Explicit asymptotic velocity of the boundary between particles and antiparticles

Details Explicit asymptotic velocity of the boundary between particles and antiparticles Explicit asymptotic velocity of the boundary between particles and antiparticles

2011-10-21

arxiv.org/abs/1110.4776v1

Mathematics

Probability

25 pages

Scientific paper

On the real line initially there are infinite number of particles on the positive half-line., each having one of $K$ negative velocities $v_{1}^{(+)},...,v_{K}^{(+)}$. Similarly, there are infinite number of antiparticles on the negative half-line, each having one of $L$ positive velocities $v_{1}^{(-)},...,v_{L}^{(-)}$. Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of $\beta(t)$ - the coordinate of the last collision before $t$ between particle and antiparticle.

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