RANDOM MATRICES and ANDERSON LOCALIZATION
|
|
- Marion Morrison
- 5 years ago
- Views:
Transcription
1 RANDOM MATRICES and ANDERSON LOCALIZATION Luca G. Molinari Physics Department Universita' degli Studi di Milano Abstract: a particle in a lattice with random potential is subject to Anderson localization, which affects low T transport properties of disordered materials. After 50 years the Anderson model continues to be an active area of research. I present some analytic properties of block tridiagonal matrices, for the study of localization in d>1 Milan, april 2, 2009
2 Isaac Newton Institute for Mathematical Sciences Mathematics and Physics of Anderson localization: 50 Years After 14 July - 19 December 2008
3 summary The Anderson model Determinants of block tridiagonal matrices and spectral duality Jensen's theorem and the spectrum of exponents. Energy spectra of non Hermitian Anderson matrices The Argument Principle, hole & halo in complex spectra of tridiagonal matrices
4 THE ANDERSON MODEL d=1,2: p.p. spectrum, exponential localization d=3: a.c. to p.p. spectrum, metal-insulator transition
5 Phase diagram 3D Anderson model localized states extended states
6 UCF MIT dynamical localization QHE QUANTUM CHAOS: - sound - light - matter waves BEC
7 Low T conductivity of amorphous semicond. σ exp [-(c/t)^⅟4] (Mott, 1979: phononassisted hopping between localized states) Weakly disordered metal films 1/σ -log T Random alloys Ref: B.Kramer and A.MacKinnon, Localization: theory and experiment, Rep. Progr. Phys. 56 (1993) MIT in 2D heterojunctions, Si-MOS? (PRL, 2008) Charge localization & Polaron formation in Na_xWO_3 (MIT with x) (PRL, 2006) OPTICS!
8 THEORY Theorems (Spencer, Ishii, Pastur,...) Kubo formula weak disorder (Stone, Altshuler,...) Energy levels and b.c. (Thouless, Hatano & Nelson, level curvatures,... ) Transfer matrix and Lyap spectrum scaling (Kramer&MacKinnon), DMPK eq., conductance &scattering (Buttiker and Landauer),... Supersymmetry, BRM (Efetov, Fyodorov & Mirlin)
9 Some basic old ideas Adimensional conductance g(l)=h/e² L^(d-2)σ Scattering ( lead-sample-lead) g ~ tr tt* (t=transm. matrix) DMPK Periodic b.c.: Thouless conductance g ~ d²e/dφ² /Δ (Bloch phase) One parameter scaling d(log g) / d(log L) = β(g)
10
11 J. Phys. I France 4 (1994) 1469
12 THE HAMILTONIAN MATRIX Block Tridiagonal Matrix A block is Hamiltonian matrix of a section
13 THE TRANSFER MATRIX Eigenvalues of T(E) grow (decay) exponentially in the number of blocks. The rates are the exponents ξ_a(e)
14 Anderson D=1 tridiagonal random matrices Hatano and Nelson (1996) (Herbert-Jones-Thouless formula)
15 SPECTRAL DUALITY z^n is an eigenvalue of T(E) iff E is eigenvalue of H(z^n)
16 determinants of block tridiagonal matrices L.G.M, Linear Algebra and its Applications 429 (2008) 2221
17 Anderson model: duality Exponents describe decay lenghts of Anderson model. They are obtained from nonherm. energy spectrum via Jensen's identity
18 A formula for the exponents (a deterministic variant of Thouless formula) m=3 ξ no formula of Thouless type is known in D>1 (only for sum of exps, xi=0)
19 the exponents ξ m=3, n=50, w=7
20 non-hermitian energy spectra (Anderson 2D) m=5 m=10 n=100, w=7, xi=1.5
21 Anderson 2D (m=3,n=8) (xi fixed, change phase) (change xi and phase)
22
23 Non-Hermitian tridiagonal complex matrices I (with G. Lacagnina)
24 Non-Hermitian tridiagonal complex matrices II
25 BAND RANDOM MATRICES complex, no symmetry
26 conclusions Spectral duality + Jensen's identity --> exponents of single transfer matrix in terms of eigenvalues of Hamiltonan matrix with non-hermitian b.c. Spectral duality + Argument principle --> holes in spectrum of Hamiltonian matrix with non Hermitian b.c. Theory can be extended to T*T (Lyapunov exponents)? Metal insulator transition (D=3)?? Band Random Matrices?
