We derive a mathematical mechanism of infrared catastrophe from the idea for the proof in [22, 23] and generalize it so that we can apply it to several models in quantum field theory. We define the Carleman operator from the operator-theoretical pull-through formula on ground states. Characterizing infrared catastrophe by the Carleman operator, we study the mechanism of infrared catastrophe. An...

The characteristic features of the collapse of the ground state in trapped one-component attractive Bose-Einstein condensates are studied by applying the catastrophe theory. From numerically obtained stable and unstable solutions of the Gross-Pitaevskii equation, we derive the catastrophe function defining the stability of the stationary points on the Gross-Pitaevskii energy functional. The bif...

Microtubules are long filamentous protein structures that randomly alternate between periods of elongation and shortening in a process termed dynamic instability. The average time a microtubule spends in an elongation phase, known as the catastrophe time, is regulated by the biochemical machinery of the cell throughout the cell cycle. In this light, observed changes in the catastrophe time near...