- One Ph.D. position is for working on the anomalous diffusion problem. Random walks are used to model diffusion process. In the usual one dimensional random walk model, the average displacement of the walker after a time t, is proportional to t^{1/2} . However, it is possible to have diffusion processes in which the average displacement is different - we plan to work on few such systems.
- One Ph.D. position is for working on the dynamical analysis of molecular spectra. The aim is to understand dynamics from the information within experimental spectra and to apply for understanding internal molecular energy flow and reaction dynamics. We plan to develope new bifurcation analysis method using catastrophe map for polyad breaking effective Hamiltonian.
- One Ph.D. position is for working on the quantum thermodynamics of small systems. Our plan is to construct a finite bath with variable temperature in which heat flows between a system and the bath environment in time evolution of an initial pure state. Baths of various numbers of oscillators areconsidered. The evolution of the pure state toward an equilibrium state will be analyzed. It is suggested that realizations of these finite-size effects may be attained in case of small molecules.
- One Ph.D. position is for working on the coherence in quantum biology. The greatest challenges in achieving quantum computing is avoiding decoherence. It is of great interest that extraordinarily long decohrence time have been found in the FMO complex, which is in green sulfur bacteria. Using computational tools we plan to understand the origin of this long decoherence time so that new systems with longer decoherence time can be predicted.
- One Ph.D. position is for working on constructing effective Hamiltonian using quantum computer. The effective Hamiltonian is constructed using experimental or simulated data using optimization method. Classical optimization algorithms in often take a long time to compute and require huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed optimization algorithms. We plan to leverage quantum parallelism to speed-up optimization algorithm.
- One Ph.D. position is for working on the energy transfer mechanism in nano-systems. We plan to look at the mechanism of energy transfer from a dye molecule to a nano-system, using computational tools. Some of these systems have found extensive applications in sensing chemicals.
- One Ph.D. position is for working on the Path Integral Methods for multi-state problems. Multi-state problems are important both in quantum and statistical mechanics, but analytically solvable models are very few. We plan to use path integral based methods for finding analytical solution of more model systems, which is considered to be analytically intractable so far.
- One Ph.D. position is for working on the dynamics of spreading of infectious disease. Using simple model system it is possible to predict the dynamics of spreading of infectious diseases. We plan to apply our model for different diseases, by estimating different parameters of the model using real time data. We expect to provide the effect of different schemes for controlling spreading of the disease.
- One Ph.D. position is for working on the Mathematical Modelling of Alzheimer's Disease. Alzheimer is a neuro-degenerative disorder wherein the patient suffers from dementia. Random walk model is generally used to understand dementia. We plan to use an appropriate equation to understand the pattern of memory loss in an Alzheimer's patient. The advantage of this model is the following, very less information is required as input to predict the future condition of the patient.
- One Ph.D. position is for working on Understanding the Effect of Dynamical Barrier on Bond Breaking Process. For molecules such as H2O, D2O and CH2 large volumes of classical vibrational phase space are found to be non-dissociating even well above dissociation energy of a single bond. Classical dynamical study suggests the existence of dynamical constant of motion, which will have the effect of creating a classical dynamical barrier, preventing dissociation and hence the resulting non-RRKM behavior. The standard approach to build effective spectroscopic Hamiltonian is well understood for systems below the dissociation energy of a single bond. But here we need to incorporate the effect of continuum into the effective spectroscopic Hamiltonian, which is one of the key challenges in this area.
- One Ph.D. position is for working on Non-adiabatic mechanism for photosynthetic energy transfer. Plan is to propose a non-adiabatic model for photosynthetic energy transfer in light harvesting antennas is proposed. The non-adiabatic model is expected to lead to enhanced vibrational oscillations on the ground electronic state of these antennas.
- One Ph.D. position is for working on Exactly solvable light-matter interaction models. Plan is to propose exactly solvable quantum models for understanding light-matter interaction associated with the propagation of laser pulses through gaseous media. The goal is to provide a quantum mechanical description which can integrate Maxwell and Schr ̈odinger description and provide a means to realistically simulate nonlinear optical experiments.
- One Ph.D. position is for working on Understanding the unusual properties of metamaterials. Ever since their first experimental demonstration in 2000, the interest in metamaterials has increased tremedously. Here the plan is to understand few unexpexted properties of electromagnetic metamaterials in details.