THE FLOW EQUATION APPROACH TO MANY-PARTICLE SYSTEMS

By EMMA PEREZ

CONTENTS INTRODUCTION MOTIVATION FLOW EQUATIONS: BASIC IDEAS OUTLINE AND SCOPE OF THIS BOOK REFERENCES TRANSFORMATION OF THE HAMILTONIAN ENERGY SCALE SEPARATION POTENTIAL SCATTERING MODEL KONDO MODEL FLOW EQUATION APPROACH IN?NITESIMAL UNITARY TRANSFORMATIONS CHOICE OF GENERATOR FLOW EQUATIONS EXAMPLE: POTENTIAL SCATTERING MODEL SETTING UP THE FLOW EQUATIONS METHODS OF SOLUTION STRONG-COUPLING CASE EVALUATION OF OBSERVABLES EXPECTATION VALUES ZERO TEMPERATURE NONZERO TEMPERATURE CORRELATION FUNCTIONS FLUCTUATION–DISSIPATION THEOREM EXAMPLES RESONANT LEVEL MODEL INTERACTING MANY-BODY SYSTEMS NORMAL-ORDERING BOSONS FERMIONS IMPORTANT COMMUTATORS NORMAL-ORDERED EXPANSIONS NORMAL-ORDERING WITH RESPECT TO WHICH STATE? EXPANSION IN 1ST ORDER (1-LOOP RESULTS) EXPANSION IN 2ND ORDER (2-LOOP RESULTS) TRANSFORMATION OF THE SPIN OPERATOR SPIN CORRELATION FUNCTION AND DYNAMICAL SUSCEPTIBILITY PSEUDOGAP KONDO MODEL SPIN–BOSON MODEL FLOW OF THE HAMILTONIAN LOW-ENERGY OBSERVABLES RESONANT BEHAVIOR INTERACTING FERMIONS IN D > 1 DIMENSIONS FLOW EQUATIONS AND FERMI LIQUID THEORY FLOW EQUATIONS AND MOLECULAR-FIELD TYPE HAMILTONIANS OTHER APPLICATIONS CONSTRUCTION OF E?ECTIVE HAMILTONIANS: THE FR¨OHLICH TRANSFORMATION RE-EXAMINED BLOCK-DIAGONAL HAMILTONIANS MODERN DEVELOPMENTS STRONG-COUPLING BEHAVIOR: SINE–GORDON MODEL SINE–GORDON MODEL FLOW EQUATION ANALYSIS CONVENTIONAL SCALING VS FLOW EQUATIONS STEADY NON-EQUILIBRIUM: KONDO MODEL WITH VOLTAGE BIAS KONDO MODEL IN NON-EQUILIBRIUM CORRELATION FUNCTIONS IN NON-EQUILIBRIUM: SPIN DYNAMICS REAL TIME EVOLUTION: SPIN–BOSON MODEL OUTLOOK AND OPEN QUESTIONS