Theoretical Research Programs
Principle Investigator: Lev Kaplan
Tulane Group Members: Matt Smith, Athanasios Chalastaras
As the study of quantum systems with non-integrable classical analogues, this field addresses fundamental questions about quantum-classical correspondence and semiclassical methods for generic quantum systems, bringing together methods, insights, and examples from areas as diverse as condensed matter and mesoscopic physics, atomic, optical, molecular, and chemical physics, nuclear physics, microwave physics, nonlinear dynamics, statistical mechanics, and mathematical physics. The goal is to develop a framework and set of techniques relevant to a broad range of complex physical phenomena and transcending the peculiarities of specific physical models.
Specific areas of interest have included:
1) Electron-electron interactions in chaotic quantum dots (application to
statistics of conductance peaks)
2) Statistics of branching for electron flow through a smoooth random potential
3) "Scarring" of quantum wave functions by classical periodic orbits
4) Accuracy of semiclassical approximations and the quantization ambiguity
5) Wave function and spectral properties of systems with two-body random
interactions (application to nuclear binding energies and spin spectra)
6) "Bootstrapping" of short-time dynamical information to predict long-time
behavior for chaotic quantum dynamics
7) Diffusion and anomalous localization in disordered systems
8) Resonance and tunneling statistics for metastable chaotic wells
Tulane Group Members: Raymond Duplessis, Rhett McNorton
This research group is a highly theoretical one working in the art of density functional theory to calculate the Density of States (DOS) or the electronic structure of materials. This all-important aspect of a material lies at the heart of all
solid-state physics, by knowing structure of an atom's electronic shell provides the ability to basically describe or predict all other associated properties. The calculation of atoms' electronic structure requires massive computational power and deft approximations for even relatively basic systems, which is why this group utilizes its own Supercomputing Center to perform VASP calculations.
Research topics mainly consist of the extraction of the
magnetic properties of solids and their interfaces, including the
measurement of materials' anisotropy,magnetization, phase structure and the density of states. Current focus is on the search for a half-metallic material by virtue of a doped metallic semiconductor. These highly exotic materials exist in nature in an anti-ferromagnetic state, and are highly coveted because they play an important role in high temperature superconductors and compressed magnetic storage media. The group is also investigating the phase transitionings of certain binary metallic alloys, which are described by the composition of the unit cell, whether it has all of atom A, all of B or a mixture of both. These phases are interpreted through a graphical representation that relates the different phases by the structures thermal energy and it's molecular concentration. This is beneficial for devices in the realm of electronics, such as circuit gates,switches,loads,etc. There also exists possibilities elsewhere outside of the computer, common things, such as color changing materials and morphable solids to name a few.
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Our group is studying coherent population control of electrons in atoms. We are developing analytic methods to understand how to move electrons from one state to another in an atom when we want, where we want, as completely as we want, as fast as we want, keeping it there as long as we want, using simple mathematics. The trick is to take advantage of degenerate states where quantum energy fluctuations are absent. In this case time correlations are eliminated and the physics and the mathematics both simplify. When non-degeneracy is reintroduced we are able to study quantum time correlations. These effects are observable in some data, e.g. in polarization of light emitted from excited atomic levels. This enables us to understand how time works in quantum mechanical systems.
Current research interests are primarily focused on various aspects of quantum control, concerning a variety of applications ranging from quantum information and quantum computation to modification of paths of chemical reactions. Recent work regarding the development of analytical description of dynamics of N-state quantum systems, especially two- and three-state systems, is most likely to be used for practical applications (e.g. as a physical realization of a qubit - a quantum version of the classical computer bit). Recent work also concerns the role of time correlation and time ordering in the dynamics of the quantum systems interacting with external fields, under the motivation of understanding reaction dynamics and coherent control in the time domain. In particular, we are interested in the study of observable effects of time ordering, and understanding the related problem of time correlation in few body dynamics, corresponding to a system of a few dynamically coupled qubits. We have used both analytic and numerical solutions to study effects of time ordering in multiply kicked systems.
