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Arindam Chakraborty

Publications and source records attributed to Arindam Chakraborty.

At least 19 recordsLinked to original sources
arXiv2026

On some signatures of Lie-Hamilton System in Quantum Hamilton Jacobi Equation

The general forms of Quantum Hamilton Jacobi Equation for a particle of constant mass, position dependent effective mass and non-Hermitian Effective mass Swanson model have been considered. It has been found that the said equations can be recast in the form of Cayley-Klein Riccati equations which admit a Lie-Hamilton structure. The possible expressions of Lie symmetry and Lie Integral have also been considered.

quant-ph↗
arXiv2025

Frequency-Dependent Polarization Propagator Calculation for Quantum Dots Using Optimized Inverse Krylov Subspace and Folded-Spectrum Method

Accurate prediction of the frequency response of quantum dots under electromagnetic radiation is essential for investigating absorption spectra, excitonic effects, and nonlinear optical behavior in quantum dots and semiconductor nanoparticles. The polarization propagator provides a rigorous framework for evaluating these properties, but its construction is computationally demanding. Challenges arise from the level of electron correlation, the size of the excitonic basis, and the cost of evaluating two-electron integrals. This work addresses these difficulties by developing first- and second-order frequency-dependent polarization propagator calculations for PbS and CdS quantum dots. The propagator is formulated using the electron propagator approach and expressed as the resolvent of the Hamiltonian superoperator. Light-matter interaction is treated using the dipole approximation and represented in a particle-hole excitation operator basis. The correlated ground state is treated at the MP2 level, and all response-matrix terms up to second order in the fluctuating potential are included. A frequency-dependent inverse Krylov subspace method is derived and combined with the folded-spectrum technique to isolate excitation energies within a chosen frequency window. This strategy avoids full diagonalization of the response matrix and significantly reduces computational cost for large systems. The method is implemented in a matrix-free manner in which no explicit response matrix is assembled, and all operations rely on matrix-vector products. UV-VIS excitation spectra of PbS and CdS quantum dots were computed, demonstrating that the inverse Krylov subspace projection approach provides an efficient and accurate approximation for excitation spectra when full diagonalization is computationally prohibitive.

physics.chem-ph↗
arXiv2025

Witt type Realizations of 2-D Cayley-Klein Algebras with non-zero curvatures

The article presents various Witt type vector field realizations of 2-D Cayley-Klein algebras with non-vanishing curvatures. The expressions of the vector fields involve Jacobi elliptic functions whose moduli are directly related to the parameters that appear in the corresponding matrix representation obtained from a bi-orthogonal set of vectors. First, the realizations are obtained with the values of the moduli lying in the unit interval (0, 1). The parameter of biorthogonality plays a crucial role in this context. Later, with the help of modular transformation, realizations involving arbitrary moduli have been obtained.

math-ph↗
arXiv2023

Bi-orthogonal spinors associated to T -pseudo-Hermitian Rashba Hamiltonian : Time reversal in Clifford Algebra Cl3(R) and Pseudo-Supersymmetry

A non-Hermitian version of Rashba Hamiltonian has been introduced motivated from the Levy-leblond type linearisation of Schrodinger equation in a Galilean invariant frame-work. The said Hamiltonian is found to be pseudo-Hermitian under fermionic time-reversal and its eigen-spinors show bi-orthogonality. The whole discussion has been cast in a Clifford algebraic frame-work and the said biorthogonality has been variously understood in terms of time-reversal operator and Clifford involutions. The possibility of an equivalent version of Kramers' degeneracy theorem has been explored and the super-symmetric and pseudo-super-symmetric structures relating to the present system are also discussed.

math-ph↗
arXiv2022

Bi-orthogonal eigen-spinors related to T-pseudo-Hermitian Pauli Hamiltonian : Time reversal and Clifford Algebra

A set of two-parameter bi-orthogonal eigen-spinors has been constructed from a deformed pseudo- Hermitian extension of Pauli Hamiltonian and its Hermitian conjugate. The Hamiltonians thus obtained are iso-spectral to the original Pauli Hamiltonian. A pair of spin-projection operators has been constructed as an essential ingredient of a possible bi-orthogonal quantum mechanics. An analogue of Kramers theorem in pseudo-Hermitian setting has also been inferred in a conjectural sense. The properties of time reversal and bi-orthogonality have been elaborated in the frame work of Clifford algebra Cl3, where the spinors have been viewed as elements of left ideal and the relevant inner-products are understood in terms of different involutions leading to elements of a division ring. The whole process of present construction is found to be based on both direct and time reversed Cl3 generators. A new variant of Kustaanheimo-Stiefel transformation has been introduced with the help of spinor operator.

