Field Theories In Condensed Matter Physics
Field Theories inCondensed Matter PhysicsEdited bySumathi RaoHarish-Chandra Research InstituteAllahabadloPInstitute of Physics PublishingBristol and Philadelphia
ContentsPrefacexiiiIntroduction117Quantum Many Particle PhysicsPinaki ntroduction to many particle physics1.3.1 Phases of many particle systems1.3.2 Quantities of physical interest1.3.3 Fermi and Bose liquidsPhase transitions and broken symmetry1.4.1 Phase transitions and symmetry breaking .1.4.2 Symmetry breaking and interactions in ВЕСNormal Fermi systems: model problems1.5.1 Neutral fermions: dilute hardcore Fermi gas1.5.2 Charged fermions: the electron gasElectrons and phonons: Migdal-Eliashberg theory .1.6.1 Weak coupling theory: BCS1.6.2 The normal state: Migdal theory1.6.3 BCS theory: Greens function approach . . .1.6.4 Superconductivity: Eliashberg theory . . .Conclusion: 'field theory' and many particle physics8810101214222225313439464852565863
viii2CONTENTSCritical PhenomenaSomendra M. le2.1.1 Large system: Thermodynamic limit .Where is the problem?Recapitulation - A few formal stuff2.3.1 Extensivity2.3.2 Convexity: StabilityConsequences of divergenceGeneralized scaling2.5.1 One variable: Temperature2.5.2 Solidarity with thermodynamics2.5.3 More variables: Temperature and field2.5.4 On exponent relationsRelevance, irrelevance and universalityDigression2.7.1 A first-order transition: a l2.7.2 Example: Polymers : no "ordering" .Exponents and correlations2.8.1 Correlation function2.8.2 Relations among the exponents2.8.3 Length-scale dependent parametersModels as examples: Gaussian and ф42.9.1 Specific heat for the Gaussian model .2.9.2 Cut-off and anomalous dimensions2.9.3 Through correlationsEpilogue3 Phase Transitions and Critical PhenomenaDeepak Kumar3.13.23.33.4IntroductionThermodynamic stabilityLattice gas : mean field approximationLandau 3105106107110112119120121126134
al correlationsBreakdown of mean field theoryGinzburg-Landau free energy functionalRenormalisation group (RG)RG for a one dimensional Ising chainRG for a two-dimensional Ising modelGeneral features of RG3.11.1 Irrelevant variablesRG scaling for correlation functionsRG for Ginzburg-Landau model3.13.1 Tree-level approximation3.13.2 Critical exponents for d 43.13.3 Anomalous dimensionsPerturbation series for d 4Generalisation to a n-component modelTopological DefectsAjit M. 032092132162172192274.34.44.54.64.74.8The subject of topological defectWhat is a topological defect?4.2.1 Meaning of order parameter4.2.2 Spontaneous symmetry breakdown(SSB) . .4.2.3 SSB in particle physics4.2.4 Order parameter spaceThe domain wall4.3.1 Why defect?4.3.2 Why topological?4.3.3 Energy considerationsExamples of topological defectsCondensed matter versus particle physicsDetailed understanding of a topological defect . . .4.6.1 Free homotopy of maps4.6.2 Based homotopy and the fundamental groupClassification of defects using homotopy groups . .Defect structure in liquid crystals
CONTENTS4.94.8.1 Defects in nematics4.8.2 Non abelian ж\ - biaxial nematicsFormation of topological defects228230231Introduction to BosonizationSumathi Rao and Diptiman Sen2395.15.2Fermi and Luttinger liquidsBosonization5.2.1 Bosonization of a fermion with one chirality5.2.2 Bosonisation with two chiralities5.2.3 Field theory near the Fermi "momenta . . .5.3 Correlation functions and dimensions of operators5.4 RG analysis of perturbed models . .5.5 Applications of bosonization5.6 Quantum antiferromagnetic spin 1/2 chain5.7 Hubbard model5.8 Transport in a Luttinger liquid - clean wire . . . .5.9 Transport in the presence of isolated impurities . .5.10 Concluding tum Hall EffectR. ssical Hall effectQuantized Hall effectLandau problemDegeneracy countingLaughlin wavefunctionPlasma analogyQuasi-holes and their Laughlin wavefunctionLocalization physics and the QH plateauxChern-Simons theoryVortices in the CS field and quasiholesJain's theory of composite fermions336337338340341342. . . 344345348354355
CONTENTS7 Low-dimensional Quantum Spin SystemsIndrani Böse7.17.27.37.47.5IntroductionGround and excited statesTheorems and rigorous results for antiferromagnets7.3.1 Lieb-Mattis theorem7.3.2Marshall's sign rule7.3.3Lieb, Schultz and Mattis theorem7.3.4 Mermin-Wagner theoremPossible ground states and excitation spectra . . .The Bethe AnsatzXI359360365369369370372376376387
Field Theories in Condensed Matter Physics Edited by Sumathi Rao Harish-Chandra Research Institute Allahabad loP Institute of Physics Publishing Bristol and Philadelphia . Contents Preface xiii Introduction 1 1 Quantum Many Particle Physics 7 Pinaki Majumdar 1.1 Preamble 8
in condensed matter physics. [6] P. W. Anderson, Basic Notions in Condensed Matter Physics, Benjamin (1984). Inspirational but not tutorial — a highly subjective view of modern condensed matter physics from one of the most influential figures. [7] S. Coleman, Aspects in Symmetry — Selected Erice Lectures (CUP), 1985. Chapter
Topological field theories in Condensed Matter (eg., Quantum Hall fluids) Bill Unruh: Dumb Holes: The physics around black holes can be modeled . by condensed matter systems (sound waves, surfaces in fluids. giving clues to where the particles in black hole evaporation come .
common basis for this fortunate convergence between condensed matter and relativistic field theories. 1. Introduction In a study of the spectrum for a one-dimensional, spinless Fermi field coupled to a broken symmetry Bose field, Jackiw and Rebbi (JR) [1] noted the occurrence of a
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These condensed interim financial statements were approved for issue on 29 August 2020. The financial statements have been reviewed, not audited. Condensed consolidated statement of profit or loss 5 Condensed consolidated statement of comprehensive income 6 Condensed consolidated balance sheet 7
07 Condensed consolidated statement of financial position 08 Condensed consolidated statement of changes in equity 09 Condensed consolidated statement of cash flows . MultiChoice Group / Condensed consolidated interim financial statements for the period ended 30 September 2020 / 01. slightly more than the prior year due to higher
In fact, condensed matter physics is by far the largest single subfield of physics (the annual meeting of condensed matter physicists in the United States attracts over 6000 physicists each year!). Sadly a first introduction to the topic can barely scratch the surface of what constitutes the broad field of condensed matter.
Keywords --- algae, o pen ponds, CNG, renewable, methane, anaerobic digestion. I. INTRODUCTION Algae are a diverse group of autotrophic organisms that are naturally growing and renewable. Algae are a good source of energy from which bio -fuel can be profitably extracted [1].Owing to the energy crisis and the fuel prices, we are in an urge to find an alternative fuel that is environmentally .
