Research
On this page, you can read about my current research as well as see some of the key results obtained.
Post Doctoral ETH Zürch (2011-2013)
Currently, I have four ongoing projects which are described below.
Provenance data collection
"Provenance data collection" is really the wrong title of this project - at least from my perspective. This project officially deals with collecting provenance data to increase reproducibility of research projects. However, clearly no wants to collect provenance data manually as it is a rather big work. Therefore the real title of this project should be "How one can automate literally anything in theoretical physics". Subsequently, provenance data collection comes for free.
The first part of this project has been the development of BatchQ which soon will find its way to Github under MIT license.
Fast CPU/GPU implementation of the Ising model
The Ising model, which was invented in 1920 by Wilhelm Lenz, was first solved in one dimension by Ernest Ising in 1925, and later in two dimensions by Lars Onsager. While the original motivation was the study of ferromagnetism, the model has many other compelling applications including chaotic systems lattice gases, spin glasses and correlated bits.
An approach to solve the Ising model is the special purpose machine Janus which is based on field-programmable gate arrays (FPGAs). Each FPGA is capable of performing spin updates at a speed of 16 ps/spin flip in the 3D model.
Currently, the best multi-spin codes produced for CPUs reach a spin flip level at approximately 250 flips/microsecond for the 2D Ising model. State-of-the-art GPU code performs on average at 12 flips/nanosecond for the 2D model, and the best performance archived is around 29 flips/nanosecond. For comparison Janus reach ~65 flips/nanosecond for the 3D model.
This is an ongoing project which aims towards using GPU technology to beat the special purpose machine Janus.
Fractional Fourier Analysis
This project aims towards establishing a Fourier theory for the Palmer model. Such a theory is useful as it allows computation of complicated integrals with little effort.
Integration routine in Maple
During the autumn 2011 I have developed a fast integration routine in Maple 13. The routine exploits a result derived by David R. Herrick in 1976 to compute a large class of integrals. The article is currently under review, but here are some preliminary results:
PhD study (2008-2011)
Below you find key results related to the research done during a three-year Ph. D. study, where I have investigated charged excitons, also known as trions (if you are unfamiliar with trions think of the ionised hydrogen molecule) in carbon nanotubes (CNTs). Trions occur in doped CNTs under optical excitation as a result of an exciton bound to a free or bound carrier. During this period I have applied two different models, namely, a cylinder model and a fractional dimensional model.
Trions in carbon nanotubes
The optical processes in CNTs are governed by excitons and thus, in doped CNTs excitons in combination with a free carrier may bind to form a three-particle complex, the trion. In 2009 we estimated the trion binding energy of trions on the surface of a cylinder using an effective model. In this article, we demonstrated that trions are stable at room temperature and we investigated the singlet and triplet wave functions.
We continued the previous study in 2010 where we extended the model to gain a better accuracy of our previous results. Subsequently we investigated the correlation energy in CNTs in a Hartree-Fock study. We found that the Hartree-Fock approximation did not predict the ground state energy with sufficient accuracy. Finally we concluded that trions are stable particles at room temperature for CNTs with radius less than 8Å.
Trions in fractional dimensional spaces
The first three-particle problem modelled in fractional dimensional space was done by D. R. Herrick and F. H. Stillinger in 1975 (Phys. Rev. A, 11(1):42) in a study of the helium atom. Later, F. H. Stillinger gave a more detailed mathematical description of the model (J. Math. Phys., 18(6):1224). Much later a more general model was developed by C. Palmer and P. N. Stavrinou (J. Phys. A: Math. Gen., 37:6987).
While the Herrick-Stillinger model has been subject to many studies, the Palmer model has only received little attension. In the first article Herrick and Stillinger gave the solution to a quite general integral in which the integrand was of an exponentially decaying form (see Eq. (28)-(34) in Phys. Rev. A, 11(1):42, 1975). Exponentially decaying functions are in general a very good choice in the description of localised states. In a study of the trion in fractional dimensional spaces we exploited this result making an basis expansion of the general solution. Motivated by our previous investigations we examined the correlation energy and demonstrated that for trions this energy is rather large (see image left side) - independently of the dimension of the system. Consequently the Hartree-Fock approximation does not describe trions sufficiently.
Later we applied the Palmer model in quantum Monte Carlo study of the trion in fractional dimensional spaces. We found an extremely good agreement between the results obtained in these studies in comparison with our previous results. Using the approximate solution we estimated the trion binding energy in CNTs. The result can be seen in the figure the left side. During this work we developed a Monte Carlo framework which is available online (with source under MIT license).
You can find more about my work with Monte Carlo techniques on quantumempire.org.
Publication list
7. T. F. Rønnow, Evaluation of a general class of integrals through extension of the integral routine in Maple, Submitted.
6. T. F. Rønnow, T. G. Pedersen, B. Partoens, Biexcitons in Fractional Dimensional Semiconductors, Phys. Rev. B 85 04512 (2012).
5. T. F. Rønnow, T. G. Pedersen, B. Partoens, K. K. Berthelsen, Variational Quantum Monte Carlo Study of Charged Excitons in Fractional Dimensional Space, Phys. Rev. B, 84 035316 (2011).
4. T. F. Rønnow, T. G. Pedersen and H. D. Cornean, Optical absorption of charged excitons in semiconducting carbon nanotubes, (to appear in Physica E).
3. T. F. Rønnow, T. G. Pedersen and H. D. Cornean, Dimensional and correlation effects of charged excitons in low-dimensional semiconductors. Phys. A: Math. Theor. 43 474031 (2010)
2. T. F. Rønnow, T. G. Pedersen and H. D. Cornean, Correlation and dimensional effects of trions in carbon nanotubes, Phys. Rev. B 81 205446 (2010).
1. T. F. Rønnow, T. G. Pedersen and H. D. Cornean, Stability of singlet and triplet trions in carbon nanotubes, Phys. Lett. A, 373, 1478 (2009).
