Time-dependent Fourier Grid Hamiltonian Method Research Articles

Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control.

The effects of discontinuously time-varying perturbations on the dynamics of a particle moving in harmonic, symmetric double well and symmetric triple well potentials, are investigated both classically and quantum mechanically. The quantum dynamics is followed using the time-dependent Fourier grid Hamiltonian (TDFGH) method while the classical dynamics is analyzed within the framework of classical Hamiltonian mechanics. Depending on the spatial symmetry of the perturbation and the characteristic features of the reversal time , different types of 'phase space' structures are observed in each of the potentials. For symmetric double and triple well potentials, quantum dynamics reveals that complete destruction of tunnelling (CDT) can be achieved in the presence of a time-dependent spatially asymmetric perturbing field that is continuous in time. Any discontinuity in time-variation of the perturbation may induce over the barrier transition. The relevance of these results in the context of (i) tunnelling control and (ii) quantum computing with 3-state or 2-state quantum registers is briefly discussed.

Thermal modulation in Zeno and anti-Zeno effects on quantum measurement

ABSTRACTWe have proposed the mathematical formulations of quantum Zeno and anti-Zeno effects at non-zero temperature on vibrational population transfer and dissociation of a diatomic system. The proposed formulation has been tested for diatomic systems HBr+ and HI using time-dependent Fourier grid Hamiltonian method. The effect of temperature on the dynamics is incorporated through the population distribution at different vibrational states following Boltzmann distribution formula. It has been found that with increase in temperature Zeno effect increases and anti-Zeno effect decreases in case of survival probability on ground vibrational state. In case of dissociation, with increase in temperature Zeno effect increases while anti-Zeno effect remains almost same.

Theoretical study of Zeno and anti-Zeno effects on photodissociation dynamics: A model approach

Zeno and anti-Zeno effects in the evolution of the multi-photonic dissociation dynamics of the diatomic molecule HBr[Formula: see text] owing to repeated measurements demand if the system in the initial state have been studied. The effects have been calculated numerically for the case of vibrational population transfer and dissociation dynamics of HBr[Formula: see text] taking it as a model. We use time-dependent Fourier grid Hamiltonian (TDFGH) method as a mathematical tool in presence of intense radiation field as perturbation. The effects have been explored through a probable mechanism of population transfer from the ground vibrational state to the different upper vibrational states which ultimately go to the dissociation continuum. The results show significant differences in the mechanism of population transfer and the significant role of time interval of measurement ([Formula: see text] in Zeno and anti-Zeno effects. In case of survival probability of ground vibrational states, there is Zeno effect when the frequency of the laser to which the molecule is submitted is near the vibrational [Formula: see text] to [Formula: see text] resonance, while there is anti-Zeno effect if it is far from this resonance.

Fermi accelerator: A new insight from quantum theory of motion

Quantum localization is observed in the Fermi accelerator model with monochromatic fluctuation using the Ehrenfest description of quantum dynamics as well as through the quantum theory of motion (QTM). The effects of variations in time period and amplitude of an oscillating wall for a particle in a box, on energy and quantum phase space structures are analyzed. The effects of fluctuation decay with an increase in distance from the fluctuating wall. It is also observed that small amplitude as well as high frequency fluctuation provides enhanced quantum localization. The “quantum phase space structure” in the Ehrenfest description is constructed by following time-dependent Fourier grid Hamiltonian method while that for the grid points are formed from their trajectories obtained from QTM. © 2015 Wiley Periodicals, Inc.

Photodissociation dynamics of triatomic molecule in presence of pulsed and bichromatic laser field

The photodissociation dynamics of a triatomic molecule in the presence of pulsed and bichromatic electric field have been investigated. We have considered MgH2 molecule in its ground state potential energy surface. The time-dependent Fourier Grid Hamiltonian method is invoked to follow the dissociation dynamics as a function of field strength, frequency, phase difference, etc.

