Gaussian Wave Functions Research Articles

Current Density in Saturn's Equatorial Current Sheet: Cassini Magnetometer Observations

AbstractThe equatorial current sheet at Saturn is the result of a rapidly rotating magnetosphere. The sheet itself exhibits periodic seasonal and diurnal movements as well as aperiodic movements of a currently unknown origin, along with periodic thickening and thinning of the magnetodisc, and azimuthal changes in the thickness due to local effects in the magnetosphere. In this paper aperiodic movements of the magnetodisc are utilized to calculate the height‐integrated current density of the current sheet using a Harris current sheet model deformed by a Gaussian wave function. We find a local time asymmetry in both the radial and azimuthal height‐integrated current density. We note that the local time relationship with height‐integrated current density is similar to the relationship seen at Jupiter, where a peak of ∼0.04 A/m at ∼3 SLT (Saturn local time) is seen inside 20 RS. The divergence of the radial and azimuthal current densities are used to infer the parallel currents, which are seen to diverge from the equator in the prenoon sector and enter the equator in the premidnight sector.

Computational investigations into the structural and electronic properties of Cd n Te n (n = 1-17) quantum dots.

Size-tunability of the electronic and optical properties of semiconductor quantum dots and nanoclusters is due to the quantum size effect, which causes variations in the electronic excitations as the particle boundaries are changed. Recently, CdSe and CdTe quantum dots have been used in energy harvesting devices. Despite these promising practical applications, a complete understanding of the electronic transitions associated with the surfaces of the nanoparticles is currently lacking and is difficult to achieve experimentally. Computational methods could provide valuable insights and allow us to understand the electronic and optical properties of quantum dots and nanoclusters. Hollow cage and endohedral or core–shell cage structures for CdnTen clusters have been reported before. We have performed systematic density functional theory (DFT) studies on the structure and electronic properties of the CdnTen (n = 1–17) clusters. As the number of atoms increases in the CdnTen clusters, the predicted geometries change from simple planar structures to more complicated 3D-structures. Two classes of the most stable structures were elucidated for clusters with n = 10–17: (i) hollow cage structures with an empty center; and (ii) endohedral or core–shell cage structures with one or more atoms inside the cage. Noticeably higher highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps were observed for the hollow cage isomers as compared to the core–shell structures. The highest occupied molecular orbitals of all of the clusters studied were shown to be localized on the surface of the cage for the hollow cage structures, while in the case of the core–shell structures, the HOMO electron densities were found to be distributed both on surface and the interior of the structures. Most of the small size clusters CdnTen (n = 2–9) showed minimal values for the dipole moments (close to zero) owing to the highly ordered and symmetric configurations of these structures. For isomers of the larger clusters (n = 10–17), it was observed that the core–shell structures have higher values for the dipole moments than the hollow cage species because of the highly symmetric structures of the hollow cages. Core–shell cage structures exhibited lower polarizability than the respective hollow cage structures.

An Improved Analysis of Masses and Decay Constants of Heavy Flavour Mesons within Variational Approach

We employ the variational method to study the properties such as masses, decay constants, oscillation frequency and branching ratios of leptonic decays of heavy flavour mesons with linear cum coulomb Cornell potential. Gaussian function, Coulomb wave function and Airy function are taken as the trial wave-function of variational method in this study. Our analysis suggests that Gaussian trial wave-function provides results which are in close proximity with the experimental results. We also make a comparison with the results from QCD Sum rules and lattice QCD, as well as with recent PDG data.

Approximation methods in the study of boson stars

We analyze the accuracy of the variational method in computing physical quantities relevant for gravitationally bound Bose-Einstein condensates. Using a variety of variational ans\"atze found in existing literature, we determine physical quantities and compare them to exact numerical solutions. We conclude that a "linear+exponential" wavefunction proportional to $(1 + \xi)\exp(-\xi)$ (where $\xi$ is a dimensionless radial variable) is the best fit for attractive self-interactions along the stable branch of solutions, while for small particle number $N$ it is also the best fit for repulsive self-interactions. For attractive self-interactions along the unstable branch, a single exponential is the best fit for small $N$, while a sech wavefunction fits better for large $N$. The Gaussian wavefunction ansatz, which is used often in the literature, is exceedingly poor across most of the parameter space, with the exception of repulsive interactions for large $N$. We investigate a "double exponential" ansatz with a free constant parameter, which is computationally efficient and can be optimized to fit the exact solutions in different limits. We show that the double exponential can be tuned to fit the sech ansatz, which is computationally slow. We also show how to generalize the addition of free parameters in order to create more computationally efficient ans\"atze using the double exponential. Determining the best ansatz, according to several comparison parameters, will be important for analytic descriptions of dynamical systems. Finally, we examine the underlying relativistic theory, and critically analyze the Thomas-Fermi approximation often used in the literature.

