Presenter's Name(s)

Jiangyong YuFollow

Primary Faculty Mentor Name

Adrian Del Maestro

Secondary Mentor NetID

hbarghat

Secondary Mentor Name

Hatem Barghathi

Status

Undergraduate

Student College

College of Arts and Sciences

Program/Major

Physics

Primary Research Category

Engineering & Physical Sciences

Presentation Title

Stable Recursion Relation for the Canonical Partition Function of Non-Interacting Fermions

Time

9:50 AM

Location

Williams Family Room

Abstract

While the thermodynamics of a system of non-interacting fermions can be straightforwardly determined in the grand canonical ensemble, results for a specific number of N particles are more difficult to obtain. In this talk we will present a general recursion scheme for the canonical partition function of free fermions with a quadratic energy level spacing as might be present for ultracold fermionic atoms confined inside a box trap. Exact results for the entropy, specific heat and one and two particle occupation probabilities are numerically obtained to arbitrary precision and compared with their corresponding grand canonical values. The numerical stability of the recursion relation allows us to quantify deviations from Wicks theorem in the canonical ensemble for a variety of temperatures and densities.

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Stable Recursion Relation for the Canonical Partition Function of Non-Interacting Fermions

While the thermodynamics of a system of non-interacting fermions can be straightforwardly determined in the grand canonical ensemble, results for a specific number of N particles are more difficult to obtain. In this talk we will present a general recursion scheme for the canonical partition function of free fermions with a quadratic energy level spacing as might be present for ultracold fermionic atoms confined inside a box trap. Exact results for the entropy, specific heat and one and two particle occupation probabilities are numerically obtained to arbitrary precision and compared with their corresponding grand canonical values. The numerical stability of the recursion relation allows us to quantify deviations from Wicks theorem in the canonical ensemble for a variety of temperatures and densities.