Thermodynamics of harmonically trapped fermions in one dimension via non-uniform lattice Monte Carlo (2015)

Undergraduate: Dhruv Mittal

Faculty Advisor: Joaquin Drut
Department: Physics & Astronomy

---

By characterizing the thermodynamic properties of one dimensional systems of a certain class of particle called fermions, we can obtain benchmarks for many-body problems that are useful in nuclear and condensed matter physics, as well as in experiments with ultra-cold atoms. Energies and particle numbers were calculated numerically by means of a non-uniform lattice Monte Carlo simulation. The parameter-space of the problem was explored: the system temperature, particle interaction strength, and chemical potential were varied, and the values of various thermodynamic properties were examined. In particular, we determine the density, pressure, compressibility, and a many-body parameter called Tan's contact for a variety of short-range attractively interacting fermions confined within a potential energy well in the shape of a quantum harmonic oscillator.