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

Tyler D. Blanton

Published Aug 21, 2019• 0 citations

Abstract

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 will 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 if the coupling is above a certain finite threshold g[c]. In contrast, a one-flavor system is just a free particle and can only exist in scattering states (i.e., g[c] = ∞). Although non-integer flavor numbers N[f] have no obvious physical meaning, they are mathematically valid and can be used to examine the analytic relationship between N[f] and g[c]. We used computational methods to vary N[f] in the continuum interval (1,2] in an effort to determine the manner in which g[c] → ∞ as N[f] → 1+. We used Fortran and Python to calculate many-body quantum systems with parameters N[f] and g. Specifically, we used the projection Monte Carlo method to calculate the ground-state energies E[0] of these systems. Plotting E[0] vs. g, we obtained the critical coupling g[c] at which bound state formation occurred for each N[f] sampled. Determining the manner in which g[c] diverges sees applications 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 ultracold atoms, where the quantum simulation of increasingly arbitrary systems is becoming a reality.

DOI: 10.17615/00f0-b531

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