Computational Physics - Department of Physics

16.11 Efficient Optimization of the Trial Wave Function 529 16.11Efficient Optimization of the Trial Wave Function Energy minimi ...

530 16 Improved Monte Carlo Approaches to Systems of Fermions d dt (||A) = (||A)tr ( A−^1 dA dt ) d dt ln||A(t) =tr ( A−^1 dA dt ...

16.12 Exercises 531 InitializeR, setαand ΨT−α(R) Suggest a move Compute ac- ceptance ratio Generate a uniformly distributed vari ...

532 16 Improved Monte Carlo Approaches to Systems of Fermions which you need to program will be discussed during the lectures. C ...

16.12 Exercises 533 φ 2 p(ri) =αrie−αri/^2. (16.53) Observe thatri= √ r^2 ix+r^2 iy+ri^2 z. Set up the Hartree-Fock equations f ...

534 16 Improved Monte Carlo Approaches to Systems of Fermions φnx,ny(x,y) =AHnx( √ ωx)Hny( √ ωy)exp(−ω(x^2 +y^2 )/ 2. The functi ...

16.12 Exercises 535 to make modules or classes of trial wave functions, both many-body wave functions and single- particle wave ...

536 16 Improved Monte Carlo Approaches to Systems of Fermions H 4 (x) = 16 x^4 − 48 x^2 + 12. They fulfil the orthogonality rela ...

Chapter 17 Bose-Einstein condensation and Diffusion Monte Carlo AbstractWe discuss how to perform diffusion Monte Carlo calculat ...

538 17 Bose-Einstein condensation and Diffusion Monte Carlo any relevant physical properties of our system since it is generally ...

17.1 Diffusion Monte Carlo 539 The second term is called abranching term. When positive, it induces a growth of the number of wa ...

540 17 Bose-Einstein condensation and Diffusion Monte Carlo GK(x,x′′,t) =〈x|e−Kt̂|x′′〉 = 1 ( 2 π)^3 N ∫ 〈x|k〉e−Dk (^2) t 〈k|x′′〉 ...

17.1 Diffusion Monte Carlo 541 17.1.1Importance Sampling Let us introduce a time independent trial wave functionΨT(x). We define ...

542 17 Bose-Einstein condensation and Diffusion Monte Carlo A(x,x′,t) =min [ 1 , GK(x′,x) GK(x,x′) |ΨT(x)|^2 |ΨT(x′)|^2 ] (17.11 ...

17.2 Bose-Einstein Condensation in Atoms 543 Importance sampling makes it also to some extent easier to deal with wave functions ...

544 17 Bose-Einstein condensation and Diffusion Monte Carlo Under such circumstances it is unavoidable to test the accuracy of t ...

17.3 Exercises 545 17.3 Exercises. 17.1.The aim of this project is to use the Variational Monte Carlo (VMC) method and evaluate ...

546 17 Bose-Einstein condensation and Diffusion Monte Carlo for the above trial wave function of Eq. (17.22). Compute also the a ...

17.3 Exercises 547 What is the expression forγ? Choose the initial value forβ=γ= 2. 82843 and set up a VMC pro- gram which compu ...

548 17 Bose-Einstein condensation and Diffusion Monte Carlo References. J. Dongarra, F. Sullivan, Computing in Science and Engi ...