Searcharxiv⌕ Search

arXiv subjects

Arindam Chakraborty

Publications and source records attributed to Arindam Chakraborty.

34 records · Page 2Linked to original sources
arXiv2017

On The Darboux Bäcklund Transformation of Optical Solitons with Resonant and Nonresonant Nonlinearity

Solitons in nonlinear optics holds a special role both in theoretical and experimental studies. Several types of evolution equations are seen to govern different situation of physical relevance. One such is the existence of both resonant and nonresonant situation in optical fibre. The corresponding evolution equation was devised by Doktorov et. al., which consists of a forced NLS equation along with two other equations for population difference and polarization. Here, we have followed an earlier formulation of Neugebauer for Darboux-Bäcklund transformation for this coupled systems. This formalism has the advantage that one can write the N-soliton solution altogether.An important difference with the usual non-linear system is that all the field variables are not present in both part of Lax operator. So we are to apply the DT to both part separately.

nlin.SI↗
arXiv2017

A New form of Krönecker product-Lax pair and coupled systems

A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Krönecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure. Actually they are all bi-Hamiltonian. A few explicit form of such equations are given also

nlin.SI↗
arXiv2017

Derivation of time-dependent transition probability for $2\mathrm{e}-2\mathrm{h}$ generation from $1\mathrm{e}-1\mathrm{h}$ state in the presence of external electromagnetic field

In this work, we investigate the effect of electromagnetic (EM) field on the generation of 2e-2h states from 1e-2h states. One of the fundamental ways by which electromagnetic (EM) waves interact with matter is by the generation of excited electronic states. The interaction of EM field with atoms and molecules is given by the field-dependent Hamiltonian. Excited states are intrinsically transient in nature because they are not stationary states of the field-dependent Hamiltonian. Consequently, the time-dependent dynamics of excited states depend strongly on the external electromagnetic field. Starting with the 1e-1h excitation in a general many-electron system, the system was propagated in time using time-dependent perturbation theory (TDPT). The expression for time-dependent transition probability of $(1\mathrm{e}-1\mathrm{h}) \rightarrow (2\mathrm{e}-2\mathrm{h})$ was evaluated for a given time $t$ up to second-order in TDPT using diagrammatic techniques. The derivation does not assume any a priori approximations to the electron-electron correlation operator and presents the derivation of a complete set of contributing diagrams associated with the full configuration interaction wave function. The result from this work show that the calculation of time-dependent transition probability can be factored into a time-independent and time-dependent components. This is a significant outcome for efficient computation of the time-dependent transition probability because it allows for pre-computation of time-independent components before the start of the calculations.

physics.chem-ph↗
arXiv2015

Development of multicomponent coupled-cluster method for investigation of multiexcitonic interactions

Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems is presented. This method provides a balanced treatment of many-particle correlation in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is the extension of the electronic structure CCSD formulation for multicomponent systems and is defined as $\vert Ψ_\mathrm{mcCC} \rangle = e^{T_1^\mathrm{I}+T_2^\mathrm{I}+T_1^\mathrm{II}+T_2^\mathrm{II}+T_{11}^\mathrm{I,II}+T_{12}^\mathrm{I,II}+T_{21}^\mathrm{I,II}+T_{22}^\mathrm{I,II}}\vert 0^\mathrm{I}0^\mathrm{II}\rangle$. The applicability of the mcCC method was demonstrated by computing biexciton binding energies for multiexcitonic systems and benchmarking the results against full configuration interaction calculations. The results demonstrated that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.

physics.chem-ph↗
arXiv2015

Visual Generalized Coordinates

An open problem in robotics is that of using vision to identify a robot's own body and the world around it. Many models attempt to recover the traditional C-space parameters. Instead, we propose an alternative C-space by deriving generalized coordinates from $n$ images of the robot. We show that the space of such images is bijective to the motion space, so these images lie on a manifold $\mathcal{V}$ homeomorphic to the canonical C-space. We now approximate this manifold as a set of $n$ neighbourhood tangent spaces that result in a graph, which we call the Visual Roadmap (VRM). Given a new robot image, we perform inverse kinematics visually by interpolating between nearby images in the image space. Obstacles are projected onto the VRM in $O(n)$ time by superimposition of images, leading to the identification of collision poses. The edges joining the free nodes can now be checked with a visual local planner, and free-space motions computed in $O(nlogn)$ time. This enables us to plan paths in the image space for a robot manipulator with unknown link geometries, DOF, kinematics, obstacles, and camera pose. We sketch the proofs for the main theoretical ideas, identify the assumptions, and demonstrate the approach for both articulated and mobile robots. We also investigate the feasibility of the process by investigating various metrics and image sampling densities, and demonstrate it on simulated and real robots.