Control of particle propagation beyond the uncertainty limit by interference between position and momentum

As shown in Phys. Rev. A 96, 020101(R) (2017), it is possible to demonstrate that quantum particles do not move along straight lines in free space by increasing the probability of finding the particles within narrow intervals of position and momentum beyond the "either/or" limit of 0.5 using constructive quantum interference between a component localized in position and a component localized in momentum. The probability of finding the particle in a corresponding spatial interval at a later time then violates the lower bound of the particle propagation inequality which is based on the validity of Newton's first law. In this paper, the problem of localizing the two state components in their respective target intervals is addressed by introducing a set of three coefficients that describe the localization of arbitrary wavefunctions quantitatively. This characterization is applied to a superposition of Gaussians, obtaining a violation of the particle propagation inequality by more than 5 percent if the width of the Gaussian wavefunction is optimized along with the size of the position and momentum intervals. It is shown that the violation of the particle propagation inequality originates from the fundamental way in which quantum interferences relate initial position and momentum to the future positions of a particle, indicating that the violation is a fundamental feature of causality in the quantum limit.

Localization Study of a Cold Atom BEC in Two-Dimensional Bessel Optical Lattices

In order to investigate the stability and dynamics properties of a cold atom Bose-Einstein Condensate (BEC) in two-dimensional Bessel optical lattices, the stability condition of the system is analyzed and the corresponding Gross-pitaevskii equation (GPE) is solved in this paper by time-dependent variational method and numerical simulation. Firstly, the Euler-Lagrange equation containing the parameters describing the system stability and the effective potential energy needed by the variational analysis method to analyze the system stability is obtained by using the adjustable exponent Gaussian trial wave function. Secondly, according to the analytical solution of Euler-Lagrange equation and the local minimum value of potential energy, the stability condition of the system is further illuminated. Finally, the influence mechanism of these parameters on the local dynamics is revealed by solving the corresponding GPE with numerical method.

Dynamics of heavy quarkonia in memory-dependent dissipative environment from Bohmian trajectory perspective

In this work, we study the dynamics of particles coupled to a dissipative environment from Bohmian trajectory perspective. The dissipation is modeled using the concept of memory-dependent derivative (MDD), which is characterized by its time-delay constant [Formula: see text] and nonsingular kernel [Formula: see text] of two parameters [Formula: see text], [Formula: see text]. By assuming a Gaussian packet wave function, we derived a MDD-Langevin equation (MDDLE). The general behavioral solution [Formula: see text] of the MDDLE is investigated for the case of Gaussian fluctuation force. Based on the miscellaneous choices of [Formula: see text], [Formula: see text], [Formula: see text], the findings are that [Formula: see text] can exhibit distinct behaviors, such as monotonic and nonmonotonic decay without zero crossings, oscillatory-like without zero and with zero crossing. Therefore, we have either diffusion or oscillatory dominate based on the problem parameters. For a harmonically bound heavy quarkonium, characterized by the angular frequency [Formula: see text], the position correlation function [Formula: see text] is then obtained and analyzed numerically. The analysis shows that this correlation function is also sensitive to the various choices of [Formula: see text] and kernel parameters. Based on these choices, the correlation function exhibits distinct behaviors: oscillation without damping, damping, and enhanced. This wide range of behavior coverage increases the versatility to fit nonlinear or memory-dependent experimental findings. The results are compared with the fractional Langevin equation.

Bohmian Trajectories for Kerr–Newman Particles in Complex Space-Time

Complexified Liénard–Wiechert potentials simplify the mathematics of Kerr–Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr–Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be multi-valued. A generalized analytic continuation is introduced which leads to an infinite number of trajectories. These include the entire set of Bohmian trajectories. This leads to multiple retarded times which come into play in complex space-time. If one weights these trajectories by their natural Bohmian weighting factors, then it is found that the particles do not radiate, that they are extended, and that they can have a finite electrostatic self energy, thus avoiding the usual divergence of the charged point particle. This effort does not in any way criticize or downplay the traditional Bohmian interpretation which does not assume the standard electromagnetic coupling to charged particles, but it suggests that a hybridization of Kerr–Newman particle theory with Bohmian mechanics might lead to interesting new physics, and maybe even the possibility of emergent quantum mechanics.

