By Elijah Smith, Ariel Zimmer

Faculty Mentor: Dr. Makhija

Abstract

According to the Eigenstates Thermalization Hypothesis (ETH), a wavepacket of energy eigenstates of a system undergoing unitary time evolution will eventually be well-described by statistical mechanics. Research on quantum asymmetric tops, rigid bodies which have three different moments of inertia along their principal axes, has indicated that wavepackets may exhibit transitions from regions of instability to regions of stability. Furthermore, numerical studies on weakly perturbed multiparticle systems indicate that the ETH holds for them. Thus, the ETH could potentially hold for asymmetric tops in the regions of instability, or when the top is perturbed by an external electric field. To investigate this, we solved the Time Independent Schrödinger Equation for asymmetric top molecules with varying degrees of symmetry and graphed expectation values of measurable operators as a function of energy. From these graphs, we were able to identify what are believed to be regions of instability. In addition, we observe regions in which the expectation values vary smoothly as a function of energy. Based on previous work, wavepackets of states in these regions could exhibit thermal behavior. As a next step, we will construct these wavepackets and compute the time evolution of the expectation values to check if the ETH holds in these regions.