math-ph↗
arXiv2022

On a Relation among Bi-orthogonal system, Quadratic Non-Hermitian Boson operators with real spectrum and Partial PT symmetry in Fock Space

A new kind of symmetry called partial PT symmetry has been considered for non-hermitian quadratic boson operators obtained from a bi-orthogonal set of vectors in C2. The symmetry behaviour has been understood in Fock space considered as a Reproducing Kernel Hilbert Space(RKHS). The reality of eigenvalues and its connection to the possibility of the aforesaid symmetry (and symmetry breaking) are studied in terms of a deformation parameter responsible for nonhermiticity

math-ph↗
arXiv2021

Construction of a new three boson non-hermitian Hamiltonian associated to deformed Higgs algebra: real eigenvalues and Partial PT-symmetry

A $γ$-deformed version of $\mathfrak{su}(2)$ algebra has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. Fusion of Jordan-Schwinger realization of complexified $\mathfrak{su}(2)$ with Dyson-Maleev representation gives a 3-boson realization of Higgs algebra of cubic polynomial type. The non-hermitian Hamiltonian thus obtained is found to have real eigenvalues and eigen states with symmetry induced orthogonality. The notion of partial ${\mathcal {PT}}$-symmetry (henceforth $\partial_{\mathcal { PT}}$) has been introduced as a characteristic feature of these multi-boson realizations. The Hamiltonian along with its eigenstates have been studied in the light of $\partial_{\mathcal { PT}}$-symmetry. The possibility of $\partial_{\mathcal { PT}}$-symmetry breaking is also discussed. The deformation parameter $γ$ plays a crucial role in the entire formulation and non-trivially modifies the eigenfunctions under consideration.

quant-ph↗
arXiv2021

Sensitivity of Indian summer monsoon rainfall forecast skill of CFSv2 model to initial conditions and the role of model biases

We analyse Indian summer monsoon (ISM) seasonal reforecasts by CFSv2 model, initiated from January (4-month lead time, L4) through May (0-month lead time, L0) initial conditions (ICs), to examine the cause for highest all-India ISM rainfall (ISMR) forecast skill with February (L3) ICs. The reported highest L3 skill is based on correlation between observed and predicted interannual variation (IAV) of ISMR. Other scores such as mean error, bias, RMSE, mean, standard deviation and coefficient of variation, indicate higher or comparable skill for April(L1)/May(L0) ICs. Though theory suggests that forecast skill degrades with increase in lead-time, CFSv2 shows highest skill with L3 ICs, due to predicting 1983 ISMR excess for which other ICs fail. But this correct prediction is caused by wrong forecast of La Nina or cooling of equatorial central Pacific (NINO3.4) during ISM season. In observation, normal sea surface temperatures (SSTs) prevailed over NINO3.4 and ISMR excess was due to variation of convection over equatorial Indian Ocean or EQUINOO, which CFSv2 failed to capture with all ICs. Major results are reaffirmed by analysing an optimum number of 5 experimental reforecasts by current version of CFSv2 with late-April/early-May ICs having short yet useful lead-time. These reforecasts showed least seasonal biases and highest ISMR correlation skill if 1983 is excluded. Model deficiencies such as over-sensitivity of ISMR to SST variation over NINO3.4 (ENSO) and unrealistic influence of ENSO on EQUINOO, contribute to errors in ISMR forecasting. Whereas, in observation, ISMR is influenced by both ENSO and EQUINOO. Forecast skill for Boreal summer ENSO is found to be deficient with lowest skill for L3/L4 ICs, hinting the possible influence of long lead-time induced dynamical drift. The results warrant the need for minimisation of bias in SST boundary forcing to achieve improved ISMR forecasts.

physics.ao-ph↗
arXiv2020

Understanding Partial PT symmetry as weighted composition conjugation in Reproducing Kernel Hilbert Space :An application to non-hermitian Bose-Hubbard type Hamiltonian in Fock space