Bichromatic fluctuations in symmetric double well potentials: Localization and control of tunneling

We have studied the effects of spatial symmetry-preserving bichromatic fluctuations in symmetric double well systems. The rate of tunneling is enhanced or suppressed depending on the temporal nature of fluctuations, number of fluctuation frequencies, the commensurability of the frequencies or the lack of it, fluctuation intensities, etc. Localization with complete quenching of tunneling, however occurs only when a symmetry-breaking perturbation is applied. The tunneling dynamics of the system is studied using the time-dependent Fourier grid Hamiltonian method and the analysis is done using the Floquet technique and the time-dependent Hellmann–Feynman theorem. We predict that by controlling the frequency and intensity ratios and the spatio-temporal nature of the fluctuating fields, a wide variety of situations can be created for effective control of tunneling.

Dipole induced photodetachment dynamics of halide anions

In this article the dynamics of photodetachment from closed shell anion in the presence of two color (bichromatic) laser field have been explored in the context of polar environmental situation. The electronic states of halide ions are modeled by a one dimensional Hamiltonian with a potential V(x) = −V0e. The two parameters V0 and σ are fixed by requiring V(x) to reproduce the experimentally observed ground state ionization energy of the halide ion concerned. The potential so generated are shown to support only one bound state. The time-dependent Fourier grid Hamiltonian method is used to follow the detachment dynamics with fairly high intensities of light. The environmental effects on the dynamics are sought to be modeled by two ways i) allowing the well depth (V0) to fluctuate randomly V0(t) = V0[1+ΔVR(t)]; R(t) randomly fluctuates between +1 and −1 with time, when ΔV (strength of fluctuation) is fixed and ii) in the presence of perturbation produced by a neighboring solvent dipole, which changes the effective potential. The detachment rate constant is studied as a function of important system parameters of the used light field. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Photoionization dynamics from [formula omitted]: a one-electron model

Quantum dynamics of photoionization from Cl 2 - is investigated by constructing a purely one-electron model Hamiltonian of the anion calibrated with the help of ab initio theoretical calculations at the MRSD-CI level. A mean-field time-dependent Fourier grid Hamiltonian method is used to investigate the modulation of the dynamics of photoionization from Cl 2 - caused by the coupling of electronic and nuclear motions. Vibrational quenching at low coupling strength is predicted to turn into vibrational enhancement of ionization at higher strengths of coupling.

Photodetachment dynamics of closed-shell anions: Effects of perturbation by a strong neighboring dipole

We have investigated the quantum dynamics of photodetachment of an electron from closed-shell anions by pulsed light in the presence of perturbation produced by a neighboring solvent dipole. The anion is modeled by a suitable one-dimensional potential and assumed to interact with the dipolar solvent molecule through ion-dipole and ion-induced dipole interactions. The dynamics is followed by invoking the time-dependent Fourier grid Hamiltonian method to solve the relevant Schrödinger equation. The detachment rates in the presence of random fluctuations in the binding energy of the anion-electron and orientation of the dipole (with respect to the anion) have been computed and compared with the rates observed for an anion with fixed binding energy and a fixed orientation of the dipole. The possibility of the detached electron being captured by the perturbing dipole is also considered. The capture probability and rate are studied as functions of important system parameters. The possibility of using the model to understand the evolution of the charge-transfer-to-solvent spectrum is explored. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 178–189, 2000

Photo-dissociation dynamics of a diatomic molecule: modelling of thermal and environmental effects

The quantum dynamics of photodissociation of a diatomic molecule interacting with ultrashort infrared laser pulses and modelled by an appropriate Morse oscillator with either a fixed or fluctuating well-depth is explored at non-zero temperatures by assuming an initial state vector consistent with the distribution of vibrational population at a given temperature. The time-dependent Schrödinger equation is solved by the time-dependent Fourier grid Hamiltonian method. The computed dissociation rate constant k ( T ) at a given intensity and frequency, of the driving field passes through a maximum at an intermediate temperature. If the well-depth of the Morse oscillator fluctuates randomly, mimicking medium-induced perturbations, k ( T ) shows a strong suppression at specific values of the fluctuation frequency and strength.

