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 non-stationary 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 is demonstrated.We derive the dressed time-dependent Kramers rate in the nonstationary regime in closed analytical form which exhibits strong non-exponential relaxation kinetics of the reaction co-ordinate. The feature can be identified as a typical non-Markovian dynamical effect.

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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 show 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 nonequilibrium 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 and gives a microscopic insight on the cooperative binding of substrate on a single oligomeric enzyme which is usually characterized by macroscopic reaction rate.

Here we consider an interchain interaction model to understand the spectral properties of aggregate of a class of conjugated polymers. The dressed eigenstates are calculated for the equivalent and inequivalent chain dimers and are symmetry classified. We have provided the Wigner function matrix to describe the quantum interference due to nonadiabaticity in the excitonic states, the energy distribution between the chains as well as the phase relation between the vibrational modes. The various disorder-induced effects on the spectra can be explained by the dimeric chains that are generally inequivalent.

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On the basis of the fermionic coherent state of Cahill and Glauber [Phys. Rev. A 59, 1538 (1999)], we have introduced here the fermionic thermocoherent state in terms of the quasiprobability distribution which shows the appropriate thermal and coherent limits as in the bosonic case or the Glauber-Lachs state. It is shown that the fermionic thermocoherent state can be realized as a displaced thermal state of fermions. Its relation with the fermionic displaced number state and the fermion-added coherent state are explored in the spirit of the bosonic case. We have investigated the nature of the average current and the suppression of noise due to the thermocoherent character of the source. The theory is applied to the problem of electronic conduction. A modification of the Landauer conductance formula is suggested which reflects the role of nonzero coherence of the source in electron transport.

On the basis of the formalism of the fermionic coherent state of Cahil and Glauber (1999 Phys. Rev. A 59 1538), we have provided an exact solution to a model of a harmonic oscillator coupled to a fermionic environment via a quantum non-demolition type interaction. Quantum phase diffusion and linear entropy dynamics show their signature felt by the suppression of decoherence with temperature in comparison to the bosonic bath case, which may be worth investigating for their application in the coherent dynamics domain at finite temperature. We have shown an unconventional motional narrowing of the quantum Kubo oscillator, which is realized from this model due to the antibunching character of fermionic quantum noise. It is possible to bring this out explicitly here by the consideration of the non-commutative property of interaction obeying the Grassmann algebra.

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 atomfield 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.