27 determinants of tridiagonal matrices
28 A formula for the exponents (a deterministic variant of Thouless formula) m=3 ξ no formula of Thouless type is known in D>1 (only for sum of exps, xi=0)
Introduction to Theory of Mesoscopic Systems
Introduction to Theory of Mesoscopic Systems Boris Altshuler Princeton University, Columbia University & NEC Laboratories America Lecture 3 Beforehand Weak Localization and Mesoscopic Fluctuations Today
More informationORIGINS. E.P. Wigner, Conference on Neutron Physics by Time of Flight, November 1956
ORIGINS E.P. Wigner, Conference on Neutron Physics by Time of Flight, November 1956 P.W. Anderson, Absence of Diffusion in Certain Random Lattices ; Phys.Rev., 1958, v.109, p.1492 L.D. Landau, Fermi-Liquid
More informationFloquet theory of photo-induced topological phase transitions: Application to graphene
Floquet theory of photo-induced topological phase transitions: Application to graphene Takashi Oka (University of Tokyo) T. Kitagawa (Harvard) L. Fu (Harvard) E. Demler (Harvard) A. Brataas (Norweigian
More informationMetal-insulator Transition by Holographic Charge Density Waves
Metal-insulator Transition by Holographic Charge Density Waves Chao Niu (IHEP, CAS) Based mainly on arxiv:1404.0777 with: Yi Ling, Jianpin Wu, Zhuoyu Xian and Hongbao Zhang (May 9, 2014) Outlines 1. Introduction
More informationApplication of the Lanczos Algorithm to Anderson Localization
Application of the Lanczos Algorithm to Anderson Localization Adam Anderson The University of Chicago UW REU 2009 Advisor: David Thouless Effect of Impurities in Materials Naively, one might expect that
More informationUniversal conductance fluctuation of mesoscopic systems in the metal-insulator crossover regime
Universal conductance fluctuation of mesoscopic systems in the metal-insulator crossover regime Zhenhua Qiao, Yanxia Xing, and Jian Wang* Department of Physics and the Center of Theoretical and Computational
More informationNumerical Analysis of the Anderson Localization
Numerical Analysis of the Anderson Localization Peter Marko² FEI STU Bratislava FzU Praha, November 3. 23 . introduction: localized states in quantum mechanics 2. statistics and uctuations 3. metal - insulator
More informationWhat is a topological insulator? Ming-Che Chang Dept of Physics, NTNU
What is a topological insulator? Ming-Che Chang Dept of Physics, NTNU A mini course on topology extrinsic curvature K vs intrinsic (Gaussian) curvature G K 0 G 0 G>0 G=0 K 0 G=0 G
More informationAdvanced Workshop on Anderson Localization, Nonlinearity and Turbulence: a Cross-Fertilization. 23 August - 3 September, 2010
16-5 Advanced Workshop on Anderson Localization, Nonlinearity and Turbulence: a Cross-Fertilization 3 August - 3 September, 010 INTRODUCTORY Anderson Localization - Introduction Boris ALTSHULER Columbia
More informationLocalization I: General considerations, one-parameter scaling
PHYS598PTD A.J.Leggett 2013 Lecture 4 Localization I: General considerations 1 Localization I: General considerations, one-parameter scaling Traditionally, two mechanisms for localization of electron states
More information3.024 Electrical, Optical, and Magnetic Properties of Materials Spring 2012 Recitation 3 Notes
3.024 Electrical, Optical, and Magnetic Properties of Materials Spring 2012 Outline 1. Schr dinger: Eigenfunction Problems & Operator Properties 2. Piecewise Function/Continuity Review -Scattering from
More informationTheory of Mesoscopic Systems
Theory of Mesoscopic Systems Boris Altshuler Princeton University, Columbia University & NEC Laboratories America Lecture 2 08 June 2006 Brownian Motion - Diffusion Einstein-Sutherland Relation for electric
More informationSymmetries in Quantum Transport : From Random Matrix Theory to Topological Insulators. Philippe Jacquod. U of Arizona