Spectroscopy and decay properties of charmonium

The mass spectra of charmonium are investigated using a Coulomb plus linear (Cornell) potential. Gaussian wave functions in position space as well as in momentum space are employed to calculate the expectation values of potential and kinetic energy respectively. Various experimental states (X(4660)(53S1), X(3872)(23P1), X(3900)(21P1), X(3915)(23P0) and X(4274)(33P1) etc.) are assigned as charmonium states. We also study the Regge trajectories, pseudoscalar and vector decay constants, electric and magnetic dipole transition rates, and annihilation decay widths for charmonium states.

Photoproduction of vector mesons in proton–proton ultraperipheral collisions at the CERN Large Hadron Collider

Photoproduction of vector mesons is computed with dipole model in proton–proton ultraperipheral collisions (UPCs) at the CERN Large Hadron Collider (LHC). The dipole model framework is employed in the calculations of vector mesons production in diffractive processes. Parameters of the bCGC model are refitted with the latest inclusive deep inelastic scattering experimental data. Employing the bCGC model and boosted Gaussian light-cone wave function for vector mesons, we obtain the prediction of rapidity distributions of [Formula: see text] and [Formula: see text] mesons in proton–proton ultraperipheral collisions at the LHC. The predictions give a good description of the experimental data of LHCb. Predictions of [Formula: see text] and [Formula: see text] mesons are also evaluated in this paper.

Entanglement of purification in free scalar field theories

We compute the entanglement of purification (EoP) in a 2d free scalar field theory with various masses. This quantity measures correlations between two subsystems and is reduced to the entanglement entropy when the total system is pure. We obtain explicit numerical values by assuming minimal gaussian wave functionals for the purified states. We find that when the distance between the subsystems is large, the EoP behaves like the mutual information. However, when the distance is small, the EoP shows a characteristic behavior which qualitatively agrees with the conjectured holographic computation and which is different from that of the mutual information. We also study behaviors of mutual information in purified spaces and violations of monogamy/strong superadditivity.

New trial wave function for the nuclear cluster structure of nuclei

A new trial wave function is proposed for nuclear physics, in which an exact solution to the long-standing center-of-mass problem is given. In the new approach, the widths of the single-nucleon Gaussian wave packets and the widths of the relative Gaussian wave functions describing correlations of nucleons or clusters are treated as variables in the explicit intrinsic wave function of the nuclear system. As an example, this new wave function was applied to study the typical ${^{20}{\rm Ne}}$ ($\alpha$+${{^{16}}{\rm O}}$) cluster system. By removing exactly the spurious center-of-mass effect in a very simple way, the energy curve of ${^{20}{\rm Ne}}$ was obtained by the variational calculations with the width of $\alpha$ cluster, the width of ${{^{16}}{\rm O}}$ cluster, and the size parameter of the nucleus. They are considered as the three crucial variational variables in describing the ${^{20}{\rm Ne}}$ ($\alpha$+${{^{16}}{\rm O}}$) cluster system. This shows that the new wave function can be a very interesting new tool for studying many-body and cluster effects in nuclear physics.

Exclusive photoproduction of vector mesons in proton–lead ultraperipheral collisions at the LHC

Rapidity distributions of vector mesons are computed in dipole model proton–lead ultraperipheral collisions (UPCs) at the CERN Larger Hadron Collider (LHC). The dipole model framework is implemented in the calculations of cross sections in the photon–hadron interaction. The bCGC model and Boosted Gaussian wave functions are employed in the scattering amplitude. We obtain predictions of rapidity distributions of J/ψ meson proton–lead ultraperipheral collisions. The predictions give a good description to the experimental data of ALICE. The rapidity distributions of ϕ, ω and ψ(2s) mesons in proton–lead ultraperipheral collisions are also presented in this paper.

Radiative transitions and the mixing parameters of the D meson

Spectroscopic parameters of heavy-light flavoured D meson are obtained within the framework of phenomenological quark-antiquark potential (Coulomb plus linear confinement) model using the Gaussian wave function. We incorporated (1/m) corrections to the potential energy term and relativistic corrections to the kinetic energy term of the hamiltonian. We obtain the radiative (electric and magnetic) transitions and the mixing parameters of the DâĹŠ oscillation. The results are compared with various experimental measurement as well as other theoretical predictions.

