A brief list of the main research interests during the last decade ending in 2007:

- The first local extension to superfluid systems of Density
Functional Theory and applied it to a number of physical systems (cold
atomic gases, atomic nuclei, neutron star crust)

- New forms of Casimir
interaction in Fermi systems (applications to neutron star crust) and developement of new methods for
calculation
of Casimir energy

- Determination of various thermodynamic properties of Fermi gases in the unitary regime within Quantum Monte Carlo calculations

- Establishment of a number of properties of unitary Fermi gases (collective modes, vortex structure, existence of a new quantum phase transition, new exotic mechanisms of superfluidity, etc.)

- Derivation from first principles of a quantum Fokker-Planck equation for (Nuclear) Large Amplitude Collective Motion and the derivation of the first quantum Fractional Fokker-Planck equation

- Profs. G.F. Bertsch and A. Bulgac have been successful in securing in 2006 the first SciDAC grant in Theoretical Nuclear Physics with a well defined focus, the determination of the nuclear energy density functional - UNEDF

Prof. Bulgac research is geared towards various aspects of strongly interacting many-body systems, mostly fermions and in particular nucleons in nuclei and neutron/nuclear matter and cold atomic gases.

At the begining of this decade (1998-2007) Prof. Bulgac concluded a long study of the dissipation and its origin in the large amplitude motion of nuclei, based on a random matrix description of the intrinsic nuclear motion. A quantum Fokker-Planck equation for large amplitude collective motion was derived within a Feynman-Vernon path integral formalism, a number of highly nontrivial exact and numerical soluutions of this equation have been obtained and, in a very unexpected development, a first derivation of a quantum fractional Fokker-Planck equation was also provided, one of the few examples of genuine quantum dissipative equations and a very unique extention to the description of Levy processes.

In collaboration with a former graduate student (Yonlge Yu, now associate professor at the Institute for Physics and Mathermatics, Wuhan, P.R. China), Piotr Magierski (professor at the Warsaw University of Technology, Poland), Andreas Wirzba (staff scientist at Institut fur Kernphysik, Julich, Germany) he put in evidence a new form of the Casimir phenomenon in fermionic systems, ranging from nuclei to neutron stars, and lately even for dilute cold atoms in traps. This new phenomenom was dubbed the Fermionic Casimir effect and it appears for example between two hard object immersed into a Fermi sea of non-interacting fermions. Various aspects of the Fermionic Casimir effect were studied for so called bubble nuclei, pasta phase in neutron stars and lately others have extended this phenomena to the physics of cold atoms in various atomic traps and optical lattices. The effects arising from various geometries, from the onset of finite temperatures, from the distortions of the regular lattices of such objects immersed in a Fermionic see, and also from their dynamics have been investigated in a lot of detail. One of the most interesting consequences of the existence of the Fermionic Casimir effect is the fact that the order in the so-called pasta phase in the crust of neutron stars is most likely destroyed and that could lead to drastic changes of its elastic and transport properties and it should be observable in the so-called starquakes.

After many years of being involved in the study of atomic clusters and their relation with the properties of nuclei Prof. Bulgac performed a number of studies of their properties at finite temperatures and of their "phase transitions."

In collaboration with Vasily Shaginyan (St. Petersburg, Russia), prof. Bulgac investigated the unusual role played by the nuclear collective modes in the Coulomb interaction in nuclei and has shown how a significant part of the Nolen-Schiffer anomaly could be accounted for in a very simple and natural manner.

Together with his former graduate student Yongle Yu, prof. Bulgac has developed for the first time a mathematically and physical correct procedure to renormalize the zero-range pairing interaction in fermionic systems. This allowed them to perform an extremely accurate study of entire isotope and isotone chains of more than 200 spherical nuclei with an unprecedented precision. All this formed the basis of what became to be known as the Superfluid Local Density Approximation (SLDA), the first consistent extention of the Density Functional Theory to superfluid systems with local pairing fields. This scheme has been applied subsequently, apart from nuclei, to the description of vortices in neutron matter, cold atomic gases. It was thus for the first time shown that the core of such vortices develop a hole in their core. In neutron stars that leads to a dramatic and totally unexpected change in the pinning properties of the vortices and in cold gases it was the key suggestion on how to make them visible and thus be put in evidence and prove that such systems are indeed superfluid. SLDA has been applied recently by prof. Bulgac to a long series of atomic systems in traps, the properties of which have been independently computed in Quantum Monte Carlo approaches by others. The quality of the agreement obtained between the SLDA and the ab initio results is indeed spectacular.

In the last few years it was realized by many that the properties of cold atomic gases are very similar to those of atomic nuclei and that lots of techniques and results relevant to both fields, and others as well, could be obtained from their study. Together with his graduate student Joaquin E. Drut and prof. Piotr Magierski, prof. Bulgac initiated a completely new program aimed at a numerical exact solution of the many fermion problem at finite temperatures within a Path Integral Monte Carlo description. Thus the thermodynamic properties of a unitary gas has been established for the first time and subsequently a full agreement with relevant cold atom experiments in trap has been demonstrated. Apart form that many other properties have been investigated as well, mostly in collaboration with others, using a variety of techniques: collective states, exotic pairing mechanisms, phase diagrams of spin imbalanced systems, the existence of a completely new class of self-bound universal dilute system, and others.

In 2006 prof. Bulgac together with prof. George Bertsch became respectively the co-PI and PI of a new national initiative on High Perfomance Computing in Low Energy Nucler Physics under SciDAC, titled Universal Energy Density Functional (UNEDF). This project funded at a level of 3 million dollars per year for five years, brings together researchers from 8 universities and six national labs, both physicists and computer scientists and aims at achieving an order of magnitude improvement in the accuracy and theoretical consistency of the description of nuclear masses, energy spectra and low energy reactions for all known approximately 2500 nuclei and with the aim of providing a reliable extrapolation to the expected 6000 nuclei or so, expected to be created at the radioactive beam facilties to come online in US and other contries in the immediate future. In the first two years prof. Bulgac in collaboration with prof. Piotr Magierski and the computer scientist Kenneth J. Roche (ORNL) are developing new codes for describing ground and excited state properties of nuclei on massively parallel computers.

Prof. Bulgac will continue in the foreseable future his studies of the properties of strongly interacting many fermion systems, in particular the description of their properties within the Quantum Monte Carlo approach, the description of nuclei and other related systems within the Density Functional Theory, the study of various new forms of pairing mechanisms, and the study of the collective modes of these systems. A major part of this research would be performed on the largest supercomputers accessible to us, in the hope that facilitating the ability to use them efficiently for the study of all/large number of nuclei will amount to a quantum leap in our low energy nuclear physics. One can think of this as a new facility to perform theoretical nuclear physics, but not on isolated nuclei or a small number of them, but on a large number/all of them and thus producing hopefuly a more reliable theory, which could have a great impact on other fields (nuclear engineering, nuclear astrophysics, and other applications). It is estimated that these new tools will also be of great use to other fields in physics.