Symmetries in Quantum Transport : From Random Matrix Theory to Topological Insulators Philippe Jacquod U of Arizona UA Phys colloquium - feb 1, 2013 Continuous symmetries and conservation laws Noether
More informationChapter 29. Quantum Chaos
Chapter 29 Quantum Chaos What happens to a Hamiltonian system that for classical mechanics is chaotic when we include a nonzero h? There is no problem in principle to answering this question: given a classical
More informationAshvin Vishwanath UC Berkeley
TOPOLOGY + LOCALIZATION: QUANTUM COHERENCE IN HOT MATTER Ashvin Vishwanath UC Berkeley arxiv:1307.4092 (to appear in Nature Comm.) Thanks to David Huse for inspiring discussions Yasaman Bahri (Berkeley)
More informationRandom Matrices, Black holes, and the Sachdev-Ye-Kitaev model
Random Matrices, Black holes, and the Sachdev-Ye-Kitaev model Antonio M. García-García Shanghai Jiao Tong University PhD Students needed! Verbaarschot Stony Brook Bermúdez Leiden Tezuka Kyoto arxiv:1801.02696
More informationDisordered Superconductors
Cargese 2016 Disordered Superconductors Claude Chapelier, INAC-PHELIQS, CEA-Grenoble Superconductivity in pure metals Kamerlingh Onnes, H., "Further experiments with liquid helium. C. On the change of
More informationTermination of typical wavefunction multifractal spectra at the Anderson metal-insulator transition
Termination of typical wavefunction multifractal spectra at the Anderson metal-insulator transition Matthew S. Foster, 1,2 Shinsei Ryu, 3 Andreas W. W. Ludwig 4 1 Rutgers, the State University of New Jersey
More informationWeak Ergodicity Breaking WCHAOS 2011
Weak Ergodicity Breaking Eli Barkai Bar-Ilan University Bel, Burov, Korabel, Margolin, Rebenshtok WCHAOS 211 Outline Single molecule experiments exhibit weak ergodicity breaking. Blinking quantum dots,
More informationIntroduction to Theory of Mesoscopic Systems
Introduction to Theory of Mesoscopic Systems Boris Altshuler Princeton University, Columbia University & NEC Laboratories America Lecture 5 Beforehand Yesterday Today Anderson Localization, Mesoscopic
More informationSolvable model for a dynamical quantum phase transition from fast to slow scrambling
Solvable model for a dynamical quantum phase transition from fast to slow scrambling Sumilan Banerjee Weizmann Institute of Science Designer Quantum Systems Out of Equilibrium, KITP November 17, 2016 Work
More informationResonant scattering in random-polymer chains with inversely symmetric impurities
Resonant scattering in random-polymer chains with inversely symmetric impurities Y. M. Liu, R. W. Peng,* X. Q. Huang, Mu Wang, A. Hu, and S. S. Jiang National Laboratory of Solid State Microstructures
More informationCOLD ATOMS AND OPTICAL DISORDER : A NEW TOOL TO STUDY QUANTUM TRANSPORT P. BOUYER
COLD ATOMS AND OPTICAL DISORDER : A NEW TOOL TO STUDY QUANTUM TRANSPORT P. BOUYER Laboratoire Charles Fabry de l Institut d Optique Palaiseau, France web site : www.atomoptic.fr TITRE S. Bernon (Talk and
More informationThe Center for Ultracold Atoms at MIT and Harvard Theoretical work at CUA. NSF Visiting Committee, April 28-29, 2014
The Center for Ultracold Atoms at MIT and Harvard Theoretical work at CUA NSF Visiting Committee, April 28-29, 2014 Paola Cappellaro Mikhail Lukin Susanne Yelin Eugene Demler CUA Theory quantum control
More informationHeat conduction and phonon localization in disordered harmonic lattices
Heat conduction and phonon localization in disordered harmonic lattices Anupam Kundu Abhishek Chaudhuri Dibyendu Roy Abhishek Dhar Joel Lebowitz Herbert Spohn Raman Research Institute NUS, Singapore February
More informationSome open questions from the KIAS Workshop on Emergent Quantum Phases in Strongly Correlated Electronic Systems, Seoul, Korea, October 2005.