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Principle Investigator: John Perdew
Tulane Group Members: Espen Sagvolden, Xiaolan (Mary) Zhou
Our research group develops the fundamentals and approximations of density functional theory for atoms, molecules and solids. Practical electronic structure calculations in both condensed matter physics and quantum chemistry now usually rely upon this theory, which can predict for example the shape of a molecule or the energy of a bond. The idea is that the complicated many-electron wavefunction can be replaced by something
simpler, such as the electron density or a set of occupied orbitals. This replacement is exact in principle, but in practice one must approximate the functional dependence of the exchange-correlation energy upon the density or orbitals.
We have developed a "Jacob's Ladder" of approximations, in which higher rungs are more accurate but make use of
more complicated ingredients. At least the first three rungs have been constructed non-empirically, using only exact constraints on the functional developed by us and by others. The first rung is the local spin density approximation, which is good enough for many solids but not for molecules. The second rung is the generalized gradient
approximation (GGA), developed here and elsewhere 1976-1996, which achieves a more useful accuracy for chemistry. The third rung is the meta-GGA, just completed here, which further improves the accuracy. Higher rungs are under development.
Our functionals are built into
standard software packages and are widely used by theorists and experimentalists. Recently we have started to work on the kinetic energy as a functional of the density, where an accurate approximation would open the door to the study of very large systems and of problems such as protein folding in water.
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This group's research interests have been traditionally focused on the quantum theory of scattering, principally few-body problems, and nuclear structure. In recent years this has evolved into theoretical treatment of classical scattering, mostly in the ocean acoustics context, and primarily involving scattering from randomly rough interfaces, including fractal geometries.
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Specific scholarship on the history of physics and astronomy in recent years has focused on a number of various topics, including the history of cosmology, the history of physics in the 19th century, and the history of astronomy, principally, archaeoastronomy.
Since 1989, Dr. Purrington has been particularly interested in the scientific revolution, and has just recently completed a mongraph project on Robert Hooke and the Royal Society.
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As one of the original discoverers in the mid 1970's of symplectic dynamical symmetry to describe geometrical collective modes in atomic nuclei and astrophysical systems, this research program encompasses several areas of theoretical and mathematical physics including representations of noncompact Lie groups, geometric quantization, differential geometry of fiber bundles, dynamical systems on co-adjoint orbits, and density functional theory.
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Principle Investigator: none
This loosely organized group focuses on techniques and innovations involved in the teaching of physics, primarily at the college level.
Current and ongoing projects include the development of new courses, technological improvements to lecture and lab courses, out-reach programs within the community, and the development of classroom demonstrations and techniques.
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Astrophysical black holes almost certainly exist, but Hawking has shown that if black holes are allowed to exist for unlimited proper time, then they will completely evaporate, and unitarity will be violated. Thus unitarity requires that the universe must cease to exist after finite proper time, which implies that the universe has the spatial topology of a three-sphere. The Second Law of Thermodynamics says the amount of entropy in the universe cannot decrease, but it can be shown that the amount of entropy already in the CBR will eventually contradict the Bekenstein Bound near the final singularity unless there are no event horizons, since in the presence of horizons the Bekenstein Bound implies the universal entropy S is less that a constant times the radius of the universe squared, and general relativity requires the radius to go to zero at the final singularity. The absence of event horizons by definition means that the universe's future c-boundary is a single point, call it the Omega Point. Thus life (which near the final state, is really collectively intelligent computers) almost certainly must be present arbitrarily close to the final singularity in order for the known laws of physics to be mutually consistent at all times. Misner has shown in effect that event horizon elimination requires an infinite number of distinct manipulations, so an infinite amount of information must be processed between now and the final singularity. The amount of information stored at any given time diverges to infinity as the Omega Point is approached, since the entropy diverges to infinity there, implying divergence of the complexity of the system that must be understood to be controlled.
Life transferring its information to a medium that can withstand the arbitrarily high temperatures near the final singularity has several implications: first, (Omega-naught - 1) is between a millionth and a thousandth, where Omega-naught is the density parameter, and second, the Standard Model Higgs boson mass must be 220 plus or minus 20 GeV.
