Path Integral Monte Carlo Simulations Of Uniform Boson And Fermion Systems

The fact that ~4He is liquid down to zero temperature under its own vapor pressure makes it a nearly perfect system for studying macroscopic quantum effects.Based on Path Integral theory by Feynman,We have programmed Path Integral Monte Carlo(PIMC)algorithm for low temperature ~4He systems and calculated the structure and energy of liquid ~4He systems between 1.17 K and 2.35 K.Our results match well with those of D.M.Ceperley's and the experiments by Robkoff,Hallock and Sears.Quantum effects could be seen in our results.We also find how quantum exchange effect affects the kinetic energy of ~4He particles.Under saturated vapor pressure,pair correlation functions of different temperature are calculated.Quantum exchange effect makes average kinetic energy larger.And temperature shows little effect on the pair correlation function.But real space PIMC could not solve the fermi sign program very well.We also write the code for Configuration Path Integral Monte Carlo method and simulate the non-interacting harmonic oscillator approaching thermodynamic equilibrium.Investigate the quantum exchange effect of fermion particles.Momentum distribution,energy and pair correlation function of uniform electron gas under different temperature and density0.8 a.u.< rs< 40 a.u.,0.5 < ? = kBT /EF< 2 are calculated by our code,which also match well with Fermi-Dirac distribution.