Bound-State Formation of Quantum Many-Flavor Systems: The Divergence of the Critical Coupling (2016)

Undergraduates: Tyler Blanton, Philip Javernick, Andrew Loheac

Faculty Advisor: Joaquin Drut
Department: Physics & Astronomy

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When multiple quantum particles of different species -- or "flavors" -- are allowed to interact via pairwise interactions, they may form bound states. If these interactions can be modeled by an attractive contact potential, the strength of the attractions depend on a single parameter: the coupling g. In 3D, when two or more flavors are present, it is possible for the system to form a bound state when g is above a certain finite threshold gc. In contrast, a one-flavor system is just a free particle and can only exist in scattering states (i.e., gc is infinite). Although non-integer flavor numbers are non-physical, they are mathematically valid and can be used to examine the analytic relationship between Nf and gc. We used computational methods to vary Nf in the continuum interval (1,2] in an effort to determine the manner in which gc diverges as Nf goes to 1. We used Fortran and Python to simulate many-body quantum systems with parameters Nf and g. Specifically, we used Projection Monte Carlo to calculate the ground-state energies E of these systems. Plotting E vs. g, we obtained the critical coupling gc at which bound-state formation occurred for each Nf sampled. Determining the manner in which gc diverges has the potential to aid in theoretical fields such as QCD -- where similar problems related to flavor number arise in the study of quarks -- as well as in the experimental study of ultra-cold atoms, where the quantum simulation of arbitrary systems is becoming a reality.