Quantum many-body dynamics Hamiltonian

Debashis Mukherjee is a Professor of Physical Chemistry and the Director of the Indian Association for the Cultivation of Science, Calcutta, India. He has been one of the earliest developers of a class of multi-reference coupled cluster theories and also of the coupled cluster based linear response theory. Other contributions by him are in the resolution of the size-extensivity problem for multi-reference theories using an incomplete model space and in the size-extensive intermediate Hamiltonian formalism. His research interests focus on the development and applications of non-relativistic and relativistic theories of many-body molecular electronic structure and theoretical spectroscopy, quantum many-body dynamics and statistical held theory of many-body systems. He is a member of the International Academy of the Quantum Molecular Science, a Fellow of the Third World Academy of Science, the Indian National Science Academy and the Indian Academy of Sciences. He is the recipient of the Shantiswarup Bhatnagar Prize of the Council of Scientihc and Industrial Research of the Government of India. 

The quantum mechanical many-body nature of the interatomic forces is taken into account naturally through the Hellmann-Feynman theorem. Since the scheme usually uses a minimal basis set for the electronic structure calculation and the Hamiltonian matrix elements are parametrized, large numbers of atoms can be tackled within the present computer capabilities. One of the distinctive features of this scheme in comparison with other empirical schemes is that all the parameters in the model can be obtained theoretically. It is therefore very useful for studying novel materials where experimental data are not readily available. The scheme has been demonstrated to be a powerful method for studying various structural, dynamical, and electronic properties of covalent systems. 

It should also be noted that full symmetry unconstrained structural relaxation is essential before the theoretical determination of any physical properties. In quantum mechanical simulations, use of a Hamiltonian with only one rr-electron orbital is untenable for dynamical relaxations even for graphite. Most authors attempt to circumvent this problem by using classical many body potentials for obtaining relaxation while still making use of the ir-electron orbital approximation for conductivity calculations. Use of two completely different methods for the same system, can introduce inconsistency in the prediction of physical properties. 

Many dynamical processes of interest are either initiated or probed by light, and their understanding requires some knowledge of this subject. This chapter is included in order to make this text self contained by providing an overview of subjects that are used in various applications later in the text. In particular, it aims to supplement the elementary view of radiation-matter interaction as a time-dependent perturbation in the Hamiltonian, by describing some aspects of the quantum nature of the radiation field. This is done on two levels The main body of this chapter is an essentially qualitative overview that ends with a treatment of spontaneous emission as an example. The Appendix gives some more details on the mathematical structure of the theory. 

---