Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1994-11-08
Nonlinear Sciences
Chaotic Dynamics
30 pages, uuencoded LaTeX file (figures included)
Scientific paper
We consider the dynamical system consisting of a quantum degree of freedom $A$ interacting with $N$ quantum oscillators described by the Lagrangian \bq L = {1\over 2}\dot{A}^2 + \sum_{i=1}^{N} \left\{{1\over 2}\dot{x}_i^2 - {1\over 2}( m^2 + e^2 A^2)x_i^2 \right\}. \eq In the limit $N \rightarrow \infty$, with $e^2 N$ fixed, the quantum fluctuations in $A$ are of order $1/N$. In this limit, the $x$ oscillators behave as harmonic oscillators with a time dependent mass determined by the solution of a semiclassical equation for the expectation value $\VEV{A(t)}$. This system can be described, when $\VEV{x(t)}= 0$, by a classical Hamiltonian for the variables $G(t) = \VEV{x^2(t)}$, $\dot{G}(t)$, $A_c(t) = \VEV{A(t)}$, and $\dot{A_c}(t)$. The dynamics of this latter system turns out to be chaotic. We propose to study the nature of this large-$N$ limit by considering both the exact quantum system as well as by studying an expansion in powers of $1/N$ for the equations of motion using the closed time path formalism of quantum dynamics.
Cooper Fred
Dawson John
Habib Salman
Kluger Yuval
Meredith Dawn
No associations
LandOfFree
Semiquantum Chaos and the Large N Expansion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Semiquantum Chaos and the Large N Expansion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semiquantum Chaos and the Large N Expansion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-229954