# Potential student research projects

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## Atomic and Molecular Physics

### Coherent control of quantum-mechanical systems

The project studies possibility of the coherent control (i.e. manipulating properties of a quantum system, such as charge density, levels populations, etc., using a suitably tailored laser pulse) for a quantum mechanical model of a molecule.

### Attosecond time-resolved atomic reactions

We apply the most advanced quantum-mechanical modeling to resolve electron motion in atoms and molecules on the atto-second (one quintillionth of a second) time scale. Our theoretical modeling, based on a rigorous, quantitative description of correlated electron dynamics, provides insight into new physics taking place on the atomic time scale.

### Atomic ionization in super-strong laser fields

Using methods of quantum many-body theory to describe elementary processes in atoms and molecules interacting with strong electromagnetic fields.

### Double electron photo-ionization of a 1D helium atom

The project studies double photon ionization of a helium atom using simplified one-dimensional model. This allows to elucidate some features of the process (such as possible existence of the effect of the Rabi oscillations in the double ionization probabilities), which (for computational reasons) are difficult to study using the 3D model.

## Photonics, Lasers and Nonlinear Optics

### Localised formations in open systems

Dissipative solitons are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. Their existence requires continuous supply of energy and matter that is available in open systems. The model explains variety of phanomena in biology and physics.

Professor Nail Akhmediev, Dr Adrian Ankiewicz, Dr Natasha Devine, Dr. Wonkeun Chang

### Extreme events in nature and in a laboratory

The concept of rogue waves was born in nautical mythology, entered the science of ocean waves and gradually moved into other fields: optics, matter waves, superfluidity. This project will allow students to enter the front edge of modern science.

Professor Nail Akhmediev, Dr Adrian Ankiewicz, Dr. Wonkeun Chang, Dr Natasha Devine

## Theoretical Physics

### Stochastic dynamics of interacting systems and integrability

There are many interesting physical statistical systems which never reach thermal equilibrium. Examples include surface growth, diffusion processes or traffic flow. In the absence of general theory of such systems a study of particular models plays a very important role. Integrable systems provide examples of such systems where one can analyze time dynamics using analytic methods.

### Introduction to quantum integrable systems

The aim of this project is to introduce quantum integrable systems which play a very important role in modern theoretical physics. Such systems provide one of very few ways to analyze nonlinear effects in continuous and discrete quantum systems.

### String theory and integrable systems

This project aims to develop and employ the full power of the theory of integrable quantum systems to new models of quantum many-body spin systems in string theory.

### Coherent control of quantum-mechanical systems

The project studies possibility of the coherent control (i.e. manipulating properties of a quantum system, such as charge density, levels populations, etc., using a suitably tailored laser pulse) for a quantum mechanical model of a molecule.

### Attosecond time-resolved atomic reactions

We apply the most advanced quantum-mechanical modeling to resolve electron motion in atoms and molecules on the atto-second (one quintillionth of a second) time scale. Our theoretical modeling, based on a rigorous, quantitative description of correlated electron dynamics, provides insight into new physics taking place on the atomic time scale.

### Atomic ionization in super-strong laser fields

Using methods of quantum many-body theory to describe elementary processes in atoms and molecules interacting with strong electromagnetic fields.

### Combinatorics and integrable systems

We will study links between integrable systems in statistical mechanics, combinatorial problems and special functions in mathematics. This area of research has attracted many scientist's attention during the last decade and revealed unexpected links to other areas of mathematics like enumeration problems and differential equations.

### Localised formations in open systems

Dissipative solitons are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. Their existence requires continuous supply of energy and matter that is available in open systems. The model explains variety of phanomena in biology and physics.

Professor Nail Akhmediev, Dr Adrian Ankiewicz, Dr Natasha Devine, Dr. Wonkeun Chang

### Exact Bohr-Sommerfeld quantisation and Conformal Field Theory

It is well known that the quasiclassical quantisation of the harmonic oscillator leads to its exact quantum mechanical spectrum. Remarkably, this result can be generalized to various anharmonic systems via mysterious connections to Conformal Field Theory.

### Mathematical Aspects of Conformal Field Theory

Conformal Field Theory (CFT) in two-dimensions describes physics of the second order transitions in statistical mechanics and also plays important role in string theory, which is expected to unify the theory of strong interaction with quantum gravity. The project aims to explore and further develop mathematical techniques of CFT.

### New connections between classical and quantum field theories

The standard correspondence principle implies that quantum theory reduces to classical theory in the limit of the vanishing Planck constant. This project is devoted to a new type connection between quantum and classical systems which holds for arbitrary finite values of the Planch constant.

### High energy scattering in gauge and string theories

It appears that the scattering amplitudes in Quantum Chromodynamics (theory of strong interactions) can be exactly calculated in certain limiting cases (e.g. in the so-called multi-Redge kinematics). This is possible due to remarkable connections of this problem to the theory of integrable systems based on the Yang-Baxter equation.

### Extreme events in nature and in a laboratory

The concept of rogue waves was born in nautical mythology, entered the science of ocean waves and gradually moved into other fields: optics, matter waves, superfluidity. This project will allow students to enter the front edge of modern science.

Professor Nail Akhmediev, Dr Adrian Ankiewicz, Dr. Wonkeun Chang, Dr Natasha Devine

### New trends in separation of variables

A separation of variables is a standard technique in classical mechanics which allows to reduce a complicated dynamics with many degrees of freedom to a set of one-dimensional problems. Surprisingly this method finds its natural generalization in the theory of quantum integrable systems. This project aims to study such systems and apply results to the theory of special functions in one and several variables.

### Variational approach to many-body problems

In recent years there was a large boost in development of advanced variational methods which play an important role in analytic and numerical studies of 1D and 2D quantum spin systems. Such methods are based on the ideas coming from the renormalization group theory which states that physical properties of spin systems become scale invariant near criticality. One of the most powerful variational algorithms is the corner-transfer matrices (CTM) method which allows to predict properties of large systems based on a simple iterative algorithm.

### Double electron photo-ionization of a 1D helium atom

The project studies double photon ionization of a helium atom using simplified one-dimensional model. This allows to elucidate some features of the process (such as possible existence of the effect of the Rabi oscillations in the double ionization probabilities), which (for computational reasons) are difficult to study using the 3D model.

*Other research projects may be found at the ANU College of Engineering & Computer Science and the Research School of Astronomy & Astrophysics*