WAVEPACKET APPROACHES TO DISSIPATIVE QUANTUM DYNAMICS

Many processes arising in Chemistry, Physics and Biology show quantum effects. Representative examples are chemical reactions involving light atoms, energy transfer in complex environments, electronic and geometrical properties of complex and bulk systems, tunneling phenomena etc. Theoretical Chemistry deals with such kind of problems with the help of numerical solutions of the Time Dependent Schrodinger Equation (TDSE). On the other hand, when classical effects are most relevant as, for example, in large dynamical systems like proteins at room temperature, Theoretical Chemistry deals with this problems with the help of numerical solution of the Newton's equations. Solving numerically the TDSE is much more expansive than solving the classical Newton's equations of motion. Thus, often mixed descriptions are used treating the system at the exact -quantum- level and the environment at the approximated classical level. When a full quantum approach is needed both for the system and for the environment (as, for example, in processes involving quantum objects, such as light atoms, energy transfer in small molecules interacting with a thermal bath at low temperature, and so on), one faces with so called Open Quantum Systems, and the corresponding dynamics is generally dissipative. In open quantum systems the wavefunction description fails because of a lack of the complete knowledge of the state. It is then necessary to switch to the density matrix description, which contains all the information. The system dynamics is affected by the presence of the bath depending on the interactions between them. If the coupling is small, than the system evolves in time without been affected by the environment. If the system is initially prepared as a pure state, then the dynamics is coherent. On the other hand if system and bath are strongly interacting, than the system dynamics is modified by the presence of the bath and described by a mixture of states. Under the condition of strong coupling, the modified dynamics is incoherent, also if the initial state of the system is pure. Based on the Multi Configuration Time Dependent Hartree (MCTDH) approach, which writes the wavefunction as linear combination of Hartree products, the MCTDH program has been developed. This program is the only one allowing to deal with large, dissipative problems (up to 100 degrees of freedom). Recently, variants of the MCTDH approach have been developed in order to increase the number of degrees of freedom which can be considered. The GMCTDH approach treats part of the MCTDH wavefunction as Gaussian functions, which are analytically known; the LCSA approach, on the other hand, can be viewed as a GMCTDH approach with selected configurations. In our project we have studied the effect of the environment on quantum systems. In particular, we have studied the influence of the environment in simple chemical process both from a theoretical and from a computational point of view. Specifically, we have developed a model to study excitoninc energy transfer in dissipative media, performed numerical simulations using the MCTDH approach, and obtained analytical expressions for the equations of motion in the so called mixed quantum-classical hydrodynamics picture.