Pranab Sarkar

Intense radiation induced dissociation dynamics of a model diatomic molecule with randomly varying binding energy

Abstract The radiation induced dissociation dynamics of a diatomic molecule interacting with the surrounding and modelled by an appropriate Morse oscillator with randomly varying binding energy (well-depth), is studied by invoking the time-dependent Fourier grid Hamiltonian method. The intensity threshold for dissociation is shown to be reduced if the well-depth of the oscillator changes randomly irrespective of the nature of the perturbing field (continuous or pulsed). Strong pulse-shape effects on the dissociation dynamics of a diatom with randomly varying well-depth are predicted. Sensitivity of the computed threshold intensity for dissociation towards variations of the isotopic mass of the diatom and noise frequency has also been probed.

A QUANTAL ENTROPY SIGNATURE FOR THE DYNAMICS OF PURE STATES : STUDIES ON SOME MODEL PROBLEMS

Abstract Von Neuman-Shannon entropy is zero for a pure state and remains so at every stage of its unitary evolution. However, a pseudo or quantal entropy ( S Q ) of a pure state reveals significant dynamical features during a unitary evolution. S Q can be identified, in a way with the entropy of ‘basis mixing’. The quantum evolution of a pure state is generally shown to be accompanied by an early loss of information followed by an information gain at a later stage. This happens irrespective of the adiabaticity or the lack of it in the evolution process. Several model problems studied tend to suggest generality of this behaviour. These include, the photo-dissociation dynamics of a diatomic molecule modeled by a Morse oscillator, photo-dissociation of a randomly perturbed Morse oscillator, destabilization of a random linear oscillator perturbed by quartic anharmonicity, generalized Rabi oscillations in a three-level metastable system, etc. Adiabatically switching from a classically regular to a classically chaotic region of a suitable Hamiltonian which is known to generate quantum chaos is shown to leave a recognizable signature on the quantum dynamics of S Q . This leads us to suggest that S Q can perhaps be used as a dynamic descriptor for the onset of quantum chaos.

The dynamics of a harmonic oscillator with time-dependent force constant and perturbed by weak quartic anharmonicity

Abstract A harmonic oscillator with time-dependent force constant when perturbed by a weak static quartic anharmonicity λ x 4 , λ small, is shown to generate new features in the dynamics. For weak coupling, both time-dependent perturbation theoretical analysis and near-exact numerical calculations predict that the excitation probability to an accessible excited state is a parabolic function of λ for a short time when all other parameters of the system are fixed. This is approximately independent of the form of the time-dependence of the harmonic force constant. Bound state populations are shown to oscillate in time when anharmonic coupling is present, due to mutual interference of the relaxing force constant and anharmonicity.

Multidimensional propagator scheme for explicitly time-dependent Hamiltonians: applications to the multiphoton dissociation dynamics of the HCN molecule

Abstract A new multidimensional time-dependent quantum mechanical method is proposed for studying the evolution of explicitly time-dependent Hamiltonians. A propagator is constructed by making use of multidimensional Floquet states. Model applications to the problem of the dissociation of a triatomic molecule (restricted to collinear geometry) in strong laser fields, particularly multimode dissociation dynamics, are encouraging.

A random walk to local minima and saddle points on a potential energy surface. A strategy based on simulated annealing

We demonstrate how the Metropolis simulated annealing method, a global stochastic minimizer, can also be used as an all-purpose extremizer capable of locating all the local minima and saddle points on a given surface, in addition to the global minimum. The demonstration is done with reference to the well studied Muller-Brown potential and a one-dimensional spin glass with random nearest-neighbour interaction. The relevance of the present strategy in the construction of reaction paths is discussed.

On the tunneling dynamics of a cubic oscillator with a time-dependent harmonic frequency

Abstract The dynamics of a 1-d cubic oscillator having a time-dependent harmonic force constant is studied numerically by invoking the time-dependent Fourier grid Hamiltonian method. The temporal variation in Kt causes the tunneling rate constant to decrease or increase, depending upon the nature of the time-dependence of K. For the exponentially increasing or decreasing force constant, the intrinsic tunneling rate constant (ktun0v) (in the limit of zero rate of relaxation of the harmonic force constant) is obtained by extrapolation of k tun v ( 1 τ ) to 1 τ = 0 . The ktun0v computed this way compares well with those obtained from the complex scaled Fourier grid Hamiltonian method. The effects of changing the form of the time-dependence of K are analysed and the possibility of mapping real systems onto the present model is explored.

Bound state population and dissociation dynamics of a Morse oscillator with oscillating well-depth and driven by intense radiation: Perturbative and numerical studies

Bound state population dynamics in a diatom modelled by an appropriate Morse oscillator with a time-dependent well-depth is investigated perturbatively both in the absence and presence of high intensity radiation. For sinusoidally oscillating well-depth, the population of themth bound vibrational level,Pmm(t), is predicted to be a parabolic function of the amplitude of the oscillation of the well-depth (ΔD0) at a fixed laser intensity. For a fixed value of ΔD0,Pmm(t) is also predicted to be quadratic function of the field intensity (ɛ0). Accurate numerical calculations using a time-dependent Fourier grid Hamiltonian (TDFGH) method proposed earlier corroborate the predictions of perturbation theory. As to the dissociation dynamics, the numerical results indicate that the intensity threshold is slightly lowered if the well-depth oscillates. Possibility of the existence of pulse-shape effect on the dissociation dynamics has also been investigated.

Noise induced tunneling suppression of a metastable quantum system driven by an oscillating field: A numerical experiment

A numerical experiment on the tunneling dynamics of a metastable quantum system placed in an oscillating field and simultaneously sybjected to a small amount of noise is reported. We demonstrate that for a fixed strength of the driving field both tunneling probability and rate show a resonance-like dependence on noise frequency. For a given field strength, the injection of a small amount of noise is shown to suppress the tunneling probability and rate of tunneling. It may be considered as an example of noise-induced stabilization of an inherently unstable system. The qualitative features of the effect appear to be independent of how noise couples to the system (e.g. linear or quadratic), i.e. the details of the shape of the potential.

Quantum dynamics of a time-dependent multidimensional non-linear oscillator and modelling of ultrafast intensity oscillations in charge transfer spectra

Quantum dynamics of a coupled two-dimensional non-linear oscillator which has its harmonic frequencies varying with time is worked out in a time-dependent variational as well as perturbative framework. The time-dependent variational calculations are done by invoking the time-dependent Fourier grid Hamiltonian method. A more general case in which the harmonic frequencies, along with the equilibrium positions, are allowed to vary with time is also investigated. The model is used to interpret ultrafast intensity oscillations that may accompany an intramolecular charge transfer transition in which the time scales of charge separation and vibration are not widely different and therefore temporally non-separable.

On the dynamics of a linear and a nonlinear quantum oscillator with randomly changing harmonic frequency

Numerical experiments with a nonlinear (λX 4 ) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When λ = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (λ> 0), a threshold is reached atλ =λ c when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of λ. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored.