Doctoral dissertation

Dissertation: Quantum mechanical paths lead to the foundations of optics

Juha Tiihonen
The optical properties of matter depend on polarizability, which is the response of atoms and molecules to electric fields. In his doctoral thesis, Juha Tiihonen utilized supercomputers to calculate polarizability out of the foundation of quantum mechanics, the path integrals.

The notion of path integrals has fascinated physicists since Richard Feynman: the quantum uncertainty emerges when a particle travels not only along one path but, in fact, along every possible path simultaneously. In quantum statistical interpretation, in turn, the trajectories occur in so-called imaginary time.

Interpretations such as these defy common sense and make most people roll their eyes.

“In the end, path integration is all about mathematical tools and algorithms which enable finding practical computational solutions to theoretical problems,” Juha Tiihonen remarks.

In his thesis, Tiihonen studied atomic and molecular polarizabilities with a computational method called path integral Monte Carlo. In the method, a supercomputer generates trillions of random paths, and the optical properties of matter can then be extracted from them with so-called estimators. Tiihonen’s thesis is a sort of a numerical recipe book in which a compilation of different polarizability estimators is derived and presented thoroughly.

A central part in method development is careful optimization and testing. Tiihonen provided the CSC and TCSC supercomputers with computational tasks that would have taken months or even years to complete with an ordinary laptop.

The results offer new conclusions on the quantum statistics behind nonlinear optics and spectroscopy.

“The path-integral approach has a simultaneous and highly accurate account of many-body correlations, thermal effects and nuclear non-adiabatic coupling. This makes the results quite unique,” Tiihonen notes.

Tiihonen has also eagerly supplemented scientific literature: for instance, many positron systems and exotic ions occur frequently in astronomy and spectroscopy, but their polarizabilities have been beyond the reach of experiments. There is a constant demand for new approaches, since the interaction between light and matter is one of the key challenges in modern science and technology. The road from basic research to patents is a long one, however.

“My first steps with the path integrals have resulted in unique challenges and prospects. Right now, my priority is to produce new scientific understanding.

Tiihonen comes from Jyväskylä, Finland, and will start his postdoctoral studies at Oak Ridge National Laboratory in Tennessee, USA this summer.

The doctoral dissertation of MSc (Tech) Juha Tiihonen in the field of computational physics entitled Thermal effects in atomic and molecular polarizabilities with path integral Monte Carlo will be publicly examined at the Faculty of Engineering and Natural Sciences of Tampere University on Friday, 5 April at 12 noon in lecture hall TB109 of the Tietotalo building in the Hervanta Campus of Tampere University (Korkeakoulunkatu 1). The opponent will be Professor Carlo Pierleoni (Università degli Studi dell'Aquilan, Italy). Professor Tapio Rantala from the Laboratory of Computational Physics will act as Chairman.

The dissertation is available online at

Photo: Jonna Jalasvirta