Se p 19 98 Selftrapping and Quantum Fluctuations in the Discrete Nonlinear Schrödinger Equation ∗

We study the robustness of the selftrapping phenomenon exhibited by the Discrete Non-linear Schrödinger (DNLS) equation against the effects of nonadiabaticity and quantum fluctuations in a two–site system (dimer). To test for nonadiabatic effects (in a semiclassi-cal context), we consider the dynamics of an electron (or excitation) in a dimer system and coupled to the vibrational degrees of freedom, modeled here as classical Einstein oscillators of mass M. For relaxed (coherent state) oscillators initial condition, the DNLS selftrap-ping transition persists for a wide range of M spanning 5 decades. When undisplaced initial conditions are used, the selftrapping transition is destroyed for masses greater than M ∼ 0.02. To test for the effects of quantum fluctuations, we performed a first-principles numerical calculation for the fully quantum version of the above system: the two–site Hol-stein model. We computed the long-time averaged probability for finding the electron at the initial site as a function of the asymmetry and nonlinearity parameters, defined in terms of the electron-phonon coupling strength and the oscillator frequency. Substantial departures from the usual DNLS system are found: A complex landscape in asymmetry–nonlinearity phase space, which is crisscrossed with narrow " channels " , where the average electronic probability on the initial site remains very close to 1/2, being substantially larger outside. In the adiabatic case, there are also low–probability " pockets " where the average electronic probability is substantially smaller than 1/2.