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

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Andreev Billiards 157 Fig. 15. Classical trajectory in an Andreev billiard. Particles in a two-dimensional electron gas are deflected by an electrostatic potential. (The dotted circles are equipotentials.) There is specular reflection at the boundaries with an insulator (thick solid lines) and Andreev reflection at the boundary with a superconductor (dashed line). The trajectory follows the motion between two Andreev reflections of an electron near the Fermi energy. The Andreev reflected hole retraces this trajectory in opposite direction. From [61] Fig. 16. Poincaré map for the Andreev billiard of Fig. 15. Each dot represents a starting point of an electron trajectory, at position x and with tangential momentum px (in dimensionless units). The inset shows the full surface of section, while the main plot is an enlargement of the central region. The drifting nearly periodic motion follows contours of constant time T between Andreev reflections. The cross marks the starting point of the trajectory shown in the previous figure. From [61]
158 C.W.J. Beenakker its momentum). The Poincaré map would then consist of a single point. At non-zero excitation energy E the retroreflection occurs with a slight change in py, because of the difference 2E in the kinetic energy of electrons (at energy EF + E) and holes (at energy EF − E). The resulting slow drift of the periodic trajectory traces out a contour in the surface of section. These are isochronous contours [61], meaning that the time T between Andreev reflections is the same for each point x, px on the contour. The adiabatic invariance of T follows from the adiabatic invariance of the action integral I over the nearly periodic motion from electron to hole and back to electron: � I = pdq =2ET . (75) Since E is a constant of the motion, adiabatic invariance of I implies adiabatic invariance of the time T between Andreev reflections. Adiabatic invariance is defined in the limit E → 0 and is therefore distinct from invariance in the sense of Kolmogorov-Arnold-Moser (KAM) [7], which would require a critical E ∗ such that a contour is exactly invariant for E
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Lecture Notes in Physics Editorial
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W. Dieter Heiss (Ed.) Quantum Dots:
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Preface Nanoscale physics, nowadays
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Contents A Guide for the Reader ...
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A Guide for the Reader Quantum dots
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The Renormalization Group Approach
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RG for Interacting Fermions 5 where
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where � is a shorthand: � ≡ 3
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RG for Interacting Fermions 9 These
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RG for Interacting Fermions 11 is i
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RG for Interacting Fermions 13 the
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RG for Interacting Fermions 15 this
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RG for Interacting Fermions 17 equa
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� p � dθp = g 2π RG for Inter
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RG for Interacting Fermions 21 the
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References RG for Interacting Fermi
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Semiconductor Few-Electron Quantum
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1.2 Implementations Semiconductor F
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GaAs n-AlGaAs AlGaAs GaAs Semicondu
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ε1 ε0 e Semiconductor Few-Electro
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250 Ω twisted pair 20 MΩ powder
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10 5 0 -5 Semiconductor Few-Electro
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G ( e / h) 2 2 1 0 Semiconductor Fe
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V R (V) V R (V) Semiconductor Few-E
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V L (V) -1.084 -1.082 -1.080 -1.078
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B // Semiconductor Few-Electron Qua
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a RESERVOIR 200 nm Semiconductor Fe
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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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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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Page 147 and 148: 138 C.W.J. Beenakker and we have de
Page 149 and 150: 140 C.W.J. Beenakker A stroboscopic
Page 151 and 152: 142 C.W.J. Beenakker largely indepe
Page 153 and 154: 144 C.W.J. Beenakker The effective
Page 155 and 156: 146 C.W.J. Beenakker Fig. 6. Ensemb
Page 157 and 158: 148 C.W.J. Beenakker 1.4 1.2 1.0 0.
Page 159 and 160: 150 C.W.J. Beenakker 〈ρ(E)〉 =
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Page 171 and 172: 162 C.W.J. Beenakker 〈ρ(E)〉 δ
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Page 175 and 176: 166 C.W.J. Beenakker 0.30 � Egap
Page 177 and 178: 168 C.W.J. Beenakker The τE-depend
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Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

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