Michael V. Pak

 Michael Pak

Contact Information

Department of Chemistry
University of Illinois
371 Rogers Adams Lab
600 South Mathews Avenue
Urbana, IL 61801
Research Assistant Professor of Chemistry

Biography

Professor Pak received a Ph.D. in quantum physics from St. Petersburg State University and a Ph.D. in quantum chemistry from Iowa State University. He joined the department in 2013 and is also affiliated with the Institute of Condensed Matter Theory.

Research Description

Quantum theory of many-body multi-component systems

To obtain an accurate wave function for a quantum system of particles of several different sorts, one needs to solve a number of problems not usually observed in one-component many-body quantum systems, e.g. the multi-electron molecular systems of conventional quantum chemistry. For instance, if our system comprises quantum particles of opposite charge, such as electron-proton or electron-positron systems, the dynamical correlation in such systems is no longer a small effect only to be considered when quantitative accuracy is required. One can no longer treat dynamical correlation as a (relatively) small correction to the mean field wave function, the way it is typically done in many-body quantum mechanics. The usual methods such as configuration interaction, CASSCF, coupled cluster methods, MP perturbation theory etc. all fail because the underlying mean field wave function is generally not a reasonable approximation to the exact wave function. We attempt to develop methods for accurately describing these quantum systems, for instance by treating the particle correlation explicitly at the wave function level, or through multi-component density functional theory.

Theory of quantization

Canonical quantization of classical systems fails when extended to all classical observables, as opposed to a selected subset of observables only, such as dynamical coordinates, their conjugate momenta and a simple Hamiltonian at most quadratic in the momenta. This failure is well known, e.g. in canonical quantization of classical fields in curved space-time. There are conventional ways of approaching this failure, such as geometric quantization. Instead, we attempt to circumvent the quantization problem altogether, by considering classical (non-quantized) fields on non-commutative geometric spaces, mostly along the lines suggested by Alain Connes’ non- commutative geometry approach. Alternatively, there are multiple relatively unexplored implication for the theory of quantization in the theory of non-commutative Hopf algebras, such as deformation quantization for quantum groups.