Some open questions from the KIAS Workshop on Emergent Quantum Phases in Strongly Correlated Electronic Systems, Seoul, Korea, October 2005. Q 1 (Balents) Are quantum effects important for physics of hexagonal
More informationLOCAL MOMENTS NEAR THE METAL-INSULATOR TRANSITION
LOCAL MOMENTS NEAR THE METAL-INSULATOR TRANSITION Subir Sachdev Center for Theoretical Physics, P.O. Box 6666 Yale University, New Haven, CT 06511 This paper reviews recent progress in understanding the
More information8.513 Lecture 14. Coherent backscattering Weak localization Aharonov-Bohm effect
8.513 Lecture 14 Coherent backscattering Weak localization Aharonov-Bohm effect Light diffusion; Speckle patterns; Speckles in coherent backscattering phase-averaged Coherent backscattering Contribution
More informationEigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
epl draft igenvectors under a generic perturbation: non-perturbative results from the random matrix approach K. Truong and A. Ossipov School of Mathematical Sciences, University of Nottingham, Nottingham
More informationThouless conductance, Landauer-Büttiker currents and spectrum
, Landauer-Büttiker currents and spectrum (Collaboration with V. Jakšić, Y. Last and C.-A. Pillet) L. Bruneau Univ. Cergy-Pontoise Marseille - June 13th, 2014 L. Bruneau, Landauer-Büttiker currents and
More informationIntroductory lecture on topological insulators. Reza Asgari
Introductory lecture on topological insulators Reza Asgari Workshop on graphene and topological insulators, IPM. 19-20 Oct. 2011 Outlines -Introduction New phases of materials, Insulators -Theory quantum
More informationHopping transport in disordered solids
Hopping transport in disordered solids Dominique Spehner Institut Fourier, Grenoble, France Workshop on Quantum Transport, Lexington, March 17, 2006 p. 1 Outline of the talk Hopping transport Models for
More informationR. Citro. In collaboration with: A. Minguzzi (LPMMC, Grenoble, France) E. Orignac (ENS, Lyon, France), X. Deng & L. Santos (MP, Hannover, Germany)
Phase Diagram of interacting Bose gases in one-dimensional disordered optical lattices R. Citro In collaboration with: A. Minguzzi (LPMMC, Grenoble, France) E. Orignac (ENS, Lyon, France), X. Deng & L.
More informationDelocalization for Schrödinger operators with random Dirac masses
Delocalization for Schrödinger operators with random Dirac masses CEMPI Scientific Day Lille, 10 February 2017 Disordered Systems E.g. box containing N nuclei Motion of electron in this system High temperature
More informationARBITRARY ROTATION INVARIANT RANDOM MATRIX ENSEMBLES HUBBARD-STRATONOVITCH TRANSFORMATION VERSUS SUPERBOSONIZATION. Mario Kieburg.
ARBITRARY ROTATION INVARIANT RANDOM MATRIX ENSEMBLES: HUBBARD-STRATONOVITCH TRANSFORMATION VERSUS SUPERBOSONIZATION Mario Kieburg Universität Duisburg-Essen Mexico, Cuernavaca, March 2009 supported by
More informationLoop current order in optical lattices
JQI Summer School June 13, 2014 Loop current order in optical lattices Xiaopeng Li JQI/CMTC Outline Ultracold atoms confined in optical lattices 1. Why we care about lattice? 2. Band structures and Berry
More informationarxiv:cond-mat/ v1 23 May 1995
Universal Spin-Induced Magnetoresistance in the Variable-Range Hopping Regime Yigal Meir Physics Department, Ben Gurion University, Beer Sheva 84105, ISRAEL arxiv:cond-mat/9505101v1 23 May 1995 Abstract
More informationAnderson Localization Looking Forward
Anderson Localization Looking Forward Boris Altshuler Physics Department, Columbia University Collaborations: Also Igor Aleiner Denis Basko, Gora Shlyapnikov, Vincent Michal, Vladimir Kravtsov, Lecture2
