Production of global vortices with quantum mediation

Abstract

We study global vortex production in (numerical) scattering experiments when the scatterer and the vortex degrees of freedom interact only due to intermediary quantum variables. We work in $2+1$ dimensions with a complex scalar field, $φ$, that supports global vortices, a real scalar field, $ψ$, that is the scatterer, and a quantum field, $ρ$, that couples to both $φ$ and $ψ$, acting as a mediator. We simulate the scattering of relativistic Gaussian wavepackets of $ψ$ and scan parameter space for regions where vortex-antivortex pairs are produced. The results show that vortex production is highly sensitive to the initial Gaussian parameters, and the parameter space is chaotic with ``holes" and isolated regions of vortex production.

Figures (8)

• Figure 1: $3\cross 3$ example of flattening 2d lattice into 1d
• Figure 2: Initial field configurations for $\phi$ and $\psi$
• Figure 3: Three snapshots of the time evolutions of fields $\phi$ and $\psi$ (top and bottom rows, respectively) for parameters $A=94$, $v=0.55$ and $k=0.05$. Columns show the system at times near peak Gaussian wavepackets overlap, during initial vortex production, and at later times, respectively.
• Figure 4: (a), (b) Energy density of $\rho$ ($\epsilon_{\rho}^R$) before and after the vortex formation respectively for parameters $A=94$, $v=0.55$ and $k=0.05$. The imprints of the $\phi$ and $\psi$ interactions are visible. (a) $\epsilon^{R}_{\rho}$ fluctuates rapidly until the formation of the first vortices, and (b) simmers down after the formation.
• Figure 5: (a) Total energies of individual fields over time for parameters $A=94$, $v=0.55$, and $k=0.05$. The interaction energies are included in $\rho$ after suitable renormalizations. The total energies for fields $\phi$ and $\psi$ include only kinetic, gradient, and potential contributions; interaction energies are not included to avoid double counting. (b) Kinetic, gradient, and potential energy contributions of $\phi$ over time. The potential energy experiences a jump around the time of vortex formation at $t=1$.