arXiv subjects

Moorad Alexanian

Publications and source records attributed to Moorad Alexanian.

At least 19 recordsLinked to original sources

arXiv2026

Effective de Sitter-Schwarzschild Metrics

An earlier work that replaced the de Sitter-Schwarzschild metric for a cosmological constant Lambda <=0 by an effective anti-de Sitter black hole analytic at Lambda = 0 is here extended to the horizon structure through its three possible roots. We replace the de Sitter-Schwarzschild metric for all possible values of Lambda and the Schwarzschild radius R for the three possible available roots by either a Schwarzschild black hole whose radius depends on both R and Lambda or a de Sitter space whose cosmological constant depends on both R and Lambda.

physics.gen-ph↗

arXiv2026

Parametrized Version of the Generalized Aubry-André Model

A recently introduced recurrence-relation ansatz applied to the Bose-Hubbard model is here used in the generalized Aubry-Andre model. The resulting modified Aubry-Andre model allows for a simple parametrization of the solutions in terms of three parameters, viz., the system energy when the quasiperiodicity amplitude Delta = 0, the site mu where the particle is initially localized, and the tuning parameter -1 < alpha < 1 that determines the regions of localized or extended states. The standard Aubry-Andre form corresponds to alpha = 0.

quant-ph↗

arXiv2025

Quantum Phase Transition in the Dicke Model

We consider a previously modified Jaynes-Cummings model with single-photon cavity radiation field and atomic system exchanging a squeezed photon and deduce a normal/superradiance quantum phase transition in the Dicke model of N atoms of arbitrary spin with independent co- and counter-rotating coupling terms.

quant-ph↗

arXiv2025

Symmetric and Asymmetric Quantum Rabi Model

We introduce a modified Jaynes-Cummings model with single-photon cavity radiation field but with the atomic system instead of exchanging a single photon as in the Jaynes-Cummings model, it exchanges instead a squeezed photon. After a unitary transformation and requiring the decoupling of the spin up from the spin down, we diagonalize the resulting Hamiltonian via a Bogoliubov transformation. This allows to determine the energy eigenvalues for the quantum Rabi model. We obtain the energy eigenvalues albeit for the asymmetric Rabi model in the limit of large coupling strength, where it approaches the symmetric Rabi model energy eigenvalues.

quant-ph↗

arXiv2024

Ansatz for the Two-Dimensional Ising Model in an External Magnetic Field

An ansatz applied to the two-dimensional Ising model in an external magnetic field h gives rise to an exactly soluble model. The singularity in the magnetization found by Onsager does not survive the presence of the external magnetic field as found earlier by Lee and Yang in 1952. However, the singularity in the heat capacity remains even in the presence of the magnetic field. A surprising result is the presence of negative heat capacity for h > 0.

cond-mat.stat-mech↗

arXiv2024

A Soluble Modified Fermi-Hubbard Model

A recently introduced recurrence-relation ansatz applied to the Bose-Hubbard model is here used in the Fermi-Hubbard model. The resulting modified Fermi-Hubbard model is soluble and exhibits a continuous phase transition (second order) reminiscent of the integer quantum Hall resistance and a ground-state, first-order phase transition.

cond-mat.mes-hall↗

arXiv2024

Thermodynamics of a Modified Fermi-Hubbard Model

A recently introduced recurrence-relation ansatz applied to the Fermi-Hubbard model gives rise to a soluble model and here is used to calculate several thermodynamic observables. The constraint of unit density per site, density = 1, is applied and some of the results are compared to cases where the constraint is not imposed. The modified model exhibits a continuous phase transition (second order) reminiscent of the integer quantum Hall resistance and a ground state, first-order phase transition.

cond-mat.quant-gas↗

arXiv2024

Quantum Phase Transition in a Modified Jaynes-Cummings Model

We introduce a modified Jaynes-Cummings model with single-photon cavity radiation field but with the atomic system instead of exchanging a single photon as in the Jaynes-Cummings model, it exchanges instead a squeezed photon with squeezing parameter r. This allows us to interpolate between the Rabi model, r = infinity, and the Jaynes-Cummings model, r = 0, by varying r. The model exhibits a quantum phase transition. Accordingly, the quantum phase transition realized in the Rabi model, giving rise to superradiance, also occurs in the Jaynes-Cummings model

quant-ph↗

arXiv2024

Angular distributions and polarization correlations of the two-photon spherical states

We have analyzed in detail the angular polarization properties in the center of mass reference frame of Landau's two-photon spherical states in momentum space. The angular distributions for fixed values of $J$ and $M$ do not depend on the parity but are defined by two different functions of the polar angle between the relative momentum and the quantization axes. The two-photon polarization density matrices are derived for each values of $J$, $M$, and $P$. The linear polarization correlations of individual photons are analyzed in detail. We find, besides the usual correlation laws for $J\geq 2$ in terms of $sin$ and $cos$ of the angle between the orientation of the analyzers, correlations in terms of the sum of the orientation angles of the analyzers.