More informationPurely electronic transport in dirty boson insulators
Purely electronic transport in dirty boson insulators Markus Müller Ann. Phys. (Berlin) 18, 849 (2009). Discussions with M. Feigel man, M.P.A. Fisher, L. Ioffe, V. Kravtsov, Abdus Salam International Center
More informationarxiv: v2 [cond-mat.dis-nn] 21 Jul 2010
Two-dimensional electron systems beyond the diffusive regime P. Markoš Department of Physics FEI, lovak University of Technology, 8 9 Bratislava, lovakia arxiv:5.89v [cond-mat.dis-nn] Jul Transport properties
More informationARPES experiments on 3D topological insulators. Inna Vishik Physics 250 (Special topics: spectroscopies of quantum materials) UC Davis, Fall 2016
ARPES experiments on 3D topological insulators Inna Vishik Physics 250 (Special topics: spectroscopies of quantum materials) UC Davis, Fall 2016 Outline Using ARPES to demonstrate that certain materials
More informationAnderson Localization in the Seventies and Beyond David Thouless University of Washington Seattle, WA APS March Meeting, Pittsburgh March 19,
Anderson Localization in the Seventies and Beyond David Thouless University of Washington Seattle, WA 98195 APS March Meeting, Pittsburgh March 19, 2009 1 Importance of Anderson s 1958 paper on Absence
More informationSearch for time reversal symmetry effects in disordered conductors and insulators beyond weak localization. Marc Sanquer CEA/DRF/INAC & UGA
Search for time reversal symmetry effects in disordered conductors and insulators beyond weak localization. Marc Sanquer CEA/DRF/INAC & UGA 40 years of Mesoscopics Physics: Colloquium in memory of Jean-Louis
More informationToday: 5 July 2008 ٢
Anderson localization M. Reza Rahimi Tabar IPM 5 July 2008 ١ Today: 5 July 2008 ٢ Short History of Anderson Localization ٣ Publication 1) F. Shahbazi, etal. Phys. Rev. Lett. 94, 165505 (2005) 2) A. Esmailpour,
More informationarxiv:cond-mat/ v1 29 Dec 1996
Chaotic enhancement of hydrogen atoms excitation in magnetic and microwave fields Giuliano Benenti, Giulio Casati Università di Milano, sede di Como, Via Lucini 3, 22100 Como, Italy arxiv:cond-mat/9612238v1
More informationIntroduction to Wave Scattering, Localization and Mesoscopic Phenomena
Springer Series in Materials Science 88 Introduction to Wave Scattering, Localization and Mesoscopic Phenomena Bearbeitet von Ping Sheng Neuausgabe 2006. Buch. xv, 329 S. Hardcover ISBN 978 3 540 29155
More information2D electron systems beyond the diffusive regime
2D electron systems beyond the diffusive regime Peter Markoš FEI STU Bratislava 9. June 211 Collaboration with: K. Muttalib, L. Schweitzer Typeset by FoilTEX Introduction: Spatial distribution of the electron
More informationH = ( H(x) m,n. Ω = T d T x = x + ω (d frequency shift) Ω = T 2 T x = (x 1 + x 2, x 2 + ω) (skewshift)
Chapter One Introduction We will consider infinite matrices indexed by Z (or Z b ) associated to a dynamical system in the sense that satisfies H = ( H(x) m,n )m,n Z H(x) m+1,n+1 = H(T x) m,n where x Ω,
More informationNonlinear screening and percolation transition in 2D electron liquid. Michael Fogler
Dresden 005 Nonlinear screening and percolation transition in D electron liquid Michael Fogler UC San Diego, USA Support: A.P. Sloan Foundation; C. & W. Hellman Fund Tunable D electron systems MOSFET Heterostructure
More informationarxiv:cond-mat/ v1 [cond-mat.str-el] 25 Sep 2002
arxiv:cond-mat/0209587v1 [cond-mat.str-el] 25 Sep 2002 The 2D Mott-Hubbard transition in presence of a parallel magnetic field A. Avella and F. Mancini Dipartimento di Fisica E.R. Caianiello - Unità INFM
More informationCan we find metal-insulator transitions in 2-dimensional systems?
