A simplified ab initio treatment of diradicaloid structures produced from stretching and breaking chemical bonds.

The present investigation reports on the prospect of using state specific multireference perturbation theory (SSMRPT) with an improved virtual orbital complete active space configuration interaction (IVO-CASCI) reference function (IVO-SSMRPT) to generate potential energy surfaces (PESs) for molecular systems [such as CH4, C2H6, C2H4, H2O2, LiH, and KN] by stretching and breaking of suitable bonds with modest basis sets. We have also revisited the dissociation energy profile of triplet ketene which exhibits a step-like structure in the observed rate. The application of the method has also been made to the ionization energies of H2O. Although the perturbative corrections are obtained by the diagonalization of the effective Hamiltonian, in IVO-SSMRPT, only one physically relevant solution is achievable. It is parameter free and does not require any threshold to avoid the intruder problem. It is strictly size-extensive and size-consistent provided that local orbitals are used. The PESs obtained with our approach are smooth all along the reaction path. Our estimates are in close agreement with the available reference data indicating that IVO-SSMRPT is a robust paradigm for the accurate computation of ground, excited and ionized states as it captures the mutual inter-play of different flavors of correlation effects in a balanced and accurate way.

Quantum stochastic dynamics in the presence of a time-periodic rapidly oscillating potential: nonadiabatic escape rate.

Escape from a metastable state in the presence of a high-frequency field (where the driving becomes nonadiabatic) underlies a broad range of phenomena of physics and chemistry, and thus its understanding is of paramount importance. We study the problem of intermediate-to-high-damping escape from a metastable state of a dissipative system driven by a rapidly oscillating field, one of the most important classes of nonequilibrium systems, in a broad range of field driving frequencies (ω) and amplitudes (a). We construct a Langevin equation using quantum gauge transformation in the light of Floquet theorem and exploiting a systematic perturbative expansion in powers of 1/ω using "Kapitza-Landau time window". The quantum dynamics in a high-frequency field are found to be described by an effective time-independent potential. The temperature dependence of escape rate and the change of its form with varying parameters of the field have been analyzed. It may decrease upon increasing the temperature which is contingent on the effects of intricate interplay between external modulation and dissipation. The crossover temperature between tunnelling and thermal hopping increases with an increase in external modulation so that quantum effects in the escape are relevant at higher temperatures. These observations are uncommon and counterintuitive and, therefore, of considerable interest. Our results might be valuable for the exploration of the dynamics of cold atoms in electromagnetic fields.

Escape rate for a quantum particle moving in a time-periodic rapidly oscillating potential: a time-independent approach.

We explore, in the quantum regime, the stochastic dynamics of a time-periodic, rapidly oscillating potential (having a characteristic frequency of ω) within the framework of a time-dependent system-reservoir Hamiltonian. We invoke the idea of a quantum gauge transformation in light of the standard Floquet theorem in an attempt to construct a Langevin equation (bearing a time-independent effective potential) by employing a systematic perturbative expansion in powers of ω^{-1} using the natural time-scale separation. The time-independent effective potential (corrected to ω^{-2} in leading order) that acts on the slow motion of the driven particle can be employed for trapping. We proceed further to evaluate the rate of escape of the driven particle from the metastable state in the high-temperature limit. We also envisage a resonance phenomena, a true hallmark of the system-reservoir quantization. This development would thus serve as a model template to investigate the trapping mechanism, as well as an appropriate analog to understand the dynamics of a fluctuation-induced escape process from the trap.

Controlling activated processes of nonadiabatically, periodically driven dynamical systems: a multiple scale perturbation approach.

We arrive at the escape rate from a metastable state for a system of Brownian particles driven periodically by a space dependent, rapidly oscillating external perturbation (with frequency ω) in one dimension (one of the most important class of nonequilibrium system). Though the problem may seem to be time-dependent, and is poised on the extreme opposite side of adiabaticity, there exists a multiple scale perturbation theory ("Kapitza window") by means of which the dynamics can be treated in terms of an effective time-independent potential that is derived as an expansion in orders of 1/ω to the order ω(-3). The resulting time-independent equation is then used to calculate the escape rate of physical systems from a metastable state induced by external monochromatic field in the moderate-to-large damping limit and to investigate the effect of ω on the resulting rate in conjunction with the thermal energy. With large value of ω, we find that the environment with moderate-to-large damping impedes the escape process of the particle while high amplitude of the periodic driving force allows the particle to cross the barrier with a large escape rate. A comparison of our theoretical expression with numerical simulation gives a satisfactory agreement.

Time-independent description of rapidly driven systems in the presence of friction: multiple scale perturbation approach.

The dynamics of a classical system driven by a rapidly oscillating field (with frequency ω) in the presence of friction has been investigated using the multiple scale perturbation theory (MSPT). By exploiting the idea of separation of time scales, the slow motion has been computed in a systematic expansion in the inverse of ω to the order ω(-3). This perturbation series can be viewed as a generalization of the calculation presented by Landau and Lifshitz for Kapitza's pendulum (where the point of suspension is moved periodically) in the presence of friction. The radiation induced dynamics of the system is found to be described by an effective time-independent potential with friction that controls the slow motion. The explicit appearance of friction in our computed effective potential is a manifestation of the dynamical effect due to the fast motion. The present study demonstrates that MSPT can be used to understand and predict the classical dynamics of a driven system in the presence of friction.

