Density matrix and path integrals

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Table of contents

1 Bosons at low temperature 
1.1 Bose-Einstein condensation
1.2 Ultracold atomic gases
1.3 Density matrix and path integrals
1.4 Recursion method for non-interacting bosons
2 Few-body physics with strong interactions
2.1 Two-body physics
2.1.1 Scattering theory
2.1.2 Two-body density matrix
2.1.3 Correlation functions
2.2 Three-body physics and Efimov effect
2.2.1 Efimov trimers
2.2.2 Three-body-cutoff model
2.3 Ultracold atoms with strong interactions
2.3.1 Feshbach resonances
2.3.2 Signatures of the Efimov effect
3 Path-Integral quantum Monte Carlo
3.1 Monte Carlo sampling
3.1.1 Direct sampling
3.1.2 Markov-chain Monte Carlo
3.1.3 Variable-dimensionality sampling
3.2 Sampling quantum paths
3.2.1 Path integrals and Monte Carlo
3.2.2 Closed-sector moves
3.2.3 Open-sector moves
3.2.4 Sector-changing moves
3.3 Observables
3.3.1 Spatial correlation functions
3.3.2 Permutation cycles and superfluid densits
3.3.3 One-body-reduced density matrix
3.3.4 Momentum distribution and condensate fraction
3.4 Additional aspects related to PIMC
3.4.1 Superfluid transition and finite-size scaling
3.4.2 Large-momentum tail of n (k)
4 Many-body unitary bosons
4.1 Imaginary-time discretization revisited
4.2 Efimov liquid
4.2.1 Liquid/gas phase coexistence
4.2.2 QMC observation of the Efimov liquid
4.3 Normal-gas phase
4.3.1 Momentum distribution
4.3.2 Contact density
4.4 BEC phase
4.4.1 Critical temperature
4.4.2 Momentum distribution
4.4.3 Contact density
5 Classical three-body hard-core model 
5.1 Sampling configurations at fixed pressure
5.1.1 Box rescaling
5.1.2 Insertion/removal move
5.2 Packing problem
5.2.1 Variational ansätze
5.2.2 Simulated annealing
5.3 Finite-pressure phase diagrams
5.3.1 Two dimensions
5.3.2 Three dimensions