Can we find metal-insulator transitions in 2-dimensional systems? Marcelo Kuroda Term Essay for PHYS498ESM, Spring 2004 It has been almost a quarter of a century since the belief of the non existence metallic
More informationRigid Body Motion in a Special Lorentz Gas
Rigid Body Motion in a Special Lorentz Gas Kai Koike 1) Graduate School of Science and Technology, Keio University 2) RIKEN Center for Advanced Intelligence Project BU-Keio Workshop 2018 @Boston University,
More informationThermal transport in strongly correlated nanostructures J. K. Freericks
Thermal transport in strongly correlated nanostructures J. K. Freericks Department of Physics, Georgetown University, Washington, DC 20057 Funded by the Office of Naval Research and the National Science
More informationEhud Altman. Weizmann Institute and Visiting Miller Prof. UC Berkeley
Emergent Phenomena And Universality In Quantum Systems Far From Thermal Equilibrium Ehud Altman Weizmann Institute and Visiting Miller Prof. UC Berkeley A typical experiment in traditional Condensed Matter
More informationI. PLATEAU TRANSITION AS CRITICAL POINT. A. Scaling flow diagram
1 I. PLATEAU TRANSITION AS CRITICAL POINT The IQHE plateau transitions are examples of quantum critical points. What sort of theoretical description should we look for? Recall Anton Andreev s lectures,
More informationNumerical study of localization in antidot lattices
PHYSICAL REVIEW B VOLUME 58, NUMBER 16 Numerical study of localization in antidot lattices 15 OCTOBER 1998-II Seiji Uryu and Tsuneya Ando Institute for Solid State Physics, University of Tokyo, 7-22-1
More informationOptical Characterization of Solids
D. Dragoman M. Dragoman Optical Characterization of Solids With 184 Figures Springer 1. Elementary Excitations in Solids 1 1.1 Energy Band Structure in Crystalline Materials 2 1.2 k p Method 11 1.3 Numerical
More informationDisordered Quantum Systems
Disordered Quantum Systems Boris Altshuler Physics Department, Columbia University and NEC Laboratories America Collaboration: Igor Aleiner, Columbia University Part 1: Introduction Part 2: BCS + disorder
More informationTensor network simulations of strongly correlated quantum systems
CENTRE FOR QUANTUM TECHNOLOGIES NATIONAL UNIVERSITY OF SINGAPORE AND CLARENDON LABORATORY UNIVERSITY OF OXFORD Tensor network simulations of strongly correlated quantum systems Stephen Clark LXXT[[[GSQPEFS\EGYOEGXMZMXMIWUYERXYQGSYVWI
More informationIntroduction to Mesoscopics. Boris Altshuler Princeton University, NEC Laboratories America,
Not Yet Introduction to Mesoscopics Boris Altshuler Princeton University, NEC Laboratories America, ORIGINS E.P. Wigner, Conference on Neutron Physics by Time of Flight, November 1956 P.W. Anderson, Absence
More informationCoherent backscattering in Fock space. ultracold bosonic atoms
Coherent backscattering in the Fock space of ultracold bosonic atoms Peter Schlagheck 16.2.27 Phys. Rev. Lett. 112, 1443 (24); arxiv:161.435 Coworkers Thomas Engl (Auckland) Juan Diego Urbina (Regensburg)
More informationInequivalent bundle representations for the Noncommutative Torus
Inequivalent bundle representations for the Noncommutative Torus Chern numbers: from abstract to concrete Giuseppe De Nittis Mathematical Physics Sector of: SISSA International School for Advanced Studies,
More informationSymmetry, Topology and Phases of Matter
Symmetry, Topology and Phases of Matter E E k=λ a k=λ b k=λ a k=λ b Topological Phases of Matter Many examples of topological band phenomena States adiabatically connected to independent electrons: - Quantum
More informationTopological Kondo Insulator SmB 6. Tetsuya Takimoto
Topological Kondo Insulator SmB 6 J. Phys. Soc. Jpn. 80 123720, (2011). Tetsuya Takimoto Department of Physics, Hanyang University Collaborator: Ki-Hoon Lee (POSTECH) Content 1. Introduction of SmB 6 in-gap
More informationIntermediate valence in Yb Intermetallic compounds
Intermediate valence in Yb Intermetallic compounds Jon Lawrence University of California, Irvine This talk concerns rare earth intermediate valence (IV) metals, with a primary focus on certain Yb-based
More informationStatistical properties of eigenvectors in non-hermitian Gaussian random matrix ensembles
JOURNAL OF MATHEMATICAL PHYSICS VOLUME 4, NUMBER 5 MAY 2000 Statistical properties of eigenvectors in non-hermitian Gaussian random matrix ensembles B. Mehlig a) and J. T. Chalker Theoretical Physics,
More informationSuperconducting fluctuations, interactions and disorder : a subtle alchemy
Les défis actuels de la supraconductivité Dautreppe 2011 Superconducting fluctuations, interactions and disorder : a subtle alchemy Claude Chapelier, Benjamin Sacépé, Thomas Dubouchet INAC-SPSMS-LaTEQS,
More informationA typical medium approach to Anderson localization in correlated systems.
