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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., Comment: 21 pages

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., Comment: 11 pages

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, Comment: 9 pages

A $\gamma$-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 $\gamma$ plays a crucial role in the entire formulation and non-trivially modifies the eigenfunctions under consideration., Comment: 13 pages

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., Comment: 33 pages, 4 tables, 9 figures and 1 appendix

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, Comment: 9 pages

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., Comment: 13 pages, 3 figures, 3 tables

A $\gamma$-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 $\gamma$ plays a crucial role in the entire formulation and non-trivially modifies the eigenfunctions under consideration.

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.

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., Comment: 13 pages

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.

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., Comment: 16 pages

A new form of Darboux-B\"acklund 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., Comment: 12 pages 8 figures

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-B\"acklund 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., Comment: 6 pages no figures

A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker 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, Comment: 12 pages no figures

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., Comment: 18 pages, 5 figures, 106 equations, diagrammatic representation

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.

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 $\vert \Psi_\mathrm{mcCC} \rangle = e^{T_1^\mathrm{I}+T_2^\mathrm{I}+T_1^\mathrm{II}+T_2^\mathrm{II}+T_{11}^\mathrm{I,II}+T_{12}^\mathrm{I,II}+T_{21}^\mathrm{I,II}+T_{22}^\mathrm{I,II}}\vert 0^\mathrm{I}0^\mathrm{II}\rangle$. 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., Comment: 17 pages

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.