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breakdown of perturbation approach ! Fermi liquid theory - - PowerPoint PPT Presentation
breakdown of perturbation approach ! Fermi liquid theory - - PowerPoint PPT Presentation
Fermi liquid theory 1 Concept of Landau's Fermi liquid theory elementary excitations of interacting Fermions are described by almost independent fermionic quasiparticles state of Fermi liquid described simply by quasiparticle distribution
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Fermi liquid theory
couplings:
symmetric (charge) antisymmetric (spin)
spherical symmetry:
Legendre Polynomials
Landau parameters:
charge spin 3
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Fermi liquid theory - physical properties
specific heat: compressibility: spin susceptibility:
change of Fermi volume spin splitting
- f Fermi sea
T
thermal softening
- f Fermi surface
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Fermi liquid theory - Gallilei invariance
momentum shift for all particles
shifted Fermi sea
''bare particle'' view quasiparticle view
current density quasiparticle motion induced motion intrinsic consistency
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Fermi liquid theory - 3He Fermi liquid
diminished enhanced enhanced
strong short-range repulsion
Fermi liquid
longer-ranged attraction
superfluid
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Fermi liquid theory Microscopic considerations
Hamiltonian
contact interaction „perturbation“ kinetic energy
Fermi liquid theory
Landau parameters Rayleigh-Schrödinger perturbation theory
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Fermi liquid theory Microscopic considerations
Rayleigh-Schrödinger energy: Distribution function
characterizes unperturbed state
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Fermi liquid theory Microscopic considerations
Rayleigh-Schrödinger 9
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Fermi liquid theory Microscopic considerations
Rayleigh-Schrödinger
Fermi sea
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Fermi liquid theory Microscopic considerations
Rayleigh-Schrödinger
Fermi sea
cutoff
interaction range weak K-dependence
„screening“
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Fermi liquid theory Microscopic considerations
Rayleigh-Schrödinger cancels relabeling 12
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Fermi liquid theory Microscopic considerations
Rayleigh-Schrödinger 13
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Fermi liquid theory Microscopic considerations
Rayleigh-Schrödinger variation: 14
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Fermi liquid theory Microscopic considerations
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Fermi liquid theory Microscopic considerations
Lindhard function
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Fermi liquid theory Microscopic considerations
Lindhard function
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Fermi liquid theory Microscopic considerations
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Fermi liquid theory Microscopic considerations
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Fermi liquid theory Microscopic considerations
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Fermi liquid theory Microscopic considerations
Landau parameters: 21
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Fermi liquid theory Microscopic considerations
Landau parameters:
repulsive interaction
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Fermi liquid theory Microscopic considerations
repulsive interaction less compressible more spin polarizable higher effective mass
ferromagnetism 23
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Fermi liquid theory Microscopic considerations
distribution function ground state 24
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Fermi liquid theory Microscopic considerations
distribution function 3-dimensional Fermigas 25
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Fermi liquid theory Microscopic considerations
distribution function Z
quasiparticle weight
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Fermi liquid theory one-dimensional systems
Landau parameters
breakdown of perturbation approach !
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distribution function 1-dimensional Fermigas
non-perturbative
Fermi liquid theory one-dimensional systems
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distribution function 1-dimensional Fermigas
non-perturbative
Z=0
no quasiparticle weight
not a Fermi liquid
Tomonaga Luttinger liquid Fermi liquid theory one-dimensional systems
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