Stochastic Quantization for a System of N identical interacting Bose Particles
speaker: Laura Morato (Università di Verona)abstract: We apply Stochastic Quantization to a system of $N$ interacting identical Bosons in an external potential $\Phi$, by means of a general stationary-action principle. The collective motion is described in terms of a Markovian diffusion on $\R{3N}$, with joint density $\hat\rho$ and entangled current velocity field $\hat V$, in principle of non-gradient form, related one to the other by the continuity equation. Dynamical equations relax to those of canonical quantization, in some analogy with Parisi-Wu stochastic quantization. Thanks to the identity of particles, the one-particle marginal densities $\rho$, in the physical space $\R{3}$, are all the same and it is possible to give, under mild conditions, a natural definition of the single-particle current velocity, which is related to $\rho$ by the continuity equation in $\R{3}$. The motion of single particles in the physical space comes to be described in terms of a non-Markovian three-dimensional diffusion with common density $\rho $ and, at least at dynamical equilibrium, common current velocity $v$. The three-dimensional drift is perturbed by zero-mean terms depending on the whole configuration of the $N$-boson interacting system. Finally we discuss in detail under which conditions the one-particle dynamical equations, which in their general form allow rotational perturbations, can be particularized, up to a change of variables, to Gross-Pitaevskii equations.
timetable:
Mon 16 Jul, 9:00 - 9:25, Aula Dini
documents:
BosePisa07.pdf2.pdf
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