## Quantum Chaos and Quantum Information

**Principal Investigator: Lev Kaplan**

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 Investigator: Jianwei Sun**

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:

- 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.
- New insights into difficult electron systems, e.g., strongly-correlated electron systems.
- Ionic dynamics for realistic modeling of materials, e.g., finite temperature and pressure effects, and for electron-phonon coupling.
- Computational design of cheap and environmentally friendly catalysts based on 2D materials for energy applications.
- Quantum materials including superconducting and topological materials.

## Quantum Technologies and Ultrafast Nonlinear Optics

**Principal Investigator: Denys I. Bondar**

Our group conducts theoretical and computational research at the boundary of quantum technology and ultrafast nonlinear optics. Of particular interest is the exploration how quantum control can be used to produce on-demand nonlinear optical properties, and how tailored nonlinear optical effects can enhance information processing tasks. Our research recently featured in Nature Materials, Physics, PhysicsWorld, US Army, Tulane News etc.

The other active research thrusts include

- Optics including quantum, ultrafast, nonlinear, and incoherent
- Optical communication and sensing
- Nonequilibrium quantum statistical mechanics
- Many-body quantum physics
- Quantum-classical analogies
- Quantum-classical hybrids
- Tunneling of complex systems (BEC)

A few more details:

*High performance computing via nonlinear optics*: The dominant paradigm of solid-state digital computers is bound to reach the technological limits with no viable alternative in sight. Thus, it is time to seek novel physical realizations of computing. We evaluate the possibility of utilizing nonlinear optical effects as a computational platform. This may pave the way for the development of new physical realization of computation.

*Quantum reservoir engineering:*Realistic models of large quantum systems must include dissipative interactions with an environment, which may be of various natures (e.g., spontaneous emission, fluorescence, collisions, etc). It is widely believed that the dissipative forces destroy quantum features. This opinion is being challenged by reservoir engineering. In particular, it is possible to preserve and even enhance the quantum dynamical features of a system by judiciously coupling the system to a dissipative environment. Moreover, dissipative dynamics opens unique possibilities, not offered by potential forces, such as the violation of Newtonâ€™s third law.

*Novel optical technology exploring quantum-classical analogies:*Optical analogs of quantum phenomena rely upon the resemblance of the Schrodinger equation to the wave equation with the paraxial approximation, where the wavefunction is replaced by the electric field. Using this analogy, we are developing new optical technologies for sensing and communication by adapting quantum reservoir engineering to the realm of classical optics.

*Quantum-classical hybrids:*The interplay between quantum and classical systems is one of the most fascinating open questions of modern science. In particular, classical-quantum hybrid systems, in which both quantum and classical degrees of freedom interact, lies at the heart of several scientific disciplines ranging from chemistry to quantum gravity. Despite its importance, a fully consistent classical-quantum theory has eluded the countless attempts to develop one. In order to describe the hybrid systems, we are utilizing the Koopman-von Neumann (KvN) theory, which provides a quantum-like description of classical mechanics in terms of wave functions and self-adjoint operators. The KvN approach is based on a fundamental observation: both classical and quantum evolutions are represented by unitary transformations. Although widely used in dynamical system theory, the KvN method remains unknown in other areas. The KvN approach is diametrically opposite to the phase-space representation of dynamics, which has been the basis of all the previous attempts to construct hybrid systems, providing a classical-like description of quantum dynamics in terms of momenta and coordinates.

*Theory of theories:*We are living in the age of omnipresent data. A much-needed capability is to convert the collected data, irrespective of its nature, into knowledge characterizing the phenomenon that generated the data. This is a bottom-up approach, when a dynamical model is inferred from observed data. Whereas, the top-to-bottom approach refers to when a model is proposed first and then its predictions are confronted with observations (e.g., the least action principle). We are developing the bottom-up framework of Operational Dynamical Modeling that will allow physical models to be distilled directly from measured data in a systematic way. This approach will not only enable to obtain efficient models for complex systems, but also solve open problems in nonequilibrium quantum dynamics.

## Nuclear Physics

**Principal Investigator: Daniel Purrington (Emeritus)**

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 Purrington (Emeritus)**

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**

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.