arXiv subjects

Debraj Nath

Publications and source records attributed to Debraj Nath.

12 recordsLinked to original sources

arXiv2026

Information theoretic measures of isotropic Dunkl oscillator in spherical coordinates

An information theoretic analysis is done for the isotropic harmonic oscillator potential within the Dunkl-Schr\"odinger framework in spherical coordinates. Starting from the exact analytical eigensolution, various quantum information measures such as Shannon entropy, R\'enyi information, Tsallis entropy are derived. Besides, their relative measures like relative Shannon, relative R\'enyi, relative Tsallis as well as corresponding divergences (Jensen-Shannon, Jensen-R\'enyi, Jensen-Tsallis) are also obtained. In order to get Shannon entropy, a novel factorization method is introduced. This is facilitated through the use of well-known weighted Lebesgue measure. The results from the Dunkl case agree exactly with the non-Dunkl scenario, when Dunkl parameters vanish. The reflection operators and Dunkl parameters considerably influence the above measures. These are portrayed in graphical forms.

math-ph↗

arXiv2026

Quantum information and statistical complexity of hydrogen-like ions in Dunkl-Schr\"odinger system

In this work, we present analytical solutions of Schr\"odinger equation for Coulomb potential in presence of a Dunkl reflection operator. Expressions are offered for eigenvalues, eigenfunctions and radial densities for H-isoelectronic series (Z=1-3). The degeneracy in energy in absence and presence of the reflection has been discussed. The standard deviation, Shannon entropy, R\'enyi entropy in position space have been derived for arbitrary quantum states. Then several important complexity measures like L\'opez-Ruiz-Mancini-Calbet (LMC), Shape-R\'enyi complexity (SRC), Generalized R\'enyi complexity (GRC), R\'enyi complexity ratio (RCR) are considered in the analytical framework. Representative results are given for three one-electron atomic ions in tabular and graphical format. Changes in these measures with respect to parity and Dunkl parameter have been given in detail. Most of these results are offered here for the first time.

quant-ph↗

arXiv2025

Quantum dynamics in confined pseudo-harmonic oscillator in a time-dependent moving

In this work, we present analytical solution of Schr\"odinger equation of confined pseudoharmonic potential in presence of a moving boundary condition, for an arbitrary angular momentum state. It turns out that an important quantity to probe the problem is internuclear distance ratio, which depends on the solution of Ermakov equation. The minimum value of time-dependent (TD) Heisenberg uncertainty product always remains greater than that of the minimum uncertainty product h/2. The TD average energy is derived analytically in a closed form and the corresponding average force and average pressure are defined. Moreover, time correlation function of two states for the case of six selected diatomic molecules (CO, NO, ScH, CH, H2, N2) is obtained. It is found to depend on internuclear distance ratio at two different time domains. The TD survival probability and average life-time of molecule in a confined quantum system are defined. Expressions are offered for quantum similarity measure, dissimilarity and quantum similarity index. The latter is given for a pair of molecules. The obtained results are compared with available literature, wherever possible. To our knowledge this is the first detailed report of a non-harmonic central potential in a TD moving boundary condition.

quant-ph↗

arXiv2025

Information theoretic measures within Schr\"odinger-Dunkl framework in spherical coordinates

In this article, we have presented analytical solution of Schr\"odinger-Dunkl equation with Deng-Fan molecular potential in spherical coordinates. The ro-vibrational energy of some selected diatomic molecules ScH, TiH, VH and CrH are obtained under a simple, new approximation to the centrifugal term in presence of three reflection operators and Dunkl parameters. The angular wave functions are obtained in terms of Jacobi polynomial, whereas radial wave functions in terms of hypergeometric function. The analytical results of Shannon entropy, expectation, Heisenberg uncertainty, entropic moment, disequilibrium, R\'enyi entropy and Tsallis entropy of marginal density (radial r, and angular {\theta}, {\phi}) and total density functions are obtained in Schr\"odinger-Dunkl system with respect to the weighted Lebesgue measure. This has been possible by making use of factorization method for Shannon entropy. The absolute per cent deviation between the analytical and numerical results for all the information theoretic measures remain well within 0.0001%. The effect of reflection operators on angular wave solutions and on information theoretic measures are shown. In essence, a number of statistical measures have been reported for Deng-Fan potential in the Dunkl-Schr\"odinger framework.

quant-ph↗

arXiv2024

Stability analysis of multiple solutions of three wave interaction with group velocity dispersion and wave number mismatch

This paper explores the analytical approach for obtaining the multiple solutions of three-wave interacting system in (1+1) dimensions. We present a novel approach by expressing the wave solutions in terms of Jacobi elliptic functions and delve into specific cases involving hyperbolic functions. Additionally, the paper focuses on analysing the linear stability of two kinds of solutions: (a) periodic and (b) one or two-hump bright solitons due to group velocity and group velocity dispersion. For linear stability, we solve the eigenvalue problem by Fourier collocation method, where Fourier coefficients are defined analytically and compared numerically. On the other hand, we check the linear stability by direct numerical simulations with Pseudospectral method along special derivatives $(t)$ and 4th order Runge-Kutta method in temporal direction $(z)$. Then it is confirmed by Crank-Nicholson finite difference method. Furthermore, we introduce a special case known as constant magnitude wave solution and examine its modulational instability in presence of group velocity dispersion. In addition, the influence of group velocities and wave vector mismatch are investigated.

