<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Q</mml:mi> </mml:math> -ball superradiance: Analytical approach

It was recently discovered that waves scattering off a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Q</a:mi> </a:math> ball can extract energy from it. We present an analytical treatment of this process by adopting a multistep function approximation for the background field, which yields perturbative solutions expressed in terms of Bessel functions. For thin-wall <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>Q</c:mi> </c:math> balls, the amplification factors reduce to simple sinusoidal functions, which explains the multipeak structure of the spectrum and identifies the physical quantities that determine it. For instance, at high frequencies, the peak spacing is simply the inverse of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>Q</e:mi> </e:math> -ball size. The analytical solution further enables us to delineate the full range of possible amplification factors. For general <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>Q</g:mi> </g:math> balls, this analytical framework also substantially improves the efficiency of evaluating the amplification factors.