Ashok Sethia

Discretized path integral method and properties of a quantum system

Using the discretized path integral formalism we develop a numerically convenient and accurate method for evaluating the finite time propagator (and density matrix) of a given system. The eigenfunctions and energies of large number of states of the system are also found. We demonstrate the accuracy of the method by computing eigenvalues, eigenfunctions, position and flux autocorrelation functions and complex time propagators for a large number of systems and comparing these results with those available from other sources. In all the cases we find very good agreement. The method thus provides a very simple and accurate procedure for the study of static and dynamic properties of a quantum system.

Eigenstates from the discretized path integral

Abstract A numerically convenient and accurate method for evaluating eigenstates of a quantum system with an arbitrary angular momentum ( l ) is proposed using the discretized version of the path integral. The accuracy of the method is examined by comparing the calculated results with analytical solutions for simple systems.

Density matrix and eigenstates for an excess electron in water

Abstract We extend the molecular theory of the solvated electrons [Chandler, Singh and Richardson, J. Chem. Phys. 81, 1975 (1984)] to calculate the density matrix for an excess electron in water. Using this density matrix, the numerically obtained solvent induced interaction [Miura and Hirata, J. Phys. Chem. 98, 9649 (1994)] and our developed method [Sethia, Sanyal and Singh, J. Chem. Phys. 93, 7268 (1990)], we have calculated the eigenstates of the electron in water. These results show that the excees electron in water behaves almost like a free particle with effective mass m* in a constant potential well.

Quantum dynamics: Path integral approach to time correlation functions in finite temperature

We propose a method to calculate time correlation functions using path integral formulation of quantum mechanics. The accuracy of the proposed method is examined by comparing the calculated result with exact and centroid molecular dynamics results.

Electron self-trapping in two-dimensional fluid

Abstract The behavior of an excess electron in two-dimensional classical liquid has been studied with the aid of the Chandler, Singh and Richardson (CSR) theory [J. Chem. Phys. 81 (1984) 1975]. The size or dispersion of the wavepacket of a solvated electron is very sensitive to the interaction between the electron and fluid atoms, and exhibits complicated behavior in its density dependence. The behavior is interpreted in terms of an interplay among three causes: the excluded volume effect due to solvent, the pair attractive interaction between the electron and a solvent atom, and a balance of the attractive interactions from different solvent atoms.

Density matrix for an excess electron in a classical fluid: Results for a one-dimensional system

We extend the theory of Chandler, Singh, and Richardson [J. Chem. Phys. 81, 1975 (1984)] to calculate the density matrix for an excess electron in a classical liquid like bath. For a one-dimensional fluid of hard rods and for two model potentials representing the electron fluid atom interaction (one representing the excluded volume effect and the other attractive interaction), we calculate the density matrix using the values of solvent induced potential surfaces for the electron found from our earlier calculations [Phys. Rev. B 42, 6090 (1990)]. The resulting density matrix is diagonalized and values of energies and wavefunctions of the electron including the effective mass and root mean square (RMS) displacement Rβ in imaginary time βℏ. The transition of the electron to a state of self-trapping is visualized through a sudden change in the value of Rβ or the effective mass m* at a value of β or solvent density ρs*. For a potential model of hard rods, we find that the RMS displacement Rβ for a given solven...

Interplay Between the Repulsive and Attractive Interaction and the Spacial Dimensionality of an Excess Electron in a Simple Fluid

The behavior of an excess electron in a one, two and three dimensional classical liquid has been studied with the aid of Chandler, Singh and Richardson (CSR) theory [J. Chem. Phys.81, 1975 (1984)]. The size or dispersion of the wavepacket associated with the solvated electron is very sensitive to the interaction between the electron and fluid atoms, and exhibits complicated behavior in its density dependence. The behavior is interpreted in terms of an interplay among four causes: the excluded volume effect due to solvent, the pair attractive interaction between the electron and a solvent atom, the thermal wavelength of the electron (λe), a balance of the attractive interactions from different solvent atoms and the range of repulsive interaction between electron and solvent atom. Electron self-trapping behavior in all the dimensions has been studied for the same solvent-solvent and electron-solvent interaction potential and the results are presented for the same parameter in every dimension to show the comparison between the various dimensions.