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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

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Linear Scaling Pseudo Fermi-Operator Expansion for Fractional Occupation.

Susan M Mniszewski¹, Romain Perriot², Emanuel H Rubensson³

¹Computer, Computational, and Statistical Sciences Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States.

Journal of Chemical Theory and Computation

|November 20, 2018

Summary

This summary is machine-generated.

Recursive Fermi-operator expansion methods are extended to include fractional occupation numbers, enabling free energy calculations with approximate Fermi-Dirac distributions. This approach enhances electronic structure calculations across various methods.

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Area of Science:

Computational chemistry
Quantum mechanics
Materials science

Background:

Recursive Fermi-operator expansion methods are limited to zero electronic temperature and integer occupation numbers.
Calculating the idempotent density matrix is crucial for electronic structure theory.

Purpose of the Study:

To modify recursive Fermi-operator expansion methods for fractional occupation numbers.
To develop a method for calculating the entropy term of free energy with approximate Fermi-Dirac distributions.

Main Methods:

Modification of recursive Fermi-operator expansion.
Inclusion of fractional occupation numbers and pseudo Fermi-Dirac distribution.
Calculation of the entropy term for free energy.

Main Results:

The proposed methodology successfully incorporates fractional occupation numbers.
The entropy term of the free energy can be calculated using the modified methods.
The approach is validated across density functional tight-binding, Kohn-Sham DFT, and Hartree-Fock theories.

Conclusions:

The generalized recursive Fermi-operator expansion methods provide a robust framework for electronic structure calculations at finite temperatures.
This work extends the applicability of these methods to a broader range of systems and conditions.
The accurate calculation of free energy is essential for understanding chemical and physical processes.