Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-25
J.Phys.A41:352003,2008
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, 12 figures
Scientific paper
10.1088/1751-8113/41/35/352003
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems extended into the complex domain. Three models are examined: the quartic double-well potential $V(x)=x^4-5x^2$, the cubic potential $V(x)=frac{1}{2}x^2-gx^3$, and the periodic potential $V(x)=-\cos x$. For the quartic potential a wave packet that is initially localized in one side of the double-well can tunnel to the other side. Complex solutions to the classical equations of motion exhibit a remarkably analogous behavior. Furthermore, classical solutions come in two varieties, which resemble the even-parity and odd-parity quantum-mechanical bound states. For the cubic potential, a quantum wave packet that is initially in the quadratic portion of the potential near the origin will tunnel through the barrier and give rise to a probability current that flows out to infinity. The complex solutions to the corresponding classical equations of motion exhibit strongly analogous behavior. For the periodic potential a quantum particle whose energy lies between -1 and 1 can tunnel repeatedly between adjacent classically allowed regions and thus execute a localized random walk as it hops from region to region. Furthermore, if the energy of the quantum particle lies in a conduction band, then the particle delocalizes and drifts freely through the periodic potential. A classical particle having complex energy executes a qualitatively analogous local random walk, and there exists a narrow energy band for which the classical particle becomes delocalized and moves freely through the potential.
Bender Carl M.
Brody Dorje C.
Hook Daniel W.
No associations
LandOfFree
Quantum effects in classical systems having complex energy 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 Quantum effects in classical systems having complex energy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum effects in classical systems having complex energy will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-728251