Anomalies on Quantum Gases in One and Two Dimensions



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This dissertation utilizes particle physics and quantum field theory (QFT) background to advance an approach to the study of quantum scaling anomalies in low-dimensional (2D and 1D) ultracold Fermi gases. Deeper studies of these aspects of atomic physics will not only further our fundamental understanding of the physics but will also likely impact the ability to control and manipulate these systems. The precise connection between 2D quantum scaling anomalies and Tan contact term is established and used to study aspects of thermodynamics of ultracold atoms, in particular, the virial expansion. The approach, beyond being a different scheme for addressing issues in atomic physics, provides a framework that seeks to add insight as well, and it has proven to do so. An extension of the ideas for 2D, two-body attractive contact interactions to 1D, 3-body attractive contact interacting fermions (three species) is also formulated in this work. We calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, We show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case, which in turn serves as a natural renormalization condition for numerical calculation of the path integral in such a system. This has opened the door to extensive theoretical investigations, as well as connections with possible experiments.



Anomalies, Ultracold, Low dimensional gases, Qft, Path integrals


Portions of this document appear in: Daza, W., Joaquín E. Drut, C. Lin, and C. Ordóñez. "Virial expansion for the Tan contact and Beth-Uhlenbeck formula from two-dimensional SO (2, 1) anomalies." Physical Review A 97, no. 3 (2018): 033630. And in: Drut, Joaquín E., Joshua R. McKenney, Wilder S. Daza, Chris L. Lin, and Carlos R. Ordóñez. "Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions." Physical review letters 120, no. 24 (2018): 243002.