cs.RO↗
arXiv2014

Determination of electron-hole correlation length in CdSe quantum dots using explicitly correlated two-particle cumulant

The electron-hole correlation length serves as an intrinsic length scale for analyzing excitonic interactions in semiconductor nanoparticles. In this work, the derivation of electron-hole correlation length using the two-particle reduced density is presented. The correlation length was obtained by first calculating the electron-hole cumulant from the pair density,and then transforming the cumulant into intracular coordinates, and finally then imposing exact sum-rule conditions on the radial integral of the cumulant. The excitonic wave function for the calculation was obtained variationally using the electron-hole explicitly correlated Hartree-Fock method. As a consequence, both the pair density and the cumulant were explicit functions of the electron-hole separation distance. The use of explicitly correlated wave function and the integral sum-rule condition are the two key features of this derivation. The method was applied to a series of CdSe quantum dots with diameters 1-20 nm and the effect of dot size on the correlation length was analyzed.

physics.atm-clus↗
arXiv2013

Infinite-order diagrammatic summation approach to explicitly correlated congruent transformed Hamiltonian

A resolution of identity approach to explicitly correlated congruent transformed Hamiltonian (CTH) is presented. One of the principle challenges associated with the congruent transformation of the many-electron Hamiltonian is the generation of three, four, five, and six particle operators. Successful application of the congruent transformation requires efficient implementation of the many-particle operators. In this work, we present the resolution of identity congruent transformed Hamiltonian (RI-CTH) method to handle many-particle operators. The resolution of identity was used to project the explicitly correlated operator in a N-particle finite basis to avoid explicit computation of the many-particle operators. Single-particle states were obtained by performing Hartee-Fock calculations, which were then used for construction of many-particle states. The limitation of the finite nature of the resolution of identity was addressed by developing partial infinite order (PIOS) diagrammatic summation technique. In the PIOS method, the matrix elements of the projected congruent transformed Hamiltonian was expressed in terms of diagrammatic notation and a subset of diagrams were summed up to infinite order. The RI-CTH and RI-CTH-PIOS methods were applied to isoelectronic series of 10-electron systems (Ne,HF,H2O,NH3,CH4) and results were compared with CISD and CCSD(T) calculations. One of the key results from this work is that for identical basis set, the RI-CTH-PIOS energies are lower than CISD and CCSD(T) values.

physics.chem-ph↗
arXiv2013

Effect of dot size on exciton binding energy and electron-hole recombination probability in CdSe quantum dots

Exciton binding energy and electron-hole recombination probability are presented as the two important metrics for investigating effect of dot size on electron-hole interaction in CdSe quantum dots. Direct computation of electron-hole recombination probability is challenging because it requires an accurate mathematical description of electron-hole wavefunction in the neighborhood of the electron-hole coalescence point. In this work, we address this challenge by solving the electron-hole Schrodinger equation using the electron-hole explicitly correlated Hartree-Fock (eh-XCHF) method. The calculations were performed for a series of CdSe clusters ranging from $\mathrm{Cd}_{20}\mathrm{Se}_{19}$ to $\mathrm{Cd}_{74608}\mathrm{Se}_{74837}$ that correspond to dot diameter range of 1-20 nm. The calculated exciton binding energies and electron-hole recombination probabilities were found to decrease with increasing dot size. Both of these quantities were found to scale as $D_\mathrm{dot}^{-n}$ with respect to the dot diameter D. One of the key insights from this study is that the electron-hole recombination probability decreases at a much faster rate than the exciton binding energy as a function of dot size. It was found that an increase in the dot size by a factor of 16.1, resulted in a decrease in the exciton binding energy and electron-hole recombination probability by a factor of 14.4 and $5.5\times10^{6}$, respectively.

physics.chem-ph↗
arXiv2012

Variational solution of congruent transformed Hamiltonian for many-electron systems using full configuration interaction calculation