quant-ph↗

arXiv2023

Nonlocal Potentials and Crystalline Order in One and Two Dimensions

We revisit the seminal 1968 proof of the absence of crystalline order in two dimensions and analyze the importance played in the quantum theorem by the assumption of local pair potentials. We relax the assumption of local potentials and consider instead nonlocal pair potentials. We show that the 1/k2-singularity that occurs in the Bogoliubov inequality, which leads to no crystalline order in two dimensions for local potentials and nonzero temperatures, does not occur for nonlocal potentials. Accordingly, crystalline order in one and two dimensions cannot be ruled out for nonlocal pair potentials at finite temperatures.

quant-ph↗

arXiv2023

Nearest-Neighbor Tunneling Ansatz in the Bose-Hubbard Mode

A recently introduced recurrence-relation ansatz applied to the Jaynes-Cummings-Hubbard model is here applied to the Bose-Hubbard model that reduced the model to an easily soluble model. The results obtained for the two-point density correlations resemble somewhat those obtained recently also but in a much more complicated fashion. Our ansatz may be of value for the solution of many-body quantum mechanical problems.

cond-mat.quant-gas↗

arXiv2023

Particle-Hole Ansatz in the Jaynes-Cummings-Hubbard Model

A recurrence relation ansatz between annihilation operators applied to the hopping interaction term of the Jaynes-Cummings-Hubbard model (JCHM) reduces the JCHM to that of the ordinary Jaynes-Cummings model (JCM), albeit, with a boson energy depending on the hopping strength. This allows us to calculate the phase diagram for the Mott-to-superfluid phase transition and the critical hopping strength as a function of the detuning.

quant-ph↗

arXiv2022

The Dynamics of a Modified Jaynes-Cummings Model

We introduce a dynamical system that instead of exchanging a single photon as in the atomic system of the usual Jaynes-Cummings model (JCM), it exchanges instead a squeezed coherent photon. Accordingly, the creation and annihilation photon operators in the JCM are replaced by the creation and annihilation operators of squeezed coherent states, respectively. This transformation generates a photon Hamiltonian that modifies the JCM that includes terms usually omitted in the JCM when making the rotating-wave approximation and, in addition, the transformation introduces atom exchange terms absent in the JCM.

quant-ph↗

arXiv2022

One-dimensional Dynamics for a Discontinuous Singular Map and the Routes to Chaos

We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points. In particular, routes to chaos exist that do not exhibit period-doubling whereas period-doubling is the sole route to chaos in the logistic map. Aperiodic maps are found that lead to cobwebs with x = infinity as accumulation points, where every neighborhood contains infinitely many points generated by the map.

nlin.CD↗

arXiv2022

Collapse and revival of $n$-photon coherent states and $n$-photon squeezed coherent states

We introduce the set of $n$-photon coherent states and the set of $n$-photon squeezed coherent states and study their collapse and revival and compare their behavior with the collapse and revival of the corresponding zero-photon coherent states and zero-photon squeezed coherent states, respectively. The set of $n$-photon squeezed coherent states ($n=0,1,2,\cdots$) forms a basis of the Hilbert state of photons and may be of some interest. We notice that the presence of a few extra photons in the $n$-photon states as compared to the corresponding zero-photon states makes a large difference in the behavior of their collapse and revival. This indicates the large effect that a few extra photons makes in the $n$-photon states as compared to the corresponding zero-photon states in their collapse and revival.

quant-ph↗

arXiv2021

Bose-Einstein Condensation and quasicrystals

We consider interacting Bose particles in an external local potential. It is shown that large class of external quasicrystal potentials cannot sustain any type of Bose-Einstein condensates. Accordingly, at spatial dimensions $D\leq 2$ in such quasicrystal potentials a supersolid is not possible via Bose-Einstein condensates at finite temperatures. The latter also hold true for the two-dimensional Fibonacci tiling. However, supersolids do arise at $D\leq 2$ via Bose-Einstein condensates from infinitely long-range, nonlocal interparticle potentials.

cond-mat.quant-gas↗

arXiv2021

Conflicts Between Science and Religion: Epistemology to the Rescue

Both Albert Einstein and Erwin Schrödinger have defined what science is. Einstein includes not only physics, but also all natural sciences dealing with both organic and inorganic processes in his definition of science. According to Schrödinger, the present scientific worldview is based on the two basic attitudes of comprehensibility and objectivation. On the other hand, the notion of religion is quite equivocal and unless clearly defined will easily lead to all sorts of misunderstandings. Does science, as defined, encompass the whole of reality? More importantly, what is the whole of reality and how do we obtain data for it? The Christian worldview considers a human as body, mind, and spirit (soul), which is consistent with Cartesian ontology of only three elements: matter, mind, and God. Therefore, is it possible to give a precise definition of science showing that the conflicts are actually apparent and not real?

physics.hist-ph↗

arXiv2021

Bose-Einstein Condensation and Supersolids

We consider interacting Bose particles in an external potential. It is shown that a Bose-Einstein condensate is possible at finite temperatures that describes a supersolid in three dimensions (3D) for a wide range of potentials in the absence of an external potential. However, for 2D, a self-organized supersolid exists for finite temperatures provided the interaction between bosons is nonlocal and of infinitely long-range. It is interesting that in the absence of the latter type of potential and in the presence of a lattice potential, there is no Bose-Einstein condensate and so in such a case, a 2D supersolid is not possible at finite temperatures. We also propose the correct Bloch form of the condensate wave function valid for finite temperatures, which may be used as the correct trial wave function.

cond-mat.quant-gas↗