A typical medium approach to Anderson localization in correlated systems. N.S.Vidhyadhiraja Theoretical Sciences Unit Jawaharlal Nehru center for Advanced Scientific Research Bangalore, India Outline Models
More informationMesoscopic Physics. Smaller is different
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
More informationOrthogonality Catastrophe
Filiberto Ares Departamento de Física Teórica Universidad de Zaragoza Orthogonality Catastrophe Martes Cuantico, April 17 What is Orthogonality Catastrophe (OC)? 2 / 23 2 / 23 What is Orthogonality Catastrophe
More informationTheory of Aperiodic Solids:
Theory of Aperiodic Solids: Sponsoring from 1980 to present Jean BELLISSARD jeanbel@math.gatech.edu Georgia Institute of Technology, Atlanta School of Mathematics & School of Physics Content 1. Aperiodic
More informationPolariton Condensation
Polariton Condensation Marzena Szymanska University of Warwick Windsor 2010 Collaborators Theory J. Keeling P. B. Littlewood F. M. Marchetti Funding from Macroscopic Quantum Coherence Macroscopic Quantum
More informationLearning about order from noise
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Mikhail Lukin, Anatoli
More informationTopological protection, disorder, and interactions: Life and death at the surface of a topological superconductor
Topological protection, disorder, and interactions: Life and death at the surface of a topological superconductor Matthew S. Foster Rice University March 14 th, 2014 Collaborators: Emil Yuzbashyan (Rutgers),
More informationTopological Physics in Band Insulators IV
Topological Physics in Band Insulators IV Gene Mele University of Pennsylvania Wannier representation and band projectors Modern view: Gapped electronic states are equivalent Kohn (1964): insulator is
More informationPhysics 127b: Statistical Mechanics. Renormalization Group: 1d Ising Model. Perturbation expansion
Physics 17b: Statistical Mechanics Renormalization Group: 1d Ising Model The ReNormalization Group (RNG) gives an understanding of scaling and universality, and provides various approximation schemes to
More informationObservation of two-dimensional Anderson localization of light in disordered optical fibers with nonlocal nonlinearity
Observation of two-dimensional Anderson localization of light in disordered optical fibers with nonlocal nonlinearity Claudio Conti Institute for Complex Systems National Research Council ISC-CNR Rome
More informationFundamentals and New Frontiers of Bose Einstein Condensation
Contents Preface v 1. Fundamentals of Bose Einstein Condensation 1 1.1 Indistinguishability of Identical Particles.......... 1 1.2 Ideal Bose Gas in a Uniform System............ 3 1.3 Off-Diagonal Long-Range
More informationSpectral Universality of Random Matrices
Spectral Universality of Random Matrices László Erdős IST Austria (supported by ERC Advanced Grant) Szilárd Leó Colloquium Technical University of Budapest February 27, 2018 László Erdős Spectral Universality
More informationWhat is Quantum Transport?
What is Quantum Transport? Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. http://www.physics.udel.edu/~bnikolic Semiclassical Transport (is boring!) Bloch-Boltzmann
More informationDouble Transition Effect in Anderson Transition
Turk J Phys 25 2001), 431 438. c TÜBİTAK Double Transition Effect in Anderson Transition Hüseyin AKTAŞ Department of Physics, Faculty of Sciences and Arts, University of Kırıkkale, Kırıkkale-TURKEY Received
More informationarxiv: v1 [cond-mat.other] 20 Apr 2010
Characterization of 3d topological insulators by 2d invariants Rahul Roy Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK arxiv:1004.3507v1 [cond-mat.other] 20 Apr 2010
More informationCritical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets. In collaboration with: Olexei Motrunich & Jason Alicea
Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets In collaboration with: Olexei Motrunich & Jason Alicea I. Background Outline Avoiding conventional symmetry-breaking in s=1/2 AF Topological
More informationin BECs Fabian Grusdt Physics Department and Research Center OPTIMAS, University of Kaiserslautern, Germany
1 Polaron Seminar, AG Widera AG Fleischhauer, 05/06/14 Introduction to polaron physics in BECs Fabian Grusdt Physics Department and Research Center OPTIMAS, University of Kaiserslautern, Germany Graduate
More informationAditi Mitra New York University
Superconductivity following a quantum quench Aditi Mitra New York University Supported by DOE-BES and NSF- DMR 1 Initially system of free electrons. Quench involves turning on attractive pairing interactions.
