hartree-fock approximation for bec revisited hartree-fock approximation for bec revisited jürgen...
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Hartree-Fock approximation for BEC Hartree-Fock approximation for BEC revisitedrevisited
Jürgen BosseJürgen BosseFreie Universität BerlinFreie Universität Berlin
Panjab University, Chandigarh 3rd March, 2014
Overview
Introduction Thermodynamic Variational Principle Review: HFA for T >Tc
T ≤ Tc : Exc modified by <N02>
HFA including ground-state fluctuations T ≤ Tc : chemical potential
grand-canonical potential
A = - ( H r - Nop )A+B = - ( H - Nop )
e.g., interacting bosons in a trap
Variational Principle
1. Calculate GCP-upper bound using reference hamiltonian of single-particle type2. Find effective hamiltonian (HF) from extremum conditions for upper-bound
grand-canonical potential
A = - ( H r - Nop )A+B = - ( H - Nop )
e.g., interacting bosons in a trap
Variational Principle
1. Calculate GCP-upper bound using reference hamiltonian of single-particle type2. Find effective hamiltonian (HF) from extremum conditions for upper-bound
average occupation number of state | k >
inadequate for bosonsincondensed phase(T ≤ Tc)
Calculation of GCP-upper bound
average occupation number of state | k >
inadequate for bosonsincondensed phase(T ≤ Tc)
Calculation of GCP-upper bound
average occupation number of state | k >
Calculation of GCP-upper bound
<Nkk>
(1-clk)
ground-state fluctuationsmodify Exc
<Nkk> <Nll>
[{j},{j}, N0, f0]
Fluctuation effect on chemical potential appears to be small
ng
2ng
Uniform Gas of s=0 Bosons Interacting via Repulsive Contact
ideal interacting