Dr. Aniruddha Chakraborty
School of Basic Sciences
Indian Institute of Technology Mandi
Mandi, Himachal Pradesh 175001
India
ph: +(91)1905-237930
achakrab
Understanding the dynamics of barrierless reactions in solution is an interesting problem for theoretical as well as experimental research. A reasonably good model for such reaction would be a particle executing one dimensional random walk on two potential wells in presence of point-like coupling between them. Exact solution of this model was proposed by us. This is an interesting & important work in this field. Our method of solution is used further to solve few related problems.
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Nonadiabatic transition due to potential curve crossing is one of the most important mechanism to effectively induce electronic transitions in collisions. We consider two curves crossing each other & there is a point-like coupling between two curves, which causes transition from one curve to another. Exact solution of this model was proposed by us! This is an interesting & important work in this field. Our method of solution is used extensively to solve few related problems.
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Two-state nano-mechanical systems (mechanical equivalent of 'bit') are very interesting examples for the possibility of observing quantum effects in them. The compression of a nano-rod would cause it to buckle. There are now two possible states, and the system is interesting, as a potential nano-sized device. We have developed quantum mechanical methods for the calculation of the rate of transitions between the two states, due to thermal fluctuations and tunneling. Our method goes beyond the standard method (Transition State Theory).
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Understanding the kinetics of loop formation of long chain polymer molecules has been an interesting research field both, to experimentalists and theoreticians. Loop formation is believed to be an initial step in understanding several protein events. The theories of loop formation dynamics are in general approximate. The looping dynamics of a single polymer chain having reactive end-groups hav been modeled by simplest possible option. In our model, dynamics of end-to end distance is mathematically represented by an equation for a random walking under harmonic potential. Looping process is ensured by adding a sink of arbitrary strength in that equation. We have also incorporated the effect of all other chemical reactions involving either one or both of the end-group on rate of end-to-end loop formation - to the best of our knowledge this is the first time this has been done in any analytical model.
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A reliable potential energy surface is required for studying the dynamics of a molecule in a particular electronic state. For polyatomic molecules, a global potential energy surface is out of reach of current computational capabilities. So one possible way to make progress is to use analytical functions with several parameters to fit the experimental data for constructing an effective Hamiltonian. One can use these effective Hamiltonians to extract new information about dynamics from information encoded in experimental spectra and to use these informations to understand internal molecular energy flow and reaction dynamics. Even when the potential energy surface is available, effective Hamiltonians are constructed from the exact Hamiltonian in order to simplify the subsequent analysis. We have recently developed the first genrealized polyad-breaking effective spectroscopic Hamiltonian for understanding bond dissociation process.
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Two electron atom is the most simplest system to study electron correlation. The doubly excited states of atoms with two outer electrons, exhibit molecule-like collective motion. There are even frozen planet state observed in two electron systems, where the electrons become locked into place on the same side of the nucleus. There are evidence for molecule like collective effects in atoms with three outer electrons. A simple effective spectroscopic Hamiltonian is proposed for double excited two electron atom for understanding independent particle, shielding and correlation effect. The Hamiltonian is constructed by nonlinear least square fit of spectra of two electron systems. An open question in this area is the applicability of this type of correlation to motion of electrons in molecule.
The motion of electrons in quantum dots have many properties in common with ro-vibrational motion of molecules. In fact for highly excited two electron quantum dot, the motion of electrons is much like the ro-vibrational motion of triatomic molecule. Naturally all the effects of anharmonicity are expected to be present in case of motion of electrons in a quantum dot. We have very recently constructed the effective spectroscopic Hamiltonian for motion of electrons in a quantum dot by non linear least square fit of the exact spectrum & we attemped to assign quantum numbers to different electronic states using our effective Hamiltonian.
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Temperature and heat flow are two important quantities in understanding the heat conduction. When temperure distribution is not uniform at all points of a system, then heat flows in the direction of decreasing temperature. In general Fourier equation is used in understanding heat conduction, which is valid only for a homogeneous isotropic solid. But in reality we have solids of different shapes, e.g., we can have a cylinder with nonuniform cylindricity. We solve two dimensional version of this problem to understand the effect of this type of nonuniformity on thermal diffusivity. Our conclusion is valid for systems with higher dimension & is independent of shape of the system.
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Now the question we would be addressing here is the following, what fraction of pixel data is necessary to regenerate the whole pixel data. The pixel data set can be easily converted to a Hermitian data matrix. For a large enough matrix it is difficult, if not impossible to regenerate the whole pixel data. Our method is based on how to express the large matrix in terms of suitable but smaller effective matrices, so it is computationally less expensive & fast. Instead of storing the big data matrix one may store all eigenevalues and a smaller part of the whole matrix. The same method is used for correcting 'defects' in image.
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The Boltzmann distribution (the most probable distribution of energy - in thermal equilibrium) is one of the most important concepts used in physics, chemistry and biology. Often in different experimetal situations, system may not be in thermal equilibrium to start with, then the system will find the most probable state by a random search among all possible energy distributions and thus in principle, can take long time depending on the size of the system. An analysis using our simple model shows that a small and physically reasonable energy bias against locally unfavorable energy distribution, of the order of a few KT, can reduce the time-scale of the process by a significant size.
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Understanding Dynamics in the C60 single molecule transistor
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An electron near a metal surface feels the charge of its image in the metal. So near a metal surface the electron moves under the influence of that attractive potential that supports quantized energy levels whose wave function lie outside the metal surface & whose energy lie in the band gap. Harris et. al., have carried out interesting studies of this image potential states using two-photon photo-emission proces in the case of metal with polar adsorbates. As there does not seem to be any theoretical investigation on this problem, we investigated this problem. In our model, we account for the interaction of the dipole moment of the adsorbate with the lectric field exerted by the lectron perpendicular to the surface.
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For IIT Mandi Students (B.Tech./M.Tech./M.S./M.Sc./Ph.D.) - You are always welcome to inquire about working on a project (irrespective of your discipline). For more details - visit my office!
Dr. Aniruddha Chakraborty
School of Basic Sciences
Indian Institute of Technology Mandi
Mandi, Himachal Pradesh 175001
India
ph: +(91)1905-237930
achakrab