rev. B64, 245324 (2001), V. Belinicher, E. Ginossar, and S. Levit, cond-mat/0109005, Y. Alhassid and S. Malhotra, cond-mat/0202453. 13, 14 17. U. Sivan et al, Phys. Rev. Lett. 77, 1123 (1996); S. R. Patel et al, Phys. Rev. Lett. 80, 4522 (1998). 13 18. F. Simmel et al, Phys. Rev. B59, 10441 (1999); D. Abusch-Magder et al,Physica E 6, 382 (2000). 13, 14 19. Y. M. Blanter, A. D. Mirlin, and B. A. Muzykantskii, Phys. Rev. Lett.78, 2449 (1997), R. O. Vallejos, C. H. Lewenkopf, and E. R. Mucciolo, Phys. Rev. Lett.81, 677 (1998). 14
Page 1 and 2: Lecture Notes in Physics Editorial
Page 3 and 4: W. Dieter Heiss (Ed.) Quantum Dots:
Page 5: Preface Nanoscale physics, nowadays
Page 9 and 10: Contents A Guide for the Reader ...
Page 11 and 12: A Guide for the Reader Quantum dots
Page 13 and 14: The Renormalization Group Approach
Page 15 and 16: RG for Interacting Fermions 5 where
Page 17 and 18: where � is a shorthand: � ≡ 3
Page 19 and 20: RG for Interacting Fermions 9 These
Page 21 and 22: RG for Interacting Fermions 11 is i
Page 23 and 24: RG for Interacting Fermions 13 the
Page 25 and 26: RG for Interacting Fermions 15 this
Page 27 and 28: RG for Interacting Fermions 17 equa
Page 29 and 30: � p � dθp = g 2π RG for Inter
Page 31: RG for Interacting Fermions 21 the
Page 35 and 36: Semiconductor Few-Electron Quantum
Page 39 and 40: 1.2 Implementations Semiconductor F
Page 43 and 44: GaAs n-AlGaAs AlGaAs GaAs Semicondu
Page 49 and 50: ε1 ε0 e Semiconductor Few-Electro
Page 53 and 54: 250 Ω twisted pair 20 MΩ powder
Page 61 and 62: 10 5 0 -5 Semiconductor Few-Electro
Page 63 and 64: G ( e / h) 2 2 1 0 Semiconductor Fe
Page 67 and 68: V R (V) V R (V) Semiconductor Few-E
Page 69 and 70: V L (V) -1.084 -1.082 -1.080 -1.078
Page 71 and 72: B // Semiconductor Few-Electron Qua
Page 77 and 78: a RESERVOIR 200 nm Semiconductor Fe
Page 81 and 82: 4.5 QPC Versus SET Semiconductor Fe
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a reservoir dot Semiconductor Few-E
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a b c V P (mV) 10 5 0 ∆I QPC E F
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Semiconductor Few-Electron Quantum
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Spin-down counts 200 100 a Semicond
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6.7 Unresolved Issues Semiconductor
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98 M. Pustilnik and L.I. Glazman Co
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100 M. Pustilnik and L.I. Glazman F
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102 M. Pustilnik and L.I. Glazman (
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104 M. Pustilnik and L.I. Glazman A
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106 M. Pustilnik and L.I. Glazman t
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110 M. Pustilnik and L.I. Glazman
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112 M. Pustilnik and L.I. Glazman f
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114 M. Pustilnik and L.I. Glazman 5
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116 M. Pustilnik and L.I. Glazman U
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122 M. Pustilnik and L.I. Glazman d
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124 M. Pustilnik and L.I. Glazman G
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126 M. Pustilnik and L.I. Glazman d
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132 C.W.J. Beenakker e e N I N S Fi
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134 C.W.J. Beenakker 2 Andreev Refl
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136 C.W.J. Beenakker F E x 8d/hv ga
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138 C.W.J. Beenakker and we have de
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140 C.W.J. Beenakker A stroboscopic
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142 C.W.J. Beenakker largely indepe
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144 C.W.J. Beenakker The effective
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146 C.W.J. Beenakker Fig. 6. Ensemb
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148 C.W.J. Beenakker 1.4 1.2 1.0 0.
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150 C.W.J. Beenakker 〈ρ(E)〉 =
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152 C.W.J. Beenakker P 0.5 0.4 0.3
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154 C.W.J. Beenakker P(x) 0.4 0.3 0
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156 C.W.J. Beenakker tunnel/ Egap 4
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158 C.W.J. Beenakker its momentum).
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160 C.W.J. Beenakker E00 = π� =
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162 C.W.J. Beenakker 〈ρ(E)〉 δ
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164 C.W.J. Beenakker As described i
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166 C.W.J. Beenakker 0.30 � Egap
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168 C.W.J. Beenakker The τE-depend
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170 C.W.J. Beenakker that a fully m
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172 C.W.J. Beenakker (τ−,τ+), w
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174 C.W.J. Beenakker 61. P. G. Silv
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