Quantum chaos and Henon-Heiles model: Dirac's variational approach with Jackiw-Kerman function
نویسندگان
چکیده
A simple semiclassical H\'enon-Heiles model is constructed based on Dirac's time-dependent variational principle. We obtain an effective Hamiltonian using a Hatree-type two-body trial wavefunction in the Jackiw-Kerman form. Numerical results show that quantum effects can fact induce chaos non-chaotic regions of classical model.
منابع مشابه
Effect of a magnetic flux line on the quantum beats in the Henon-Heiles level density.
The quantum density of states of the Henon-Heiles potential displays a pronounced beating pattern. This has been explained by the interference of three isolated classical periodic orbits with nearby actions and periods. A singular magnetic flux line, passing through the origin, drastically alters the beats even though the classical Lagrangian equations of motion remain unchanged. Some of the ch...
متن کاملA Conservative Numerical Integration Algorithm for Integrable Henon–Heiles System
A new conservative numerical integration algorithm for the integrable Henon–Heiles system is presented which conserves all of the constants of motion.
متن کاملSimple variational approach to the quantum Frenkel-Kontorova model.
We present a simple and complete variational approach to the one-dimensional quantum Frenkel-Kontorova model. Dirac's time-dependent variational principle is adopted together with a Hartree-type many-body trial wave function for the atoms. The single-particle state is assumed to have the Jackiw-Kerman form. We obtain an effective classical Hamiltonian for the system, which is simple enough for ...
متن کاملQuantum Complex Hénon-Heiles Potentials
Quantum-mechanical PT -symmetric theories associated with complex cubic potentials such as V = x2 + y2 + igxy2 and V = x2 + y2 + z2 + igxyz, where g is a real parameter, are investigated. These theories appear to possess real, positive spectra. Low-lying energy levels are calculated to very high order in perturbation theory. The large-order behavior of the perturbation coefficients is determine...
متن کاملChaos Image Encryption based on DCT Transforms and Henon Map
The study of cryptography applications in chaotic system have been exponentially increasing in the recent years. Depending on the sensitivity to initial conditions, chaotic systems are characterized, similarity to continuous broad-band power spectrum and random behavior. The chaotic system is high sensitive to the initial condition and is a high complex nonlinear dynamic system. The chaotic seq...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Modern Physics
سال: 2023
ISSN: ['0217-751X', '1793-656X']
DOI: https://doi.org/10.1142/s0217751x2350029x