Gautam Gangopadhyay

Steady-state spectral properties of dendrimer supermolecule as a light harvesting system

We have considered the dendrimer supermolecule as comprised of two-level systems as monomer units on the nodes of a Cayley tree. Each unit undergoes dissipation and driving by an external laser field along with nearest neighbour interaction among the monomer units. We have studied the steady-state absorption spectra. The effects of Cayley tree geometry on the spectral properties are investigated through the intensity and width of the spectra. The origin of the enhanced energy transfer mechanism of the extended dendrimer in comparison to the compact one is explained.

Theory of nonstationary activated rate processes: Nonexponential kinetics

We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features of non-Markovian Langevin dynamics with a fluctuating barrier. Making use of the Fokker-Planck description, we calculate the barrier dynamics in the steady-state and nonstationary regimes. The Kramers-Grote-Hynes reactive frequency has been computed in closed form in the steady state to illustrate the strong dependence of the dynamic coupling of the system with the relaxing modes. The influence of nonequilibrium excitation of the bath modes and its relaxation on the kinetics of activation of the system mode are demonstrated. We derive the dressed time-dependent Kramers rate in the nonstationary regime in closed analytical form which exhibits strong nonexponential kinetics of the reaction coordinate. The feature can be identified as a typical non-Markovian dynamical effect.

Studies on energy transfer in dendrimer supermolecule using classical random walk model and Eyring model

We have analyzed the energy transfer process in a dendrimer supermolecule using a classical random walk model and an Eyring model of membrane permeation. Here the energy transfer is considered as a multiple barrier crossing process by thermal hopping on the backbone of a cayley tree. It is shown that the mean residence time and mean first passage time, which involve explicit local escape rates, depend upon the temperature, size of the molecule, core branching, and the nature of the potential energy landscape along the cayley tree architecture. The effect of branching tries to create a uniform distribution of mean residence time over the generations and the distribution depends upon the interplay of funneling and local rates of transitions. The calculation of flux at the steady state from the Eyring model also gives a useful idea about the rate when the dendrimeric system is considered as an open system where the core is absorbing the transported energy like a photosynthetic reaction center and a continuous supply of external energy is maintained at the peripheral nodes. The effect of the above parameters of the system are shown to depend on the steady-state flux that has a qualitative resemblence with the result of the mean first passage time approach.

Entropic estimate of cooperative binding of substrate on a single oligomeric enzyme: An index of cooperativity

Here we have systematically studied the cooperative binding of substrate molecules on the active sites of a single oligomeric enzyme in a chemiostatic condition. The average number of bound substrate and the net velocity of the enzyme catalyzed reaction are studied by the formulation of stochastic master equation for the cooperative binding classified here as spatial and temporal. We have estimated the entropy production for the cooperative binding schemes based on single trajectory analysis using a kinetic Monte Carlo technique. It is found that the total as well as the medium entropy production shows the same generic diagnostic signature for detecting the cooperativity, usually characterized in terms of the net velocity of the reaction. This feature is also found to be valid for the total entropy production rate at the non-equilibrium steady state. We have introduced an index of cooperativity, C, defined in terms of the ratio of the surprisals or equivalently, the stochastic system entropy associated with the fully bound state of the cooperative and non-cooperative cases. The criteria of cooperativity in terms of C is compared with that of the Hill coefficient of some relevant experimental result and gives a microscopic insight on the mechanism of cooperative binding of substrate on a single oligomeric enzyme which is usually estimated from the macroscopic reaction rate.

Population trapping in the Jaynes-Cummings model with a Kerr nonlinearity in the cavity

An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.

Bloch space structure, the qutrit wavefunction and atom–field entanglement in three-level systems

We have given a novel formulation of the exact solutions for the lambda, vee and cascade three-level systems where the Hamiltonian of each configuration is expressed in the SU(3) basis. The solutions are discussed from the perspective of the Bloch equation and the atom-field entanglement scenario. For the semiclassical systems, the Bloch space structure of each configuration is studied by solving the corresponding Bloch equation and it is shown that at resonance, the eight-dimensional Bloch sphere is broken up into two distinct subspaces due to the existence of a pair of quadratic constants. Because of the different structure of the Hamiltonian in the SU(3) basis, the non-linear constants are found to be distinct for different configurations. We propose a possible representation of the qutrit wave function and show its equivalence with the three-level system. Taking the bichromatic cavity modes to be in the coherent state, the amplitudes of all three quantized systems are calculated by developing an Euler angle based dressed state scheme. Finally following the Phoenix-Knight formalism, the interrelation between the atom-field entanglement and population inversion for all configurations is studied and the existence of collapses and revivals of two different types is pointed out for the equidistant cascade system in particular.

Master equation approach to single oligomeric enzyme catalysis: Mechanically controlled further catalysis

Motivated by the single molecule enzymatic experiments, we have provided a master equation description of enzyme catalysis in a chemiostatic condition for an immobilized oligomeric molecule with many equivalent active sites. The random attachment and detachment of substrate molecules on the various active sites of the oligomeric enzyme is studied in terms of the classical parameters of the Michaelis-Menten type process. In the limit of single molecule process, the master equation approach gives the result of waiting time distribution. On the other hand, for a large number of equivalent active sites or a few numbers of active sites with large Michaelis constant, the master equation gives a Poisson distribution in the nonequilibrium steady state. For the oligomeric enzyme, the net rate of the reaction in the nonequilibrium steady state is multiplied by the number of active sites which is further enhanced by more than two orders of magnitude with the application of external force of 10-100 pN through the techniques of atomic force microscopy. Substrate flux and reaction rate constants have interesting consequences on the dynamics and at nonequilibrium steady state which can be the controlling factors for macroscopic biochemical processes.

Dynamics of cascade three-level system interacting with the classical and quantized field

We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized field with different initial conditions of the atom. For the semiclassical model, it is found that if the atom is initially in the middle level, the time-dependent populations of the upper and lower levels are always equal. This dynamical symmetry exhibited by the classical field is spoiled on quantization of the field mode. To reveal this non-classical effect, a Euler matrix formalism is developed to solve the dressed states of the cascade Jaynes-Cummings model (JCM). Possible modification of such an effect on the collapse and revival phenomenon is also discussed by taking the quantized field in a coherent state

A master equation approach to multiphoton dissociation of a Morse oscillator

Based on the previous work [Gangopadhyay and Ray, J. Chem. Phys. 96, 4693 (1992)] on the generalization of the dissipative master equation for nonlinear oscillators, a theory of multiphoton excitation and dissociation of a Morse oscillator in presence of dissipation has been formulated. Interplay of excitation and dissipation with the nonlinearity of the system has been illustrated in the calculation of dissociation probabilities and the mean first passage time for the escape problem.

An operator approach to the construction of generating functions for the product of Laguerre polynomials: the thermal average bandshape function of a molecule

We introduce two different forms of mathematical identities, involving the product of Laguerre polynomials. These identities are a direct reflection of an operator identity. It is shown that these relations are useful in calculating the thermal average bandshape function of a molecular system. For a model displaced-oscillator system we derive how the displacement between two adiabatic potential surfaces affects the bandshape function.