A new kind of symmetry behaviour introduced as partialPT-symmetry is investigated in a typical Fock space setting understood as a Reproducing Kernel Hilbert Space (RKHS). The same kind of symmetry is understood for a nonhermitian Bose-Hubbard type Hamiltonian involving two boson operators as well as its eigenstates. The phenomenon of symmetry breaking has also been considered

math-ph↗
arXiv2020

Investigation of dense manifold of particle-hole excitations in metallic nanowires using r12-correlated frequency-dependent electron-hole interaction kernel

Low-lying electronically excited states in metallic and semiconductor nanoparticles continue to be actively investigated because of their relevance in a wide variety of technological applications. However, first-principles electronic structure calculations on metallic and semiconductor nanoparticles are computationally challenging due to factors such as large system sizes, evaluation and transformation of matrix elements, and high density of particle-hole states. In this work, we present the development of the frequency-dependent explicitly-correlated electron-hole interaction kernel (FD-GSIK) to address the computation bottleneck associated with these calculations. The FD-GSIK method obtains a zeroth-order description of the dense manifold of particle-hole states by constructing a transformed set of dressed particle-holes states. Electron-hole correlation is introduced by using an explicitly correlated, frequency-dependent two-body operator which is local in real-space representation. The resulting electron-hole interaction kernel expressed in an energy-restricted subspace of particle-hole excitations is derived using the Lowdin's partitioning theory. Finally, the excitation energies are calculated using an iterative solution of the energy-dependent, generalized pseudoeigenvalue equation. The FD-GSIK method was used to investigate low-lying excited states of a series of silver linear clusters and nanowires. The results from this investigation demonstrate that FD-GSIK is an effective method for investigating electronic excitations and capturing electron-hole correlation in nanomaterials.

physics.chem-ph↗
arXiv2020

A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $γ$-deformed $su(2)$ generators, Partial $\mathcal{PT}$-symmetry and Higgs algebra

A $γ$-deformed version of $su(2)$ algebra with non-hermitian generators has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. The related Jordan-Schwinger(J-S) map is combined with boson algebras to obtain a hierarchy of fusion polynomial algebras. This makes possible the construction of Higgs algebra of cubic polynomial type. Finally the notion of partial $\mathcal{PT}$ symmetry has been introduced as characteristic feature of some operators as well as their eigenfunctions. The possibility of partial $\mathcal{PT}$-symmetry breaking is also discussed. The deformation parameter $γ$ plays a crucial role in the entire formulation and non-trivially modifies the eigenfunctions under consideration.

math-ph↗
arXiv2019

Construction of a few Quantum mechanical Hamiltonians via L$\acute{e}$vi-Leblond type Linearization:Spinor states and Supersymmetry

A number of new L$\acute{e}$vi-Leblond type equations admitting four component spinor solutions have been proposed. The pair of linearized equations thus obtained in each case lead to Hamiltonians with characteristic features like L-S coupling and supersymmetry. The relevant momentum operators have often been understood in terms of Clifford algebraic bases producing Schr$\ddot{o}$dinger Hamiltonians with L-S coupling. As for example Hamiltonians representing Rashba effect or three dimensional harmonic oscillator have been constructed. The supersymmetric nature of one dimensional oscillator has also been appreciated.

quant-ph↗
arXiv2019

The Statistical Face of a Region under Monsoon Rainfall in Eastern India

A region under rainfall is a contiguous spatial area receiving positive precipitation at a particular time. The probabilistic behavior of such a region is an issue of interest in meteorological studies. A region under rainfall can be viewed as a shape object of a special kind, where scale and rotational invariance are not necessarily desirable attributes of a mathematical representation. For modeling variation in objects of this type, we propose an approximation of the boundary that can be represented as a real valued function, and arrive at further approximation through functional principal component analysis, after suitable adjustment for asymmetry and incompleteness in the data. The analysis of an open access satellite data set on monsoon precipitation over Eastern India leads to explanation of most of the variation in shapes of the regions under rainfall through a handful of interpretable functions that can be further approximated parametrically. The most important aspect of shape is found to be the size followed by contraction/elongation, mostly along two pairs of orthogonal axes. The different modes of variation are remarkably stable across calendar years and across different thresholds for minimum size of the region.

