Landau Fermi Liquids and Beyond 1st Edition by Tripathi 1351121972 9781351121972

Landau Fermi Liquids and Beyond 1st Edition by V. Tripathi – Ebook PDF Instant Download/DeliveryISBN:  1351121972, 9781351121972 

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ISBN-10 :  1351121972 

ISBN-13 : 9781351121972

Author:  V. Tripathi 

This book consolidates the older and more recent concepts on weakly-interacting fermions where traditional many-body techniques are adequate. Targeting primarily the advanced undergraduates and graduates, the author has included plenty of examples and problems from contemporary topics of research.

Landau Fermi Liquids and Beyond 1st Table of contents:

I Phenomenology of Fermi Liquids
1. Quasiparticle concept
1.1 Noninteracting fermions
1.1.1 Low energy properties of a fermi gas
1.2 Quasiparticles
1.2.1 Quasiparticle lifetime
1.2.2 Quasiparticle energy and interaction
1.3 Thermodynamic properties
1.3.1 Effective mass and specific heat
1.3.2 Compressibility and speed of sound
1.3.3 Pauli susceptibility
1.4 Landau postulates and bethe ansatz integrable systems
2. Pomeranchuk Stability Conditions
2.1 Fermi surface deformation and excitation free energy
2.1.1 Pomeranchuk stability conditions
2.2 Stoner ferromagnetism
3. Collective excitations and zero sound
3.1 Transport equation for a Fermi liquid
3.1.1 Limits of validity of the transport equation
3.2 Sound propagation at high frequencies
3.3 Zero sound involving spin
3.4 Damped zero sound
4. Scattering Theory
4.1 Scattering phase shift
4.2 Cross section and scattering function
4.3 Partial wave expansion
4.4 Born approximation
4.4.1 The T–matrix
4.5 Friedel sum rule
5. Fermi Liquid Regime of the Kondo Problem
5.1 The Kondo effect
5.2 Physics below the Kondo temperature
5.2.1 Failure of perturbative approaches
5.2.2 Nozières’ Fermi liquid theory for T < TK
II Microscopic Approach
6. Response of an ideal fermi gas
6.1 Thomas‐fermi and lindhard polarizability
6.1.1 Polarizability and dielectric function
6.1.2 Thomas‐Fermi polarizability
6.1.3 Lindhard polarizability
6.1.3.1 Frequency dependence
6.2 Friedel and RKKY oscillations
6.2.1 Friedel oscillations
6.2.2 RKKY interaction
6.2.2.1 Giant magnetoresistance in multilayers
6.3 Hartree and Hartree‐Fock approximations
6.3.1 Hartree approximation
6.3.2 Hartree‐Fock approximation
6.3.2.1 Fermi liquid parameters
6.3.2.2 Compressibility and susceptibility
6.4 Electrons in metal crystals
6.4.1 Electrons in a rigid lattice
6.4.2 Phonons in metals
6.4.2.1 Kohn anomalies
6.4.2.2 Dielectric function of a metal
6.4.2.3 Phonon correction to electron energies
6.5 Anderson orthogonality catastrophe
6.6 Diffusion of muons in metal crystals
6.7 Screening of transverse fields in metals
7. Collective Excitations
7.1 Plasma waves
7.2 Spin waves
8. Effect of Disorder on Electron Interactions
8.1 Altshuler-Aronov corrections to density of states
8.2 Renormalization of the electron relaxation rate
9. Bridging Phenomenological and Microscopic Aspects
9.1 Proper self‐energy Σ and vertex function Γ
9.1.1 Vertex function
9.2 ω/k singularities of the vertex function, relation to Landau f‐functions
9.3 Ward identities
9.3.1 Response functions
9.4 Luttinger’s theorem
9.5 Stoner instability and transition to ferromagnetic metal phase
9.5.1 Relation to microscopics of Landau Fermi liquid theory
9.6 Hertz theory
9.6.1 Landau‐Ginzburg‐Wilson free energy functional
9.6.1.1 Hubbard‐Stratonovich transformation
9.6.1.2 Effective free energy
9.6.2 Spin fluctuation effects
9.6.2.1 Perturbative renormalization group
9.6.2.2 Solution of Hertz‐Millis RG equations
9.6.2.3 Physical consequences of spin fluctuations
III Beyond Fermi Liquid Theory
10. Effect of Ampere Forces in Fermi Liquids
10.1 Effective action for transverse electromagnetic fluctuations in metals
10.2 Breakdown of the Landau Fermi liquid state
11. Overscreened Kondo Model and Nozières‐ulandin Theory
11.1 Formation of local magnetic moments in a metal
11.1.1 Schrieffer‐Wolff transformation
11.2 Perturbation theory for single‐channel Kondo model
11.3 Poor man’s scaling
11.4 Nozières‐Blandin theory of the overscreened Kondo model
11.4.1 Magnetic impurities in almost ferromagnetic metals
IV Open Questions
12. Electron Lifetime in a Mesoscopic Conductor
12.1 Meaning of quasiparticle decay
12.2 Qualitative estimate of transition energy
12.3 Localization transition in Fock space
13. Marginal Fermi Liquids

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