Fields of Research Applied Optics: Students will be responsible for presentations during this weekly seminar.
Foundation and Symmetries L. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i. We present a rigorous derivation of the nonlinear Dirac equation from first principles. We provide a thorough discussion of all symmetries broken and maintained.
Introduction perature and interaction sign, magnitude, and symmetry can be controlled externally. Moreover, 2D physics has Recently the first truly two-dimensional 2D solid state recently been of great interest in this context, in the form material, graphene, was created in the laboratory [1,2].
One of the Berzinskii-Kosterlitz-Thouless crossover , and 2D of the most exciting aspects of this novel material is that systems underpinned by lattices are immediately available long wavelength excitations are described by a Dirac equa- in experiments.
Thus one can study rela- graphene , we consider ultra-cold bosons. Bosonic statis- tivistic phenomena at very low velocities in an experiment tics and interactions lead to a new feature in the massless far more accessible than a particle accelerator.
The only real Dirac equation known in graphene — a naturally occurring requirement to obtain this equation is the simple hexago- nonlinear term, giving rise to a nonlinear Dirac equation. One The study of nonlinear phenomena in ultra-cold atoms, can therefore consider any solid state system constructed especially in Bose-Einstein condensates BECs [7,8], on a honeycomb lattice, including artificial systems, in or- has been enormously fruitful.
The nonlinear The most precise, cleanest, most controllable artificial mean field description given by the nonlinear Schrodinger solid state system is ultra-cold atoms in optical lattices. Vector and non-local generaliza- specifically added in by hand.
They are very versatile: Their tem- of the system is greater than one [10,11].
In this article, we present a completely new class of non- linear phenomena in BECs, based on the nonlinear Dirac Email addresses: Nonlinear Dirac equations have a long Carr. Preprint submitted to Elsevier 20 March history in the literature, particularly in the context of par- ey ticle and nuclear theory [12,13,14,15], but also in applied mathematics and nonlinear dynamics [16,17,18,19,20].
As nonlinearity is a ubiquitous aspect of Nature, it is natural to ask how nonlinearity might appear in a relativistic set- ting. However, this line of questioning has been strongly constrained by modeling, rather than first principles.
That is, there is no standard first principle of quantum electro- B n dynamics QED which is nonlinear. So, the approach has 1 been to require symmetry constraints in nonlinear mod- els. One of these constraints is the principle of relativity, i. Given that this form of nonlinear- ity, which depends only on the local condensate density, is one of the most common throughout nature, it is important a Hexagonal lattice structure to recognize that the principle of relativity may be broken by small nonlinearities even at a fundamental level, for ex- ky ample of QED [21,22].
In B A Sec. The nonlinear Dirac equation Fig. Characterization of a honeycomb lattice. Expanding in terms of Bloch states in the lowest band belonging to A or B sites of the honeycomb lattice, as The second quantized Hamiltonian for a weakly interact- shown in Fig.
The spatial dependence is then lattice formed by standing waves of three sets of counter- encapsulated outside the operator in the exponential and propagating laser beams .
The atoms experience this po- the functions u. The summation indices indicate sums over tential via the AC Stark effect. We assume that the third A or B sites. Then only integrals involv- In order to work towards the nonlinear Dirac equation, ing neighboring A-B sites remain in the sum.
This is similar i.Included are a copy of the thesis; letters from and about former refugees; photocopies of the articles, clippings, and manuscripts; photocopy of the Displaced Person's Commission's Mississippi File in the National Archives; taped interview with P.W.
Burgemeester. Mines is a global leader in research and the advancement of technology.
Led by our world-class faculty, the research conducted at Mines enhances the educational experience of our graduates. Contact Information: Alex Flournoy, Teaching Professor Physics Colorado School of Mines Golden, CO USA Coorstek Room Phone: () Fax: () Research in the Department is organized under three primary themes: subatomic physics, condensed matter physics, and applied optics.
With 23 faculty, 52 graduate students, and undergraduate physics majors, the Physics Department at Mines is a vibrant intellectual community providing high-quality education in state-of-the-art facilities.
Alex Flournoy Teaching Professor, Department of Physics. I am interested in progress toward a deeper and more complete understanding of gravitation. We have an extensive understanding of the other three fundamental forces in the Standard Model (SM) in terms of local gauge theories formulated on a fixed Lorentz invariant background spacetime.
May 02, · Finding out more about what my summer research project in theoretical nuclear physics entails! Going to spend quite a bit of time at JLab (Jefferson Lab) ove.