Effective quantum Brownian dynamics in presence of a rapidly oscillating space-dependent time-periodic field.

We explore the Brownian dynamics in the quantum regime (by investigating the quantum Langevin and Smoluchowski equations) in terms of an effective time-independent Hamiltonian in the presence of a rapidly oscillating field. We achieve this by systematically expanding the time-dependent system-reservoir Hamiltonian in the inverse of driving frequency with a systematic time-scale separation and invoking a quantum gauge transformation within the framework of Floquet theorem.

A microscopic model for noise induced transport: Heat-bath nonlinearly driven by external white noise.

This work explores the observation that, even in the absence of a net externally applied bias, a symmetric homogeneous system coupled linearly to two heat baths is capable of producing unidirectional motion simply by nonlinearly driving one of the heat baths by an external Gaussian white noise. This is quite contrary to the traditional observation that, in order to obtain a net drift current, a state-dependent dissipation, which is a consequence of nonlinear system-bath coupling, is ubiquitous.

Development of a semiclassical method to compute mobility and diffusion coefficient of a Brownian particle in a nonequilibrium environment.

We explore the issue of a quantum-noise-induced directed transport of an overdamped Brownian particle that is allowed to move in a spatially periodic potential. The established system-reservoir model has been employed here to study the quantum-noise-induced transport of a Brownian particle in a periodic potential, where the reservoir is being modulated externally by a Gaussian-colored noise. The mobility of the Brownian particle in the linear response regime has been calculated. Then, using Einstein's relation, the analytical expression for the diffusion rate is evaluated for any arbitrary periodic potential for the high-temperature quantum regime.

Realization of a Brownian engine to study transport phenomena: a semiclassical approach.

Brownian particles moving in a periodic potential with or without external load are often used as good theoretical models for the phenomenological studies of microscopic heat engines. The model that we propose here, assumes the particle to be moving in a nonequilibrium medium and we have obtained the exact expression for the stationary current density. We have restricted our consideration to the overdamped motion of the Brownian particle. We present here a self-consistent theory based on the system-reservoir coupling model, within a microscopic approach, of fluctuation induced transport in the semiclassical limit for a general system coupled with two heat baths kept at different temperatures. This essentially puts forth an approach to semiclassical state-dependent diffusion. We also explore the possibility of observing a current when the temperature of the two baths are different, and also envisage that our system may act as a Carnot engine even when the bath temperatures are the same. The condition for such a construction has been elucidated.

Escape of a driven particle from a metastable state: A semiclassical approach.

In this article we explore the dynamics of escape of a particle in the semiclassical regime by driving the particle externally. We demonstrate that under suitable approximations the semiclassical escape rate essentially assumes the structure of classical Kramers rate. Both internal (due to thermal bath) as well as external noises (due to driving) are being considered. The noises are stationary, Gaussian, and are characterized by arbitrary decaying memory kernel. Finally, we subject our formulation to rigorous numerical test under variedly changing conditions of the parameters.

Microscopic realization of cross-correlated noise processes.

We present a microscopic theory of cross-correlated noise processes, starting from a Hamiltonian system-reservoir description. In the proposed model, the system is nonlinearly coupled to a reservoir composed of harmonic oscillators, which in turn is driven by an external fluctuating force. We show that the resultant Langevin equation derived from the composite system (system+reservoir+external modulation) contains the essential features of cross-correlated noise processes.

Generalized Einstein relation in tilted periodic potential: a semiclassical approach.

This paper concerns the investigation of the quantum motion of a system in a dissipative Ohmic heat bath in the presence of an external field using the traditional system-reservoir model. Using physically motivated initial conditions, we then obtain the c-number of the generalized quantum Langevin equation by which we calculate the quantum correction terms using a perturbation technique. As a result of this, one can apply a classical differential equation-based approach to consider quantum diffusion in a tilted periodic potential, and thus our approach is easy to use. We use our expression to calculate the Einstein relation for the quantum Brownian particle in a ratchet-type potential in a very simple closed analytical form using a suitable and convenient approximation. It is found that the diffusion rate is independent of the detailed form of the potential both in quantum and classical regimes, which is the main essence of this work.

External-noise-driven bath and the generalized semiclassical Kramers theory.

We address the issue of a system that has been tacitly made thermodynamically open by externally driving the associated heat bath in an attempt to gain better insight regarding many physical situations that are akin to this problem. This work embodies the study of the quantum effects in the rate of decay from a metastable state of a Brownian particle which is in contact with a correlated noise-driven bath. We do this by initiating from a suitable system-reservoir model to derive the operator-valued Langevin equation. This further leads us to the corresponding c-number analog that includes quantum effects in leading order. Suitable mathematical treatment culminates in the quantum Fokker-Planck equation, the solution to which yields the rate expression. Finally, we put this to thorough numerical analysis.