Mesoscopic Physics - Theory of Condensed Matter PDF
Preview Mesoscopic Physics - Theory of Condensed Matter
Mesoscopic Physics Smaller is different 1. Theories of Anderson localization 2. Weak localization: theory and experiment 3. Universality and Random Matrix Theory 4. Metal-Insulator Transitions 5. Mesoscopic physics beyond condensed matter References: 1. Thouless, Phys. Rep. 13, 93 (1974). 2. Lee, Ramkrishnan, Rev. Mod. Phys. 57,387 (1985) . 3. Kramer, MacKinnon, Rep. Prog. Phys. 56, 1469 (1993). 4. Boris Altshuler, Boulder Colorado Lectures http://boulder.research.yale.edu/Boulder-2005/Lectures/index.html 1. Interference\tunneling effects in a solid. 2. These effects usually occur at What is mesoscopic intermediate scales and at relatively low physics? temperatures. 3. Disorder plays a role in most materials. 11.. RReevveeaallss uunniivveerrssaall ffeeaattuurreess ooff qquuaannttuumm Why is mesoscopic physics. physics interesting? 2. Continuation of quantum mechanics. 3. Technological applications. Are 4+1 lectures Problems are easy to understand but difficult to solve rigorously. enough? Lecture I: From Anderson to Anderson: perturbative formalism and scaling theory of localization 1. Intuition about quantum dynamics in a disordered potential. Anderson localization 22.. TThheeoorriieess ooff llooccaalliizzaattiioonn:: LLooccaattoorr eexxppaannssiioonnss a. Anderson 1957: “Absence of diffusion in certain random lattices” b. Anderson, Abou-Chacra, Thouless, 1973: “A self- consistent theory of localization” 3. Abrahms, Anderson, et al., 1979: “Scaling theory of localization” YYYYoooouuuurrrr iiiinnnnttttuuuuiiiittttiiiioooonnnn aaaabbbboooouuuutttt llllooooccccaaaalllliiiizzzzaaaattttiiiioooonnnn EEEE aaaa Random VVVV((((xxxx)))) EEEE bbbb 0 EEEE cccc XXXX WWWWWWWWiiiiiiiillllllllllllllll tttttttthhhhhhhheeeeeeee ccccccccllllllllaaaaaaaassssssssssssssssiiiiiiiiccccccccaaaaaaaallllllll mmmmmmmmoooooooottttttttiiiiiiiioooooooonnnnnnnn bbbbbbbbeeeeeeee ssssssssttttttttrrrrrrrroooooooonnnnnnnnggggggggllllllllyyyyyyyy aaaaaaaaffffffffffffffffeeeeeeeecccccccctttttttteeeeeeeedddddddd bbbbbbbbyyyyyyyy qqqqqqqquuuuuuuuaaaaaaaannnnnnnnttttttttuuuuuuuummmmmmmm eeeeeeeeffffffffffffffffeeeeeeeeccccccccttttttttssssssss???????? P. W. Anderson ∇ 2 r ˆ H = − + V (r ) ˆ HΨ = E ψ 2 m α α α r r r r 2 V(r)V(r') =V δ(r −r') 0 Metal 2222 MMeettaall <<<<rrrr >>>> IInnssuullaattoorr 2 r (t) ∝t 2 r (t) ∝const Insulator t→∞ t→∞ tttt AAbbss.. 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