Faithful Pointer for Qubit Measurement

In the context of von Neumann projective measurement scenario for a qubit system, it is widely believed that the mutual orthogonality between the post-interaction pointer states is the sufficient condition for achieving the ideal measurement situation. However, for experimentally verifying the observable probabilities, the real space distinction between the pointer distributions corresponding to post-interaction pointer states play crucial role. It is implicitly assumed that mutual orthogonality ensures the support between the post-interaction pointer distributions to be disjoint. We point out that mutual orthogonality (formal idealness) does \emph{not} necessarily imply the real space distinguishability (operational idealness), but converse is true. In fact, for the commonly referred Gaussian wavefunction, it is possible to obtain a measurement situation which is formally ideal but fully nonideal operationally. In this paper, we derive a class of pointer states, that we call faithful pointers, for which the degree of formal (non)idealness is equal to the operational (non)idealness. In other words, for the faithful pointers, if a measurement situation is formally ideal then it is operationally ideal and vice versa.

Entropic uncertainty relation based on generalized uncertainty principle

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

Spectroscopy, decay properties and Regge trajectories of the B and Bs mesons**A. K. Rai acknowledges the financial support extended by the Department of Science of Technology, India under SERB fast track scheme SR/FTP /PS-152/2012

A Gaussian wave function is used for detailed study of the mass spectra of the B and BS mesons using a Cornell potential incorporated with a \U0001d4aa(1/m) correction in the potential energy term and expansion of the kinetic energy term up to \U0001d4aa(p10) for relativistic correction of the Hamiltonian. The predicted excited states for the B and Bs mesons are in very good agreement with results obtained by experiment. We assign B2(5747) and Bs2(5840) as the 13P2 state, B1(5721) and Bs1(5830) as the 1P1 state, B0(5732) as the 13P0 state, Bs1(5850) as the state and B(5970) as the 23S1 state. We investigate the Regge trajectories in the (J,M2) and (nr,M2) planes with their corresponding parameters. The branching ratios for leptonic and radiative-leptonic decays are estimated for the B and BS mesons. Our results are in good agreement with experimental observations as well as outcomes of other theoretical models.

Cassini observations of aperiodic waves on Saturn's magnetodisc

AbstractThe location and motion of Saturn's equatorial current sheet is the result of an interplay between a quasi‐static deformation that varies in radial distance and local time, impulsive perturbations that produce large‐scale displacements, quasiperiodic perturbations near the planetary rotation period, and wave‐like structures on shorter timescales. This study focuses on the latter, aperiodic wave pulses with periods from 1 to 30 min, which are unrelated to the quasiperiodic “flapping” with a period near that of Saturn's rotation. Cassini magnetometer data were surveyed for these aperiodic structures and then fitted to a simple model in order to estimate the properties of the waves. The model consists of a modified Harris current sheet model deformed by a Gaussian pulse wave function. This then allows for the extraction of wave parameters and current sheet properties. In particular, we show an increase in current sheet scale height with radial distance from Saturn, an increase in the wave amplitude with radial distance, and the resolution of propagation directions using the wave vector fitted by the model. The dominant propagation direction is found to be radially outward from Saturn.

Excited state mass spectra, decay properties and Regge trajectories of charm and charm-strange mesons**Supported by Department of Science of Technology, India under SERB fast track scheme SR/FTP/PS-152/2012 and also to SVNIT (Institute Research Grant (Dean (R&C)/1488/2013-14))

The framework of a phenomenological quark-antiquark potential (Coulomb plus linear confinement) model with a Gaussian wave function is used for detailed study of masses of the ground, orbitally and radially excited states of heavy-light Qq̅, (Q=c,q=u/d,s) mesons. We incorporate a correction to the potential energy term and relativistic corrections to the kinetic energy term of the Hamiltonian. The spin-hyperfine, spin-orbit and tensor interactions incorporating the effect of mixing are employed to obtain the pseudoscalar, vector, radially and orbitally excited state meson masses. The Regge trajectories in the (J,M2) and (nr,M2) planes for heavy-light mesons are investigated with their corresponding parameters. Leptonic and radiative leptonic decay widths and corresponding branching ratios are computed. The mixing parameters are also estimated. Our predictions are in good agreement with experimental results as well as lattice and other theoretical models.

Predictions of ρ meson cross-sections between AdS/QCD and boosted Gaussian wave functions in the color glass condensate model

Exclusive [Formula: see text] meson production is computed in dipole model using two different light-cone wave functions in this paper. The Color-Glass-Condensate (CGC) model is implemented to compute the dipole cross-section. The two light-cone wave functions are AdS/QCD model and boosted Gaussian model. It can be seen that the predictions using the two light-cone wave functions are close to each other.