The Specific Heat of a Fermi Gas at Low Temperature: A closer look at the TlnT behavior

TL;DR

This paper investigates the low-temperature specific heat of a Fermi gas, revealing that certain diagram contributions cancel out the expected TlnT behavior, challenging previous assumptions about screening effects.

Contribution

It provides a detailed calculation showing the cancellation of TlnT behavior by new diagram contributions, offering a refined understanding of Fermi gas thermodynamics.

Findings

Cancellation of TlnT behavior due to new diagram contributions

Screening effects are not essential for the anomaly

Finite temperature effects alter the thermodynamic potential

Abstract

At finite temperature, a Fermi gas can have sates that hold simultaneously a particle and a hole with a finite probability. This gives rise to a new set of diagrams that are absent at zero temperature. The so called "anomalous" diagram is just one of the new diagrams. We have already studied the contribution of these new diagrams to the thermodynamic potential (Phys. Lett. A224, 127 (1996) ). Here we continue that work and calculate their effect on the specific heat. We will also calculate the finite temperature contribution of the ring diagrams. We conclude that the TlnT behavior due to exchange gets canceled by the new contribution of the new diagrams and screening is not essential to solve this anomaly.