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S. Habib Mazharimousavi

Publications and source records attributed to S. Habib Mazharimousavi.

At least 37 records · Page 2Linked to original sources
arXiv2021

Quantum particle on a surface: Catenary surface and Paraboloid of revolution

We revisit the Schrödinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the principal curvatures in the effective binding potential on the surface is emphasized. Furthermore, using the so-called Monge-Gauge we construct the approximate Schrödinger equation for a flat surface with small fluctuations. Finally, the resulting Schrödinger equation is solved for some specific surfaces. In particular, we give exact solutions for a particle confined on a Catenary surface and a paraboloid of revolution.

quant-ph↗
arXiv2021

Comment on "Reissner-Nordström Black Holes in the Inverse Electrodynamics Model, [arXiv:1407.4383]"

Recently, the inverse electrodynamics model (IEM) was introduced and applied to fined Reissner-Nordström black holes in the context of the general relativity coupled minimally with the nonlinear electrodynamics \cite{1}. The solution consists of both electric and magnetic fields as of the dyonic solutions. Here in this note, we show that the IEM model belongs to a more general class of nonlinear electrodynamics with $T=T_{μ}^{μ}=0$. Here $T_{μ}^{ν}$ is the energy-momentum tensor of the nonlinear electrodynamic Lagrangian. Naturally, such a dyonic RN black hole solution is the solution for this general class.

gr-qc↗
arXiv2021

Black-hole solution in nonlinear electrodynamics with the maximum allowable symmetries

The nonlinear Maxwell Lagrangian preserving both conformal and SO(2) duality-rotation invariance has been introduced very recently. Here, in the context of Einstein's theory of gravity minimally coupled with this nonlinear electrodynamics, we obtain a black hole solution which is the Reissner-Nordström black hole with one additional parameter that is coming from the nonlinear theory. We employ the causality and unitarity principles to identify an upper bound for this free parameter. The effects of this parameter on the physical properties of the black hole solution are investigated.

gr-qc↗
arXiv2021

Generalized probability and current densities: A field theory approach

We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The extended probability and particle current densities are found which satisfy the continuity equation.

quant-ph↗
arXiv2020

Step Momentum Operator

In the present study, the concept of a quantum particle with step momentum is introduced. The energy eigenvalues and eigenfunctions of such particles are obtained in the context of the generalized momentum operator, proposed recently in [13, 14]. While, the number of bound states with real energy for the particles with Hermitian step momentum inside a square well is infinite, it is finite for a particle with \mathcal{PT} -symmetric momentum.

quant-ph↗
arXiv2020

Two dimensional non-Hermitian harmonic oscillator: coherent states

In this study, we introduce a two dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time independent Schrödinger equation yields real eigenvalues with complex eigenfunctions. We also construct the coherent state of the system by using a superposition of 12 eigenfunctions. Using the complex correspondence principle for the probability density we investigate the possible modifications in the probability densities due to the non-Hermitian aspect of the Hamiltonian.

quant-ph↗
arXiv2020

Greybody factors of black holes in dRGT massive gravity coupled with nonlinear electrodynamics

In the context of the dRGT massive gravity coupled with nonlinear electrodynamics, we present new dRGT black hole solutions. Together with the thermodynamical properties of the solutions, we study the greybody factor of the corresponding black hole solution. To this end, we compute the rigorous bound on the greybody factor for the obtained dRGT black holes. The obtained results are graphically represented for different values of the theory's physical parameters. Our analysis shows that the charged dRGT black holes of nonlinear electrodynamics evaporate quicker than the charged dRGT black holes originated from linear electrodynamics.

hep-th↗
arXiv2020

A Geometrical Model for the Evolution of Spherical Planetary Nebulae Based on Thin-Shell Formalism

A spherical planetary nebula is described as a geometric model. The nebula itself is considered as a thin-shell which visualized as a boundary of two spacetimes. The inner and outer curvature tensors of the thin-shell are found in order to get an expression of the energy-momentum tensor on the thin-shell. The energy density and pressure expressions are derived using the energy-momentum tensor. The time evolution of the radius of the thin-shell is obtained in terms of the energy density. The model is tested by using a simple power function for decreasing energy density and the evolution pattern of the planetary nebula is attained.

gr-qc↗
arXiv2020

Black Holes in Double-Logarithmic Nonlinear Electrodynamics

The electric and magnetic black hole solutions are found by coupling the recently introduced nonlinear electrodynamics (NED) model, called "double logharitmic nonlinear electrodynamics" with cosmological Einstein gravity. The solutions become Reissner-Nordstrom (RN) black hole in the weak field limit and asymptotically. The electric solution is expressed as an integral equation while the magnetic black hole solution is expressed in terms of elementary functions. Hence, the thermodynamic structure of the magnetic black hole solution is analyzed by deriving the modified Smarr's formula and studying the first law of thermodynamics. Moreover, its stability is investigated by deriving the heat capacity.