Modeling quantum dynamics of photodetachment from closed-shell anions: Static versus fluctuating well-depth models

The electronic states of halide ions are modeled by a one-dimensional Hamiltonian with a potential V(x)=−V0e. The two parameters V0 and σ are fixed by requiring V(x) to reproduce the experimentally observed ground-state ionization potentials of the halide ions concerned. The potentials so generated are shown to support only one bound state in each case. The time-dependent Fourier grid Hamiltonian method is used to follow the ionization dynamics in monochromatic light of fairly high intensities. The total Hamiltonian, in the most general case, reads H(t)=P/2m−V0e−ϵ0s(t)ex sin(ωt). For pulsed fields [s(t)=sin2(πt/tp)], the computed ionization rate constants are seen to increase with increase in the peak intensity (ϵ0) of the electric field of light. The possibility of additional transient bound states being generated at the high intensities of light and its possible consequences on the observed ionization rates are explored. The environmental effects on the dynamics are sought to be modeled by allowing the well depth (V0) to fluctuate randomly [V0(t)=V0+ΔVR(t); R(t) randomly fluctuates between +1 and −1 with time, ΔV is fixed]. The ionization rate constants (kϵ) are shown to be significantly affected by fluctuations in V0 and pass through a well-defined minimum in each case for a certain specified frequency of fluctuation. An alternative model potential V(x)=−V0e−σx is also shown to yield similar results. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 469–478, 1999

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.

Tunneling dynamics of one‐ and two‐dimensional cubic oscillators with randomly fluctuating harmonic force constants: A numerical experiment

The tunneling dynamics of one- and two-dimensional cubic oscillators having randomly fluctuating harmonic force constants (Kt) are studied numerically by invoking the time-dependent Fourier grid Hamiltonian method. The influence of the frequency and strength of the fluctuation on the tunneling probability and tunneling rate is analyzed. The predicted nature of the influence depends upon whether the cubic oscillator is one- or two-dimensional. The possibility of mapping the proton-transfer systems onto the present model is explored. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 403–409, 1997

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

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.

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

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 K t 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 ( k tun 0 v ) (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 k tun 0 v 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.

Dynamics of vibrationally assisted tunnelling in model multidimensional systems. Three routes involving the Fourier grid Hamiltonian method

The multidimensional complex-scaled Fourier grid Hamiltonian (FGH) and time-dependent FGH method are invoked to study the dynamics of vibrationally assisted or subdued tunnelling in model two-dimensional systems that can mimick the behaviour of many real proton transfer systems. In the time-dependant description a Hartree-type meanfield method and a propagator method in a grid basis set are explored. The coupling between tunnelling and anharmonic vibrational modes are seen to affect the tunnelling rates in different ways depending upon the types and magnitudes of the coupling. Implications of our results with respect to H-atom or proton transfer reactions are considered.

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.

Time-dependent Fourier grid Hamiltonian method for modelling real-time quantum dynamics: Theoretical models and applications

A local grid method for modelling real-time quantum dynamical events is formulated. The formulation is straightforward for 1-D systems. For more than one dimension, appeal has to be made to mean-field approximation of the appropriate kind. The simplest mean-field model results in time-dependent Hartree-Fourier grid method. The relationship of the proposed method with some other methods available in the literature is examined. A few examples of numerical applications dealing with (i) the dynamics of dissociation and ionization processes in diatoms and atoms respectively and (ii) tunnelling dynamics in the intramolecular H-atom transfer phenomenon are presented.

A time-dependent Fourier grid Hamiltonian method. Formulation and application to the multiphoton dissociation of a diatomic molecule in intense laser field

A time-dependent Fourier grid Hamiltonian method is proposed for studying real-time quantum dynamics of simple systems. The method can work with an arbitrary number of grid points ( N). Convergence with respect to N is fast. Results of test calculations on the dynamics of dissociation of a diatomic species modelled by an appropriate Morse oscillator in a continuous high intensity non-resonant IR laser field are presented. The dissociation is predicted to be characterized by the presence of a definite threshold of laser intensity and an induction period preceeding the onset of dissociation.