TY - JOUR
T1 - Quantum manifestations of classical stochasticity. II. Dynamics of wave packets of bound states
AU - Weissman, Yitzhak
AU - Jortner, Joshua
PY - 1982
Y1 - 1982
N2 - In this paper we consider some of the consequences of classical stochasticity phenomena in the quantum mechanical Henon-Heiles and Barbanis systems. To explore classical-quantum analogies we have introduced a quantum mechanical phase space based on the coherent state representation. Quantum Poincaré maps (QPMs) were constructed from contour plots of the stationary phase-space densities. We have observed a correlation between the topological features of a QPM at an eigenenergy E and the sensitivity |dE/dε| of that energy to the strength ε of the nonlinear coupling. States with extreme values of |dE/dε|, corresponding to both high and to low values of |dE/dε|, show regular regions in the quantum phase space, while states with intermediate values of |dE/dε| span large parts of the quantum phase-space regions. These general features of the QPMs apply for almost each energy multiplet, and no qualitative change in the character of the QPMs was observed above the classical critical energy Ec for the stochastic transition. To investigate the quantum analog of classical trajectories, we have studied the dynamics of initially coherent Gaussian wave packets. We have discovered two limiting types of time evolution of intially coherent wave packets, which exhibit quasiperiodic time evolution or rapid dephasing. Quasiperiodic quantum dynamics is analogous to quasiperiodic classical trajectory dynamics, while rapid dephasing of the wave packet reflects the effects of spreading of the wave packet or/and stochastic classical dynamics. We were able to establish a correspondence between the topology of the quantum phase-space density and the wave packet dynamics. Quasiperiodic time evolution and rapid dephasing are exhibited by wave packets initially located in the regular and in the irregular regions of the quantum phase space, respectively.
AB - In this paper we consider some of the consequences of classical stochasticity phenomena in the quantum mechanical Henon-Heiles and Barbanis systems. To explore classical-quantum analogies we have introduced a quantum mechanical phase space based on the coherent state representation. Quantum Poincaré maps (QPMs) were constructed from contour plots of the stationary phase-space densities. We have observed a correlation between the topological features of a QPM at an eigenenergy E and the sensitivity |dE/dε| of that energy to the strength ε of the nonlinear coupling. States with extreme values of |dE/dε|, corresponding to both high and to low values of |dE/dε|, show regular regions in the quantum phase space, while states with intermediate values of |dE/dε| span large parts of the quantum phase-space regions. These general features of the QPMs apply for almost each energy multiplet, and no qualitative change in the character of the QPMs was observed above the classical critical energy Ec for the stochastic transition. To investigate the quantum analog of classical trajectories, we have studied the dynamics of initially coherent Gaussian wave packets. We have discovered two limiting types of time evolution of intially coherent wave packets, which exhibit quasiperiodic time evolution or rapid dephasing. Quasiperiodic quantum dynamics is analogous to quasiperiodic classical trajectory dynamics, while rapid dephasing of the wave packet reflects the effects of spreading of the wave packet or/and stochastic classical dynamics. We were able to establish a correspondence between the topology of the quantum phase-space density and the wave packet dynamics. Quasiperiodic time evolution and rapid dephasing are exhibited by wave packets initially located in the regular and in the irregular regions of the quantum phase space, respectively.
UR - http://www.scopus.com/inward/record.url?scp=0001165869&partnerID=8YFLogxK
U2 - 10.1063/1.443977
DO - 10.1063/1.443977
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AN - SCOPUS:0001165869
SN - 0021-9606
VL - 77
SP - 1486
EP - 1500
JO - The Journal of Chemical Physics
JF - The Journal of Chemical Physics
IS - 3
ER -