gr-qc↗
arXiv2020

Double-logarithmic nonlinear electrodynamics

A new model of nonlinear electrodynamics named as \emph{"double-logarithmic"} is introduced and investigated. The theory carries one dimensionful parameter of the $β$ as Born-Infeld electrodynamics. It is shown that the dual symmetry and dilatation (scale) symmetry are broken in the proposed model. The electric field of a point-like charge is derived for this model and it becomes non-singular at the origin and by use of this electric field the static electric energy of a point like charge is calculated. In the presence of an external magnetic field the theory shows the phenomenon known as vacuum birefringence. The refraction index of two polarizations, parallel and perpendicular to the external magnetic induction field are calculated. The canonical and symmetrical Belinfante energy-momentum tensors are obtained. Using the causality and unitarity principles the regions where the theory becomes causal and unitary are found.

gr-qc↗
arXiv2020

Higher Dimensional Particle Model in Pure Lovelock Gravity

In this paper, based on the thin-shell formalism, we introduce a classical model for particles in the framework of $n+1-$dimensional $\left[\frac{n}{2}\right]$-order pure Lovelock gravity. In particular, we construct a spherically symmetric particle of radius $a$ whose inside is a flat Minkowski spacetime while its outside is charged pLG solution. Knowing that in $n+1-$dimensional spherically symmetric Einstein gravity ($R$-gravity) such a particle model cannot be constructed, as we have discussed first, provides the main motivation for this study. In fact, it is the richness of Lovelock parameters that provides such a particle construction possible. On the thin-shell, the energy-momentum components are chosen to vanish, yet their normal derivatives are non-zero.

physics.gen-ph↗
arXiv2020

Thin-shell Wormholes with Ordinary Matter in Pure Gauss-Bonnet Gravity

In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by $N\geq5$-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.

gr-qc↗
arXiv2020

Higher Dimensional Particle Model in Third-Order Lovelock Gravity

By using the formalism of thin-shells, we construct a geometrical model of a particle in third-order Lovelock gravity. This particular theory which is valid at least in 7 dimensions, provides enough degrees of freedom and grounds towards such a construction. The particle consists of a flat interior and a non-black hole exterior spacetimes whose mass, charge, and radius are determined from the junction conditions, in terms of the parameters of the theory.

hep-th↗
arXiv2020

Colliding waves in a model of nonlinear electrodynamics

Bell-Szekeres (BS) solution for colliding electromagnetic waves in Einstein-Maxwell (EM) theory describes also colliding waves in nonlinear electrodynamics (NED) with an emergent cosmological constant. Our NED model covers the first leading orders to the well-known Heisenberg-Euler (HE) type in a particular gauge of pure magnetic field. Prior to the problem of collision we obtain dyonic solution for the considered NED theory in a conformally flat spacetime which has both electric and magnetic fields with constant invariants. Our sole finding is that null currents inevitably arise in the process of collision of plane waves in the HE type NED theory.

gr-qc↗
arXiv2020

Behavior of a Free Quantum Particle in the Poincaré Upper Half-Plane Geometry

Inspired by the recent work of Filho et al., a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore, granting the validity of the Heisenberg equation in a curved space, the Ehrenfest theorem is generalized and interpreted with the new position-dependent differential operator in a curved space. The modified Hamiltonian leads to a modified time-independent Schrödinger equation, which is solved explicitly for a free particle in the Poincaré upper half-plane geometry. It is shown that a "free particle" does not behave as it is totally free due to curved background geometry.

hep-th↗
arXiv2020

$\mathcal{PT}$-Symmetric Generalized Extended Momentum Operator

We develop further the concept of generalized extended momentum operator (GEMO), which has been introduced very recently in \citep{M.H2}, and propose the so called $\mathcal{PT}$-symmetric GEMO. In analogy with GEMO, the $\mathcal{PT}$-symmetric GEMO also satisfies the extended uncertainty principle (EUP) relation. Moreover, the corresponding Hamiltonian that is constructed upon the $\mathcal{PT}$-symmetric GEMO, with a real or $\mathcal{PT}$-symmetric potential, remains non-Hermitian but $\mathcal{PT}$-symmetric and consequently its energy and momentum eigenvalues are real. We apply our formalism to a quasi-free quantum particle and the exact solutions for the energy spectrum are presented.

quant-ph↗
arXiv2020

Generalized Extended Momentum Operator

We study and generalize the momentum operator satisfying the extended uncertainty principle relation (EUP). This generalized extended momentum operator (GEMO) consists of an arbitrary auxiliary function of position operator, $μ\left( x\right) $, in such a combination that not only GEMO satisfies the EUP relation but also it is Hermitian. Next, we apply the GEMO to construct the generalized one-dimensional Schrödinger equation. Upon using the so called point canonical transformation (PCT), we transform the generalized Schrödinger equation from $x$-space to $z$-space where in terms of the transformed coordinate, $z$, it is of the standard form of the Schrödinger equation. In continuation, we study two illustrative examples and solve the corresponding equations analytically to find the energy spectrum.

quant-ph↗