stat.AP↗
arXiv2018

Development of composite control-variate stratified sampling approach for efficient stochastic calculation of molecular integrals

In this work, the composite control-variate stratified sampling (CCSS) method is presented for calculation of MO integrals without transformation of AO integrals. The central idea of this approach is to obtain the 2-electron MO integrals by direct integration of 2-electron coordinates. This method does not require or use pre-computed AO integrals and the value of the MOs at any point in space is obtained directly from the linear combination of AOs. The integration over the electronic coordinates was performed using stratified sampling Monte Carlo method. This approach was implemented by dividing the integration region into a set of non-overlapping segments and performing Monte Carlo calculations on each segment. The Monte Carlo sampling points for each segment were optimized to minimize the total variance of the sample mean. Additional variance reduction of the overall calculations was achieved by introducing control-variate in the stratified sampling scheme. The composite aspect of the CCSS allows for simultaneous computation of multiple MO integrals during the stratified sampling evaluation. The main advantage of the CCSS method is that unlike rejection sampling Monte Carlo methods such as Metropolis algorithm, the stratified sampling uses all instances of the calculated functions for the evaluation of the sample mean. The CCSS method is designed to be used for large systems where AO-to-MO transformation is computationally prohibitive. Because it is based on numerical integration, the CCSS method can be applied to a wide variety of integration kernels and does not require \textit{a priori} knowledge of analytical integrals. In this work, the developed CCSS method was applied for calculation of excitonic properties in CdSe quantum dots using electron-hole explicitly correlated Hartree-Fock (eh-XCHF) and geminal-screened electron-hole interaction kernel (GSIK) methods.

physics.chem-ph↗
arXiv2018

Development of effective stochastic potential method using random matrix theory for efficient conformational sampling of semiconductor nanoparticles at non-zero temperatures

In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational bottleneck associated with performing a large number of electronic structure calculations required for conformational sampling. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the fluctuations in the deformation potential due to non-zero temperature was obtained using infinite-order moment expansion of the distribution. The formal mathematical definition of the ESP was derived using functional minimization approach to match the infinite-order moment expansion for the deformation potential. Practical implementation of the ESP was obtained using the random-matrix theory method. The developed method was applied to two proof-of-concept calculations of the distribution of HOMO-LUMO gap in the water molecule and solvated CdSe clusters at 300K. The need for large sample size to obtain statistically meaningful results was demonstrated by performing $10^5 $ ESP calculations. The results from these prototype calculations demonstrated the efficacy of the ESP method for performing efficient conformational sampling. We envision that the fundamental nature of this work will not only extend our knowledge of chemical systems at non-zero temperatures but will also generate new insights for innovative technological applications.

physics.chem-ph↗
arXiv2017

Enlarging Maurer-Cartan form via Kronecker product and construction of Coupled Integrable systems by Nilpotent, Hadamard, Idempotent and K-idempotent matrix

Coupled nonlinear integrable systems are generated from usual zero curvature equation. The relevant Maurer-Cartan forms are constructed by combining suitably chosen matrices (nilpotent, Hadamard, idempotent and k-idempotent) and Lie algebraic elements via Kronecker product. In each case a closure type property among the matrices chosen is found to be playing a key role to produce both the coupling and nonlinearity present in the system of equations obtained. The method is highly flexible and can be used to construct general systems containing 'p' number of equations. It is also shown that these new equations can be written in the Hamiltonian form (with a preassigned symplectic operator) with the trace identity introduced by Tu. Since the Lax operator is known one can obtain the hereditary operators signifying the complete integrability. Various properties of Kronecker product are found to be useful in our construction.

math-ph↗
arXiv2017

On A New Form of Darboux-Bäcklund Transformation for DNLS Equation-Mixed and Rational Type Solutions

A new form of Darboux-Bäcklund transformation and its higher order form is derived for Derivative Nonlinear Schrodinger Equation(DNLS). The new form arises due to the different form of Lax pair. It is observed that by a special choice of the eigenvalue of DB transformation one can generate a mixed form of solution(containing both algebraic and exponential dependence on (x, t) can be generated. On the other hand by adopting a new methodology due to Neugebauer et. al. it is found that purely rational solution can be constructed. The two different approach yields different class of solution and are compared.

nlin.SI↗