Dhruba Banerjee

Solution of quantum Langevin equation: Approximations, theoretical and numerical aspects

Based on a coherent state representation of noise operator and an ensemble averaging procedure using Wigner canonical thermal distribution for harmonic oscillators, a generalized quantum Langevin equation has been recently developed [Phys. Rev. E 65, 021109 (2002); 66, 051106 (2002)] to derive the equations of motion for probability distribution functions in c-number phase-space. We extend the treatment to explore several systematic approximation schemes for the solutions of the Langevin equation for nonlinear potentials for a wide range of noise correlation, strength and temperature down to the vacuum limit. The method is exemplified by an analytic application to harmonic oscillator for arbitrary memory kernel and with the help of a numerical calculation of barrier crossing, in a cubic potential to demonstrate the quantum Kramers turnover and the quantum Arrhenius plot.

Approach to quantum Kramers' equation and barrier crossing dynamics

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum-mechanical mean values of their co-ordinates and momenta we have derived a c number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers rate of barrier crossing and analyze its variation as a function of the temperature and friction. While almost all the earlier theories rest on quasiprobability distribution functions (e.g., Wigner function) and path integral methods, the present work is based on true probability distribution functions and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermally activated processes and tunneling.

Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value, which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.

Quantum Smoluchowski equation: escape from a metastable state

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within a unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.

System-reservoir theory with anharmonic baths: a perturbative approach

In this paper we develop the formalism of a general system coupled to a reservoir (the words bath and reservoir will be used interchangeably) consisting of nonlinear oscillators, based on perturbation theory at the classical level, by extending the standard Zwanzig approach of elimination of bath degrees of freedom order by order in perturbation. We observe that the fluctuation dissipation relation (FDR) of the second kind in its standard form for harmonic baths gets modified due to the nonlinearity and this is manifested through higher powers of in the expression for two-time noise correlation. On the flip side, this very modification allows us to define a dressed (renormalized) system-bath coupling that depends on the temperature and the nonlinear parameters of the bath in such a way that the structure of the FDR (of the second kind) is maintained. As an aside, we also observe that the first moment of the noise arising from a nonlinear bath can be non-zero, even in the absence of any external drive, if the reservoir potential is asymmetric with respect to one of its minima, about which one builds up the perturbation theory.

Excited state complex formation between methyl glyoxal and some aromatic bio-molecules: a fluorescence quenching study.

Fluorescence quenching of some important aromatic bio-molecules (ABM) such as 3-aminophthalhydrazide (luminol), tryptophan (Try), phenylalanine and tyrosine (Tyr) by methyl glyoxal (MG) has been studied employing different spectroscopic techniques. The interaction of MG with ABM in the excited state has been analysed using Stern-Volmer (S-V) mechanism. In the case of MG-luminol system time correlated single photon counting (TCSPC) technique has also been applied to explain the S-V mechanism. The bimolecular rate constants obtained are found to be higher than the rate constant for diffusion controlled process. A plausible explanation of the quenching mechanism has been discussed on the basis of hydrogen bonding, charge transfer and energy transfer interaction between the colliding species.

Experimental and theoretical aspects of proton transfer in 3-methyl-6-hydroxy-m-phthalic acid

The ground- and excited-state proton transfer reactions of 3-methyl-6-hydroxy-m-phthalic acid (HmPA) have been studied in different protic and aprotic solvents at room temperature and 77 K both in the presence and absence of a base. In the ground state, intramolecularly hydrogen-bonded closed conformer has been found to be the only component in nonpolar and weakly polar aprotic solvents, whereas anion is detected in highly polar aprotic solvents. The excited-state intramolecular proton transfer (ESIPT) is evidenced by a large Stokes shifted emission in nonpolar and weakly polar solvents due to the formation of enol tautomer of HmPA. Solute–solvent interaction appears to play a major role in determining the nature of the absorbing and fluorescing species. At 77 K, HmPA shows phosphorescence both in the presence and absence of a base. The observed fluorescence decay rates are relatively slow in polar solvents compared to those in nonpolar and weakly polar solvents. Semiempirical calculations with limited co...

Proton transfer reaction in 4-hydroxy-3-formyl benzoic acid at room temperature and 77 K

Abstract Proton transfer processes of 4-hydroxy-3-formyl benzoic acid (HFBA) have been investigated by means of absorption, emission and nanosecond transient spectroscopy in some nonpolar and polar aprotic solvents at room temperature and 77 K. The excited state intramolecular proton transfer (ESIPT) is evidenced by a large Stokes shifted emission (∼12xa0000 cm −1 ) in nonpolar solvents which is likely to originate from the enol tautomer of HFBA. On the other hand, intermolecular interaction occurs in proton accepting polar aprotic solvents both in the ground and excited state. At 77 K, HFBA shows phosphorescence in DMSO. It is proposed that occurrence of phosphorescence is due to the rupture of intramolecular bond and rotation of the formyl group. From the nanosecond measurements and quantum yield of fluorescence, we have estimated decay rates in polar solvents.