1 / 11

Finite Temperature Path Integral Method for Fermions and Bosons: a Grand Canonical Approach

Finite Temperature Path Integral Method for Fermions and Bosons: a Grand Canonical Approach. M. Skorobogatiy and J.D. Joannopoulos MIT. Non Zero Temperature DFT. Self-Consistent Algorithm for Finding Density Matrix. Given density matrix calculate. Given H KS calculate.

asa
Download Presentation

Finite Temperature Path Integral Method for Fermions and Bosons: a Grand Canonical Approach

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Finite Temperature Path Integral Method for Fermions and Bosons: a Grand Canonical Approach M. Skorobogatiy and J.D. Joannopoulos MIT

  2. Non Zero Temperature DFT

  3. Self-Consistent Algorithm for Finding Density Matrix Given density matrix calculate Given HKS calculate Fixing the number of particles update m Done Self-consistency is reached No Yes

  4. Ways of evaluating 1) Explicit Hamiltonian diagonalization – expansion into the eigen modes ψof a Hamiltonian 2) Implicit Hamiltonian diagonalization – expansion into any complete set of modes ψ

  5. Ways of evaluating 1) Expansion into polynomial series 2) Integral representation 3) Path integral representation – 2) assumes |ψ>=|r>, evaluates 2) by introducing intermediate states and separating kinetic and potential energies

  6. Power of Path Integral Formulation quantum particle at T P classical particles at PT

  7. Natural Variables in a Path Integral Approach hP xP

  8. Universal Functional

  9. Evaluation of D(xP,hP ) xP hP

  10. Universal Potential Fferm(1,P,xP,hP) xP hP

  11. Conclusions • Path Integral Formalism allows an elegant separation of “universal” and “system-dependent” properties for a particular problem • Universal potential can be calculated in advance and used with different systems • Advanced Monte-Carlo techniques can be used to evaluate a “system-dependent” distribution of natural variables

More Related