More informationMetal-Insulator Transitions
Metal-Insulator Transitions Second Edition N. F. MOTT Emeritus Cavendish Professor of Physics University of Cambridge Taylor & Francis London New York Philadelphia Contents Preface to Second Edition v
More informationSUPERFLUIDTY IN ULTRACOLD ATOMIC GASES
College de France, May 14, 2013 SUPERFLUIDTY IN ULTRACOLD ATOMIC GASES Sandro Stringari Università di Trento CNR-INFM PLAN OF THE LECTURES Lecture 1. Superfluidity in ultra cold atomic gases: examples
More informationTopological Phenomena in Periodically Driven Systems: Disorder, Interactions, and Quasi-Steady States Erez Berg
Topological Phenomena in Periodically Driven Systems: Disorder, Interactions, and Quasi-Steady States Erez Berg In collaboration with: Mark Rudner (Copenhagen) Netanel Lindner (Technion) Paraj Titum (Caltech
More informationDisordered metals without quasiparticles, and charged black holes
HARVARD Disordered metals without quasiparticles, and charged black holes String Theory: Past and Present (SpentaFest) International Center for Theoretical Sciences, Bengaluru January 11-13, 2017 Subir
More informationTwo Dimensional Chern Insulators, the Qi-Wu-Zhang and Haldane Models
Two Dimensional Chern Insulators, the Qi-Wu-Zhang and Haldane Models Matthew Brooks, Introduction to Topological Insulators Seminar, Universität Konstanz Contents QWZ Model of Chern Insulators Haldane
More informationGroup Theory and Its Applications in Physics
T. Inui Y Tanabe Y. Onodera Group Theory and Its Applications in Physics With 72 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Contents Sections marked with
More informationImpurities and disorder in systems of ultracold atoms
Impurities and disorder in systems of ultracold atoms Eugene Demler Harvard University Collaborators: D. Abanin (Perimeter), K. Agarwal (Harvard), E. Altman (Weizmann), I. Bloch (MPQ/LMU), S. Gopalakrishnan
More informationNumerical estimates of critical exponents of the Anderson transition. Keith Slevin (Osaka University) Tomi Ohtsuki (Sophia University)
Numerical estimates of critical exponents of the Anderson transition Keith Slevin (Osaka University) Tomi Ohtsuki (Sophia University) Anderson Model Standard model of a disordered system H W c c c V c
More informationOptical Properties of Lattice Vibrations
Optical Properties of Lattice Vibrations For a collection of classical charged Simple Harmonic Oscillators, the dielectric function is given by: Where N i is the number of oscillators with frequency ω
More informationPropagation of longitudinal waves in a random binary rod
Downloaded By: [University of North Carolina, Charlotte At: 7:3 2 May 28 Waves in Random and Complex Media Vol. 6, No. 4, November 26, 49 46 Propagation of longitudinal waves in a random binary rod YURI
More informationWeak Ergodicity Breaking
Weak Ergodicity Breaking Eli Barkai Bar-Ilan University 215 Ergodicity Ergodicity: time averages = ensemble averages. x = lim t t x(τ)dτ t. x = xp eq (x)dx. Ergodicity out of equilibrium δ 2 (, t) = t
More informationDisordered topological insulators with time-reversal symmetry: Z 2 invariants
Keio Topo. Science (2016/11/18) Disordered topological insulators with time-reversal symmetry: Z 2 invariants Hosho Katsura Department of Physics, UTokyo Collaborators: Yutaka Akagi (UTokyo) Tohru Koma
More informationFloquet Topological Insulators and Majorana Modes
Floquet Topological Insulators and Majorana Modes Manisha Thakurathi Journal Club Centre for High Energy Physics IISc Bangalore January 17, 2013 References Floquet Topological Insulators by J. Cayssol
More informationTopological phases of matter give rise to quantized physical quantities
Quantized electric multipole insulators Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017). Quantized electric multipole insulators. Science, 357(6346), 61 66. Presented by Mark Hirsbrunner, Weizhan
More informationInteracting Electrons in Disordered Quantum Wires: Localization and Dephasing. Alexander D. Mirlin
Interacting Electrons in Disordered Quantum Wires: Localization and Dephasing Alexander D. Mirlin Forschungszentrum Karlsruhe & Universität Karlsruhe, Germany I.V. Gornyi, D.G. Polyakov (Forschungszentrum
More information