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42187-AC6
Real Time Quantum Dynamics in Systems with Many Degrees of Freedom
This second year of the grant saw many of the ideas described in the proposal come to fruition and more. The SemiClassical Initial Value series Representation (SCIVR) of the quantum propagator was used in a variety of situations and shown to give encouraging results. The theory was further developed and serves as an impetus for further exciting applications.
Much effort was expended on applying the SCIVR series representation to the benchmark spin boson computations. By redefining the well known forward backward formulation of the SCIVR approximation and by further developing our time evolved Gaussian approximation (paper 2, published last year) we were able to treat successfully the spin boson problem, as described in publications 5 and 6. A key element which made this possible was to replace the very problematic computation of the prefactor with a renormalization function. This renormalization was essential to enabling the application of the methodology to systems with many degrees of freedom. The methodology developed in these publications goes beyond simple dissipative systems, as shown in publication 7, we were able to apply our methodology also to the He atom.
At this point we can safely say that it is possible to compute the zero-th and first order terms of quantum correlation functions using the SCIVR series method, for systems with up to 100 degrees of freedom. Some elements of the new methodology developed under this grant have been reviewed in publication no. 3. Challenges remain however. It would seem that for dissipative systems, one should be able to take advantage of the fact that the bath is harmonic to simplify the computation. This was in fact done in publication no. 8, where a continuum formalism was developed however numerical application is being carried out in my group at the moment. We are at present applying this formalism to vibrational relaxation and preliminary results are very encouraging. By using a continuum formalism we should be able to solve for the quantum dynamics irrespective of the number of bath modes, thus providing a real advantage of the SCIVR method relative to basis set approaches such as MCTDH.
We have applied the methodology to He atom scattering from surfaces, this work is still evolving (publication no. 9), but we have been able to show that the SCIVR method accounts correctly for the quantum interference patterns found in such scattering as well as the attenuation predicted from Debye-Waller theory.
Impact
The work on the SCIVR series method has been received with enthusiasm by the community, as evidenced by the numerous invitations to speak about this topic at important international conferences such as the ACS meeting, March, 2006 and more. The SCIVR series representation as developed under the PRF grant has become one of the important methods for computing real time quantum dynamics in complex systems.
Two of my postdocs who have been involved in this work have moved to new postdoctoral positions. Dr. Eva Martin-Fierro moved to a prestigious postdoctoral research position at the Dept. of Physics in Freiburg, Germany, Dr. Ling Wang is now a postdoctoral fellow with Professor Haobin Wang in the United States. Dr. Santanu Sengupta has returned to his home country, India, where he is applying for a job.
Publications supported by the PRF
1. E. Martin-Fierro and E. Pollak, Forward-Backward Semiclassical Initial Value Series Representation of Quantum Correlation Functions, J. Chem. Phys. 125, 164104 (2006).
2. J. Shao and E. Pollak, A new time evolving Gaussian series representation of the
imaginary time propagator, J. Chem. Phys. 125, 133502 (2006).
3. E. Pollak, The SemiClassical Initial Value Series Representation of the quantum propagator, in Quantum dynamics of complex molecular systems, edited by D.A. Micha and I. Burghardt, Springer series in Chemical Physics, 83, 259 (2006).
4. Y. Makhnovskii and E. Pollak, Hamiltonian theory of stochastic acceleration, Phys. Rev. E, 73, 041105 (2006).
5. E. Pollak and E. Martin-Fierro, A new coherent state representation for the imaginary time propagator with applications to forward-backward semiclassical initial value representations of correlation functions, J. Chem. Phys. 126, 164107 (2007).
6. E. Martin-Fierro and E. Pollak, Semiclassical initial value series solution of the spin boson problem, J. Chem. Phys. 126, 164108 (2007).
7. L. Wang and E. Pollak, Frozen Gaussian wavepacket study of the ground state of the He atom, J. Chem. Theor. Comp. 3, 344 (2007).
8. E. Pollak, Continuum limit semiclassical initial value representation for dissipative systems, J. Chem. Phys. 127, 074505 (2007).
9. S. Sengupta, E. Pollak and S. Miret-Art\'es, Semiclassical initial value representation study of inelastic He atom scattering on a Cu surface, in preparation.
