arXiv subjects

Anish Chakraborty

Publications and source records attributed to Anish Chakraborty.

6 recordsLinked to original sources

arXiv2025

Exploring Non-Markovianity in Ergodic Channels: Measuring Memory Retention through Ergotropy

In this work we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and analyze their non-Markovian dynamics using established measures. When the fixed point is a passive state, the channels exhibit ergotropy dynamics with notable thermodynamic implications. Specifically, under Markovian processes, ergotropy, a measure of the extractable work from a system under unitary evolution monotonically decreases. However, in non-Markovian dynamics, ergotropy fluctuates, leading to a backflow effect that highlights memory-induced resource recovery. Our findings suggest that this ergotropy backflow could serve as an operationally meaningful indicator of non-Markovianity, offering new perspectives on the interplay between memory effects and thermodynamic behavior in open quantum systems. This study enhances the theoretical framework for understanding energy dynamics under ergodic channels and highlights new avenues for exploring the implications of memory effects in quantum batteries.

quant-ph↗

arXiv2024

Accurate determination of excitation energy: An equation-of-motion approach over a bi-exponential Coupled Cluster theory

The calculation of molecular excited states is critically important to decipher a plethora of molecular properties. In this manuscript, we develop an equation of motion formalism on top of a bi-exponentially parametrized ground state wavefunction towards the determination of excited states. While the ground state bi-exponential parametrization ensures an accurate description of the wavefunction through the inclusion of high-rank correlation effects, the excited state is parametrized by a novel linear response operator with an effective excitation rank beyond two. To treat the ground and the excited states in the same footings, in addition to the conventional one and two-body response operators, we introduced certain two-body "generalized" response operators with an effective excitation rank of one. We introduce a projective formulation towards the determination of the perturbed amplitudes for the set of "generalized" operators. Our formulation entails a significantly small number of unknown parameters and is shown to be highly accurate compared to allied methods for several difficult chemical systems.

physics.chem-ph↗

arXiv2023

Fixing the Catastrophic Break-down of Single Reference Coupled Cluster Theory for Strongly Correlated Systems: Two Paradigms towards the Implicit Inclusion of High Rank Correlation with Low-Spin Channels

The dual exponential coupled cluster (CC) theory proposed by Tribedi et al.[J. Chem. Theory Comput. 2020, 16, 10, 6317-6328] performs significantly better than the coupled cluster theory with singles and doubles excitations (CCSD) due to the implicit inclusion of high-rank excitations. The high-rank excitations are included through the action of a set of vacuum annihilating scattering operators that act non-trivially on certain correlated wavefunctions and are determined via a set of local denominators involving the energy difference between certain excited states. This often leads the theory to be prone to intruders. In this manuscript, we show that restricting the correlated wavefunction, on which the scattering operators act upon, to be spanned by only the singlet paired determinants can avoid the catastrophic breakdown. For the first time, we present two nonequivalent approaches to arrive at the working equations, viz. the projective approach with sufficiency conditions and the amplitude form with many-body expansion. While the effect of the triple excitation is quite small around molecular equilibrium geometry, this scheme leads to a better qualitative description of the energetics in the regions of strong correlation. With a number of pilot numerical applications, we have demonstrated the performance of the dual-exponential scheme with both the proposed solution strategies while restricting the excitation subspaces coupled to the corresponding lowest spin channels.

physics.comp-ph↗

arXiv2022

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy

The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analysed as a multivariate time-discrete map where the concept of time appears in an implicit manner. With the observation that the cluster amplitudes have difference in their relaxation timescales with respect to the distributions of their magnitudes, the coupled cluster iteration dynamics are considered as a synergistic motion of coexisting slow and fast relaxing modes, manifesting a dynamical hierarchical structure. With the identification of the highly damped auxiliary amplitudes, their time variation can be neglected compared to the principal amplitudes which take much longer time to reach the fixed points. We analytically establish the adiabatic approximation where each of these auxiliary amplitudes are expressed as unique parametric functions of the collective principal amplitudes, allowing us to study the optimization with the latter taken as the independent degrees of freedom. Such decoupling of the amplitudes significantly reduces the computational scaling without sacrificing the accuracy in the ground state energy as demonstrated by a number of challenging molecular applications. A road-map to treat higher order post-adiabatic effects is also discussed.

physics.comp-ph↗

arXiv2020

Accelerating Coupled Cluster Calculations with Nonlinear Dynamics and Shallow Machine Learning

The dynamics associated with the time series of the iteration scheme of coupled cluster theory has been analysed. The phase space analysis indicates the presence of a few significant cluster amplitudes, mostly involving valence excitations, which dictate the dynamics, while all other amplitudes are enslaved. Starting with a few initial iterations to establish the inter-relationship among the cluster amplitudes, a supervised Machine Learning scheme with polynomial Kernel Ridge Regression model has been employed to express each of the enslaved variables uniquely in terms of the master amplitudes. The subsequent coupled cluster iterations are restricted to a reduced dimension only to determine those significant excitations, and the enslaved variables are determined through the already established functional mapping. We will show that our scheme leads to tremendous reduction in computational time without sacrificing the accuracy.

cond-mat.str-el↗

arXiv2020

Stability analysis of a double similarity transformed coupled cluster theory

In this paper, we have analysed the time series associated with the iterative scheme of a double similarity transformed Coupled Cluster theory. The coupled iterative scheme to solve the ground state Schr{ö}dinger equation is cast as a multivariate time-discrete map, the solutions show the universal Feigenbaum dynamics. Using recurrence analysis, it is shown that the dynamics of the iterative process is dictated by a small subgroup of cluster operators, mostly those involving chemically active orbitals, whereas all other cluster operators with smaller amplitudes are enslaved. Using Synergetics, we will indicate how the master-slave dynamics can suitably be exploited to develop a novel coupled-cluster algorithm in a much-reduced dimension.

cond-mat.stat-mech↗