The congruent transformation of the electronic Hamiltonian is developed to address the electron correlation problem in many-electron systems. The central strategy presented in this method is to perform transformation on the electronic Hamiltonian for approximate removal of the Coulomb singularity. The principle difference between the present method and the transcorrelated method of Handy and Boys is that the congruent transformation preserves the Hermitian property of the Hamiltonian. The congruent transformation is carried out using explicitly correlated functions and the optimum correlated transform Hamiltonian is obtained by performing a search over a set of transformation functions. The ansatz of the transformation functions are selected to facilitate analytical evaluation of all the resulting integrals. The ground state energy is obtained variationally by performing a full configuration interaction (FCI) calculation on the congruent transformed Hamiltonian. Computed results on well-studied benchmark systems show that for the identical basis functions, the energy from the congruent transformed Hamiltonian is significantly lower than the conventional FCI calculations. Since the number of configuration state functions in the FCI calculation increases rapidly with the size of the 1-particle basis set, the results indicate that the congruent transformed Hamiltonian provides a viable alternative to obtain FCI quality energy using a smaller underlying 1-particle basis set.

physics.chem-ph↗
arXiv2012

Development of polaron-transformed explicitly correlated full configuration interaction method for investigation of quantum-confined Stark effect in GaAs quantum dots

The effect of external electric field on electron-hole correlation in GaAs quantum dots is investigated. The electron-hole Schrodinger equation in the presence of external electric field is solved using explicitly correlated full configuration interaction (XCFCI) method and accurate exciton binding energy and electron-hole recombination probability are obtained. The effect of the electric field was included in the 1-particle single component basis functions by performing variational polaron transformation. The quality of the wavefunction at small inter-particle distances was improved by using Gaussian-type geminal function that depended explicitly on the electron-hole separation distance. The parameters of the explicitly correlated function were determined variationally at each field strength. The scaling of total exciton energy, exciton binding energy, and electron-hole recombination probability with respect to the strength of the electric field was investigated. It was found that a 500 kV/cm change in electric field reduces the binding energy and recombination probability by a factor of 2.6 and 166, respectively. The results show that the eh-recombination probability is affected much more strongly by the electric field than the exciton binding energy. Analysis using the polaron-transformed basis indicates that the exciton binding should asymptotically vanish in the limit of large field strength.

physics.chem-ph↗
arXiv2010

Analyzing the Efficiency of Mn-(C2H4) (M = Sc, Ti, Fe, Ni; n = 1, 2) Complexes as Effective Hydrogen Storage Materials

Hydrogen trapping ability of various metal - ethylene complexes has been studied at the B3LYP and MP2 level of theory using the 6-311+G(d,p) basis set. Different global and local reactivity descriptors and the associated electronic structure principles provide important insights into the associated interactions. There exist two distinct classes of bonding patterns, viz., a Kubas-type interaction between the metal and the H2 molecule behaving as a η2-ligand and an electrostatic interaction between the metal and the atomic hydrogens.

physics.atm-clus↗
arXiv2007

Gauge momentum operators for the Calogero-Sutherland model with anti-periodic boundary condition

The integrability of a classical Calogero systems with anti-periodic boundary condition is studied. This system is equivalent to the periodic model in the presence of a magnetic field. Gauge momentum operators for the anti-periodic Calogero system are constructed. These operators are hermitian and simultaneously diagonalizable with the Hamiltonian. A general scheme for constructing such momentum operators for trigonometric and hyperbolic Calogero-Sutherland model is proposed. The scheme is applicable for both periodic and anti-periodic boundary conditions. The existence of these momentum operators ensures the integrability of the system. The interaction parameter $λ$ is restricted to a certain subset of real numbers. This restriction is in fact essential for the construction of the hermitian gauge momentum operators.

hep-th↗
arXiv2007

Quasi-solvability of Calogero-Sutherland model with Anti-periodic Boundary Condition

The U(1) Calogero-Sutherland Model with anti-periodic boundary condition is studied. This model is obtained by applying a vertical magnetic field perpendicular to the plane of one dimensional ring of particles. The trigonometric form of the Hamiltonian is recast by using a suitable similarity transformation. The transformed Hamiltonian is shown to be integrable by constructing a set of momentum operators which commutes with the Hamiltonian and amongst themselves. The function space of monomials of several variables remains invariant under the action of these operators. The above properties imply the quasi-solvability of the Hamiltonian under consideration.

hep-th↗
arXiv2005

Eigenvalues of the Anti-periodic Calogero - Sutherland Model

The U(1) Calogero Sutherland Model (CSM) with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered state space is obtained in an upper triangular form. Consequently the diagonal elements become the energy eigenvalues.

hep-th↗
arXiv2005

Calogero-Sutherland Model with Anti-periodic Boundary Conditions: Eigenvalues and Eigenstates

The U(1) Calogero Sutherland Model with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered state space is obtained in an upper triangular form. Consequently the diagonal elements become the energy eigenvalues. The eigenstates are constructed using Young diagram and represented in terms of Jack symmetric polynomials. The eigenstates so obtained are orthonormalized.

math-ph↗