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Theoretical Research

Quantum Chaos and Quantum Information

Principal Investigator: Lev Kaplan

Tulane Group Members: Ron Koshita, Shreyas Sadugol

Group Website

Quantum chaos addresses fundamental questions about quantum-classical correspondence and semi-classical methods for generic quantum systems (with non-integrable classical analogues), 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 recent interest have included:

  • Quantum transport in biologically inspired systems
  • Transport in nanostructures and quantum dots
  • Quantum vacuum energy (Casimir forces) in integrable and non-integrable geometries
  • Statistics of extreme ocean waves (rogue waves)
  • Branching for electron and microwave flow in the presence of correlated disorder
  • Statistics of wave functions and transport in the presence of chaos and disorder
  • Superradiance and transport in open quantum systems
  • Wave functions beyond Random Matrix Theory (RMT)
  • Quantum-classical correspondence and the accuracy of semiclassical approximations
  • Electron-electron interactions in chaotic quantum dots (application to statistics of conductance peaks)
  • Quantum computation in linear optics (designing optimal quantum gates)
  • Quantum metrology using coherent photon states
  • Photons carrying orbital angular momentum and their interaction with matter

Condensed Matter and Materials Theory and Computation/Density Functional Theory

Principal Investigators: Jianwei Sun

Tulane Group Members:Ā  Yubo Zhang, James Furness, Jinliang Ning, Manish Kothakonda, Kanun Pokharel

The importance of materials is demonstrated by the names we use to identify human civilizations, from stone to bronze to iron to the modern silicon ages. On the microscopic scale, all materials exist as collections of atoms consisting of nuclei surrounded by much lighter electrons. The behavior of the electrons is governed by quantum mechanics and largely determines properties of materials. The grand challenge of developing the advanced materials that benefit society therefore becomes how to understand and control material processes at the level of electrons.

The high efficiency and useful accuracy of density functional theory (DFT) and its extensions (e.g., time-dependent or TD DFT), have caused them to become the most widely used electronic structure theories in chemistry, materials science, and condensed matter physics. In principle DFT is exact for the ground state energy and electron density, but in practice the exchange-correlation energy as a functional of electron density must be approximated. My research interests are in understanding the fundamental properties of the exchange-correlation energy (or the exchange-correlation potential and kernel in case of TD-DFT), using this understanding to derive more accurate and efficient approximations, and applying the approximations to predict properties and behaviors of materials and computationally design materials that are scientifically, technologically, or economically important.

I have constructed the strongly-constrained and appropriately-normed (SCAN) density functional that is physically justified, non-empirical, efficient, and accurate. SCAN predicts accurate material structures and energies, with improved electronic energy band gaps for diversely-bonded systems (including covalent, metallic, ionic, hydrogen, and van der Waals (vdW) bonds) simultaneously. SCAN significantly and systematically improves over conventional density functionals, and thus greatly advances the development of DFT and its applications in a wide range of materials. My group currently focuses on taking advantage of SCAN for density functional developments and applications, with an emphasis on:

  1. Development of a local hybrid density functional for solving the strong many-electron interaction (SMEI) originating from a degeneracy or near-degeneracy and the self-interaction error (SIE) due to the imperfect cancellation of the spurious classical Coulomb interaction between an electron and itself.
  2. New insights into difficult electron systems, e.g., strongly-correlated electron systems.
  3. Ionic dynamics for realistic modeling of materials, e.g., finite temperature and pressure effects, and for electron-phonon coupling.
  4. Computational design of cheap and environmentally friendly catalysts based on 2D materials for energy applications.
  5. Quantum materials including superconducting and topological materials.

Nuclear Physics

Principal Investigator: Daniel Purrington

Group Website

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.


History of Physics

Principal Investigator: Daniel PurringtonĀ (Emeritus)

Group Website

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 monograph project on Robert Hooke and the Royal Society.


Mathematical Physics

Principal Investigator: George Rosensteel

Tulane Group Members: Farren Curtis, Nick Sparks

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 non-compact Lie groups, geometric quantization, differential geometry of fiber bundles, dynamical systems on co-adjoint orbits, and density functional theory.


Physics Instruction

Tulane Group Members: Khazhgery "Jerry" Shakov, James McGuire

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, outreach programs within the community, and the development of classroom demonstrations and techniques.

We are also interested in building effective and productive partnerships with STEM educators at elementary and secondary levels. Some of the projects we have been involved with include professional development for local K-12 STEM teachers (Math & Science Partnership NOLA SMILE, Core Element), as well as our service learning course, Introduction to Physics Pedagogy. In that course, Tulane students experience a technology enabled constructivist approach to Physics education by observing and participating in the teaching of Physics courses with Stephen Collins at Lusher Charter School.


Relativity & Cosmology

Principal Investigator: Frank Tipler

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.