- PhD in Theoretical Physics, University of Houston, Houston, 2005 Dissertation : Minimum Uncertainity Wavelets in SUSY Quantum Mechanics , the Theory of Coherent States, the Theory of Strings, and the Fermionic Harmonic Oscillator.
- DMin in Practical Theology, Houston Graduate School of Theology, Houston, 2001 Dissertation: An Approach to the Paradigms of Spiritual Leadership for Creative and Effective Ministry.

Young Lee was born in South Korea. He studied theoretical physics at the Yonsei University where he obtained his B.S. and M.S. in 1981 and at University of Houston where he obtained his Ph.D. in 2005. He was Research Assistant at the same university (2005-2006). Since 2007, he is now serving as a Visiting Professor at the Texas Southern University. Also, he was also conferred doctoral degree (D. Min) in the field of practical theology from Houston Graduate School of Theology in 2001. He has been served as an ordained minister in Christian church for many years before he joins the physics faculty of TSU.

–

His research fields are theoretical physics in quantum fields and computational physics in statistical mechanics (condensed matter physics). In theoretical physics part, his major interests are concentrating on the foundation of quantum mechanics, quantum field theory, string theory, and black holes theory. He utilizes the minimum uncertainty wavelet model and harmonic oscillator model as implementations to explore them. Using the minimum uncertainty wavelet model which is the minimization solution of Heisenberg uncertainty, He explores the SUSY quantum mechanics, and coherent theory and string theory. In these theories, He is looking for a simple model to compare how different and similar with the traditional quantum physics.

He is also interested in medical physics which is applied of physics tomedicine. It generally concerns physics as applied to medical imaging and radiation therapy. He has a plan to introduce medical physics programming to TSU in near future. He has currently been trainned in M. D. Anderson Cancer Center.

Another present research interest is to develop the virtual laboratory in physics education. We call this virtual laboratory as Virtual Reality Laboratory for the Experimental Mathematical Modeling o Physical Systems (ViRLEMPS). This lab mainly focus on the science related students and this provide them with understanding easily the sophisticate physical phenomena and this method enable to grasp the conception of difficult mathematically formalized natural phenomena.

For the part of the computational physics, non-equilibrium statistical physics and econophysics are my present concerns to research, which aims to find the simple model and apply to the essence of experimental phenomena. These works involve the computer simulations. The followings are descriptions of the major on-going project of his research.

Minimum Uncertainty Wavelets: I explore the SUSY properties and string aspects through the recently derived constrained minimum Heisenberg uncertainty m-wavelets. The several types of raising and lowering operators play a fundamental role in the SUSY structure of these wavelets. Compared with the harmonic oscillator, the m-wavelets naturally manifest the SUSY properties. Using the results, he construct a supercoherent theory of these wavelets. In addition, the m-wavelets and harmonic oscillator belong to different classes in string theory. The results should be of interest for the supersymmetric theory of quantum fields and string theory. He derives isotropic non-Cartesian multi-dimensional solutions using the three different methods; the solution of differential equations, Fourier transformation, and the creation and annihilation operators. He derive multi-dimensional ALDAF (Associate Laguerre Distributed Approximating Functionals) which is a collection of m-wavelets. ALDAF and its non-Cartesian solutions are good approximation tools for physics and other sciences. In the application to string theory, his model is more efficient for compactification of the extra-dimension because of lower uncertainty when his model is compared with harmonic oscillator. He is preparing m-wavelet relativistic quantum mechanics and m-wavelet quantum field theory.

Fermionic Harmonic Oscillator: He explore two kinds of model which are the general superpotential model and the fractional (half-integer) harmonic oscillator. In my general superpotential model, fermionic solutions of the harmonic oscillator are generated in terms of the well-behaved Hermitian polynomial solutions. The half-integer harmonic oscillatior model shows the natural SUSY property and its solutions are generated in terms of the parabolic cylinder functions. For the case of the general superpotential model, as same as the conventional SUSY quantum mechanics, the symmetry of the fermionic state is always opposite from the symmetry of the bosonic state. Thus, if for any state the boson has symmetric function, then the fermionic state is an anti-symmetric function and vice versa. However, for the case of the fractional (half-integer) harmonic oscillator, this is only true for the broken SUSY. In the case of unbroken fractional harmonic oscillator SUSY, both bosonic and fermionic state has same symmetry function. The multi-dimensional versions of these models are considering and supercoherent theorys of the fractional harmonic oscillator is an interesting project now.

Non-Equilibrium Statistical Physics: Self-organized networks of competing Boolean model is considered. A model of Boolean agents competing in biology, ecosystems, social sciences, and economy is considered where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest players strategy id changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths. Development of canalization leads to a reduction in the variation of phenotype expression relative to the complexity of the genome has long been thought to be an important property of evolving biological systems. We show that a highly canalized state develops in the process of self-organization recently discovered in N-K Boolean networks that evolve based on a competition networks in developmental systems. Unlike other proposed evolutionary mechanism that select for canalization, this mechanism does so while maintain the systems capacity for further evolution in the steady state.

Econophysics: He utilizes two kinds of approach which are the non-Gaussian distribution of return method and self-organization model in agent network method. Analytical interpretation for the distribution of returns is expressed in terms of the diffusion rate when the consensus value is assumed to be fixed in time. The range of the behaviors observed with a simple model covers the range of non-Gaussian behaviors seen in the distribution of returns of real financial market. Also, He explores that the development of self-organization in agent-based network models of economic markets. Although individual traders in a market obey simple rules, the way that they interact and exchange information can lead to the market self-organizing into a complex state. The overall performance of the market can be affected by the self-organization of the traders. We are trying to understand the process of self-organization in markets, and how to optimize the process to maximum advantage.

ViRLEMPS: The virtual reality environments in science and engineering is just to utilize the computer as experimental laboratory and it shows and can understand the real, physical, and the three dimensional phenomena in nature. He especially focus on 3D simulation analysis will help students to understand in physics area, for example, mechanic, electromagnetism, quantum mechanic, solid state physics, and other physics field.

Other related topics: In addition to the above mentioned subjects, He also have been interesting the fractional calculus in physics application. Especially, fractional diffusion problem , fractional harmonic oscillator, and fractional Quantum Hall effect are among these interests. In the flexural oscillations of an elastic beam will be interesting to solve with fractional Laplacian. In addition, He is interested in the black holes thermodynamic theory from near horizon. PT symmetric quantum mechanics is another interesting subject. He is now trying to get the exact wave function solution of Bender and Boettecher potential.

- Kouri, D.J.; Papadakis, M., Kakadiaris, I.; Hoffman, D., J. Phys. Chem. A 107, 7318, 2003.
- Hoffman, D. K.; Kouri, D.J., Phys. Rev. A 65, 052106-1, 2002.
- Hoffman, D. K.; Kouri, D.J., Phys. Rev. Lett. 85, 5263, 2000.
- Hoffman, D. K.; Kouri, D.J., Phys. Chem. 97, 2907, 1993.
- Lee, Y., Kouri, D.J. , Hoffman, D. K.; Minimum Uncertainty Wavelets in SUSY Quantum Mechanics, The Theory of Coherent States, and String Theory, in preprint, 2005