My group is engaged in the study of large N-particle systems under quantum confinement such as Bose-Einstein condensates. An exact solution of the N-body problem is considered to be an "intractable" problem, scaling exponentially with the number of particles, N. The resources required for a solution typically double with every particle added, resulting in a current limit of ~10 particles for an exact solution. We are developing a method which circumvents this exponential scaling with N by rearranging the work so the problem now scales exponentially with order in a perturbation series. Exact solutions are possible at each order for any N. We have accomplished this by using group theoretic as well as graphical techniques. These powerful and elegant techniques "hold their own" as N increases resulting in minimum numerical effort.
We are presently pursuing several studies including the calculation of both ground and excited state energies for Bose-Einstein condensates using trap parameters that approximate current experimental conditions, the determination of an analytic many-body density profile from the first-order wavefunction and an analysis of the fundamental motions associated with excitation. A Bose-Einstein condensate is an ideal system to test a new many-body approach since it is a coherent macroscopic sample of atoms in the same quantum state.
In addition, we have started the extension of our formalism to large systems of strongly interacting fermions which are important in many fields of physics including astrophysics, nuclear, condensed matter as well as atomic physics. Our goal is to bridge the gap between a microscopic quantum Hamiltonian and the macroscopic properties of large N-particle correlated systems.
- D.K. Watson and M. Dunn, "Analysis of the growth in complexity of a symmetry-invariant perturbation method for large N-body systems," J. Phys. B 45, 095002 (2012).
- D.K. Watson and M. Dunn, "Rearranging the Exponential Wall for Large N-Body Systems," Phys. Rev. Lett. 105, 020402 (2010).
- M. Dunn, W. B. Laing, D. Toth, and D.K. Watson, "A Test of a New Interacting N-Body Wave Function," Phys. Rev. A 80, 062108 (2009).
- W.B. Laing, D.W. Kelle, M. Dunn, and D.K. Watson, "A Complete Basis for a Perturbation of the General N-Body Problem," J. Phys. A 42, 205307 (2009).
- W.B. Laing, M. Dunn, and D.K. Watson, "On the Use of Group Theoretical and Graphical Techniques to solve the N-Body Problem with General Two-Body Interactions," J. Math. Phys. 50, 062105 (2009).
- W.B. Laing, M. Dunn, and D.K. Watson, "Analytic, group-theoretic density profiles for confined, correlated N-body systems," Phys. Rev. A 74, 06360 (2006).
- M. Dunn, D.K. Watson and J.G. Loeser, "Analytic, group theoretic wave functions for confined, correlated N-body systems with general two-body interactions," Ann. Phys. 321, 1939 (2006).