nlin.PS↗

arXiv2022

Ro-vibrational energy and thermodynamic properties of molecules subjected to Deng-Fan potential through an improved approximation

Accurate solution of the Schrödinger equation with Deng-Fan potential is presented by means of Nikiforov-Uvarov method. A modified Pekeris-type approximation is proposed for the centrifugal term, from a linear combination of the $r \to 0$ and $r \to r_e$ limits. It can potentially offer a series of approximations (depending on an adjustable parameter $λ$). The existing approximations in the literature can then be recovered in certain special cases. Its efficiency and feasibility is demonstrated by a critical comparison of eigenvalues produced at various $λ$'s for four molecules, \emph{viz.}, H$_2$, LiH, HCl and CO. Analytical expressions are derived for energies, eigenfunctions and the thermodynamic properties such as vibrational mean free energy, vibrational free energy, vibrational entropy and vibrational specific heat. The effect of quantum correction on partition function and thermodynamic properties is discussed by including the correction up to 10th-order, for H$_2$ and LiH. The effect of $λ$ parameter on these properties is also studied.

physics.chem-ph↗

arXiv2022

Ro-vibrational energy analysis of Manning-Rosen and Pöschl-Teller potentials with a new improved approximation in the centrifugal term

Two physically important potentials (Manning-Rosen and Pöschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked for the centrifugal term, which is then used for their solution within the Nikiforov-Uvarov framework. This employs a recently proposed scheme, which combines the two widely used Greene-Aldrich and Pekeris-type approximations. Thus, approximate analytical expressions are derived for eigenvalues and eigenfunctions. The energies are examined with respect to two approximation parameters, $λ$ and $ν$. The original approximations are recovered for certain specials values of these two parameters. This offers a simple effective scheme for these and other relevant potentials in quantum mechanics.

quant-ph↗

arXiv2022

Analytical solution of $D$ dimensional Schrödinger equation for Eckart potential with a new improved approximation in centrifugal term

Analytical solutions are presented for eigenvalues, eigenfunctions of {\color{red} D-dimensional Schrodinger equation having Eckart potential} within Nikiforov-Uvarov method. This uses a new, improved approximation for centrifugal term, from a combination of Greene-Aldrich and Pekeris approximations. Solutions are obtained in terms of hypergeometric functions. It facilitates an accurate representation in entire domain. Its validity is illustrated for energies in an arbitrary $\ell \neq 0$ quantum state. Results are compared for a chosen set of potential parameters in different dimensions. In short, a simple accurate approximation is offered for Eckart and other potentials in quantum mechanics, in higher dimension.

quant-ph↗

arXiv2022

Majorization effect on entropic functionals: An application to a V-type three-level atom-field interacting system

Majorization effect on some entropic functionals, such as von-Neumann, Shannon, atomic Wehrl and Rényi entropies are investigated of a V-type three-level atom, which interacts with a coherent field in a resonant cavity. Fidelity, purity and linear entropy are investigated for two quantum systems, which contain photon number distributions and Husimi Q functions. A relation between majorization and localization properties of continuous density functionals is established. The results are compared and verified for continuous and discrete distributions of an atom-field interacting system.

quant-ph↗

arXiv2021

Comparison between time-independent and time-dependent quantum systems in the context of energy, Heisenberg uncertainty, average energy, force, average force and thermodynamic quantities

Exact solutions of time-dependent Schrödinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent potential whereas average energy and Heisenberg uncertainty relation are defined for time-dependent potential. Forces acting on a fixed boundary wall as well as average force acting on moving boundary wall are presented along various trajectories. For high temperature, analytical forms of partition function and the corresponding thermodynamic quantities are derived following the Euler-Maclaurin summation formula over a finite as well as an infinite domain for accurate presentation. Three quantum systems are generated with the help of point transformation, separation of variables and super-symmetric quantum mechanics from one quantum system and the corresponding results are compared among all systems, where two of them are time-independent and another two are time-dependent.

quant-ph↗

arXiv2021

Connected and disconnected stable regions of solitons of nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric potential

We have considered cubic nonlinear Schrödinger equation along with supersymmetric $\mathcal{PT}$ like potential and obtained exact stationary solutions in terms of bright and brigh-dark interacting solitons. The $\mathcal{PT}$ broken and $\mathcal{PT}$ unbroken regions are demonstrated also depicted. Connected and disconnected stable regions of bright and dark solitons are examined incorporating linear stability analysis validated by direct numerical simulations. Moreover, the strength of stability has been illustrated through excitations of bright and dark solitons.

nlin.PS↗

arXiv2021

Properties of Rényi complexity ratio of quantum states for central potential

Rényi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of Rényi complexity ratio are proved by Lebesgue measure. Some properties of Rényi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of Rényi entropy, Rényi complexity ratio, statistical complexities based on Rényi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of Rényi complexity ratio are verified for some diatomic molecules (CO, NO, N$_2$, CH, H$_2$, and ScH) and for some other quantum systems.

math-ph↗