ON THE RELEVANCE OF GAMOW STATES FOR THE DESCRIPTION OF SYSTEMS WITH TIME DEPENDENT PARAMETERS

V. V. Alekseev, V. I. Grigor’ev

Duccio Fanelli

Manuel Gadella

Manuel Jesús Maldonado Lozano

IN THIS PAPER WE GIVE THE TIME DEPENDENT DESCRIPTION OF THE SCATTERING OF A WAVE PACKET BY A SHORT RANGE POTENTIAL. WE SHOW THAT WHEN THE WAVE PACKET IS INITIALLY OUTSIDE THE SCATTERER, IT IS POSIBLE TO INTRODUCE AN APPROPIATE TIME DEPENDENT GREEN FUNCTION TO DESCRIBE THE SCATTERING PROCESS. THIS GREEN FUNCTION WILL BE EVALUATED EXPLICITLY IN TERM OF ERROR INTEGRAL FUNCTIONS, AND THE ONLY PARAMETERS THAT APPEAR IN THE GREEN FUNCTION WILL BE THE POLES OF THE S MATRIX. FROM THE ASYMPTOTIC BEHAVIOR OF THE GREEN FUNCTIOR WHEN T, WE OBTAIN RESTRICIONS ON THE POSITION OF THE POLES OF THE S MATRIX WHICH AGREE WITH THOSE DUE TO THE DEFINITION OF THE S IN TERMS OF THE DERIVATIVE MATRIX R. THE PRESENT ANALYSIS IS CARRIED OUT FOR ARBITRARY ANGULAR MOMENTUM.

A. Mondragón, E. Hernández

A. Fuliński

The solution of master equations describing the evolution in time of correlated subsystems forming an isolated system is given. It is found that near the equilibrium or stationary state the probabilities of finding of the subsystems in their quantized states and the correlation coefficients are the exponential functions of momentary values of observables, and do not depend on the initial state of the system. (auth)