توليد و نابودي ذره در مدل واكنش پخش خودگردان

Annihilation or creation of particles: an autonomous reaction-diffusion process

در اين مقاله به بررسي مدل واكنش -- پخش خودگردان براي توليد و نابودي ذرات روي پيوستار در يك ناحيه مرزدار D بعدي مي پردازيم. خودگردان بودن در اين مدل به اين معني است كه تابع هاي دو نقطه اي در سامانه را مي توان به صورت بسته نوشت. مدل معرفي مي گردد و سپس معادلات تحول و شرط مرزي رخ واره هاي چگالي را بدست آورده و رفتار اين رخ واره ها در حالت ايستا و ديناميك در حد ترموديناميك مطالعه مي گردد.

In this paper we shall consider the annihilation or creation of particles in a D-dimensional region with boundaries. Particles can be injected or extracted at the boundaries. Two general behaviours of this system are investigated: the stationary behaviour of this system, and the dominant way the system relaxes to its stationary state. Static phase transitions (discontinuous changes in the stationary profiles of the system) are investigated based on the first type of behavior. Dynamical phase transitions (discontinuous changes in the relaxation-times of the system) are studied based on the second type of behavior. This investigation is confined to systems in which the equation of evolution for one-point functions is closed autonomous systems