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In this paper, we present coherent states à la Gazeau-Klauder for a free particle in square well potential within position-deformed Heisenberg algebra . These states satisfy the Klauder’s mathematical requirement to build coherent states. Some statistical properties such as the probability distribution, the intensity correlation function and the Mandel parameter are calculated and analyzed. We find that these states are sub-Poissonian in nature. We also construct for these coherent states, the even cat states and we evaluate its Wigner function which analyses the quasiprobability distribution of these states. We graphically demonstrate that these states exhibit nonclassical behavior.

A minimum length scale of the order of Planck length is a feature of many models of quantum gravity that seek to unify quantum mechanics and gravitation. Recently, Perivolaropoulos in his seminal work [Phys. Rev.D 95, 103523 (2017)] predicted the simultaneous existence of minimal and maximal length measurements of quantum gravity. More recently, we have shown that both measurable lengths can be obtained from position-dependent noncommutativity [J. Phys. A: Math.Theor. 53, 115303 (2020)]. In this paper, we present an alternative derivation of these lengths from non-Hermitian position-dependent noncommutativity. We show that a simultaneous measurement of both lengths form a family of discrete spaces. In one hand, we show the similarities between the maximal uncertainty measurement and the classical properties of gravity. On the other hand, the connection between the minimal uncertainties and the non-Hermicity quantum mechanic scenarios. The existence of minimal uncertainties are the consequences of non-Hermicities of some operators that are generators of this noncommutativity. With an appropriate Dyson map, we demonstrate by a similarity transformation that the physically meaningfulness of dynamical quantum systems is generated by a hidden Hermitian position-dependent noncommutativity. This transformation preserves the properties of quantum gravity but removes the fuzziness induced by minimal uncertainty measurements at this scale. Finally, we study the eigenvalue problem of a free particle in a square-well potential in these new Hermitian variables., Comment: 25

More recently, we have proposed a set of noncommutative space that describes the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303 (2020)]. The interesting significant result we found is that, the generalized uncertainty principle induces a maximal measurable length of quantum gravity. This measurement revealed strong quantum gravitational effects at this scale and predicted a detection of gravity particles with low energies. In the present paper, to make evidence this prediction, we study in this space, the dynamics of a particle with position-dependent mass (PDM) trapped in an infinite square well. We show that, by increasing the quantum gravitational effect, the PDM of the particle increases and induces deformations of the quantum energy levels. These deformations are more pronounced as one increases the quantum levels allowing, the particle to jump from one state to another with low energies and with high probability densities., Comment: 18 pages

Ultrafast optical control of intramolecular charge flow was demonstrated, which paves the way for photocurrent modulation and switching with a highly wavelength-selective ON/OFF ratio. The system that was explored is a fac-[Re(CO)(3)(TTF-DPPZ)Cl] complex, where TTF-DPPZ = 4’,5’-bis(propylthio)tetrathiafulvenyl[i]dipyrido[3,2-a:2’,3’-c]phenazine. DFT calculations and AC-Stark spectroscopy confirmed the presence of two distinct optically active charge-transfer processes, namely a metal-to-ligand charge transfer (MLCT) and an intra-ligand charge transfer (ILCT). Ultrafast transient absorption measurements showed that the ILCT state decays in the ps regime. Upon excitation to the MLCT state, only a long-lived (3)MLCT state was observed after 80 ps. Remarkably, however, the bleaching of the ILCT absorption band remained as a result of the effective inhibition of the HOMO–LUMO transition.

In order to achieve an in-depth understanding of the role played by the solvent in the photoinduced low-spin (LS) → high-spin (HS) transition in solvated Fe(ii) complexes, an accurate description of the solvated complexes in the two spin states is required. To this end, we are applying state-of-the-art

In this note, we study the actions of rational quantum Olshanetsky-Perelomov systems for finite reflections groups of type D n . we endowed the polynomial ring C[x 1,..., xn ] with a differential structure by using directly the action of the Weyl algebra associated with the ring C[x 1,..., xn ] W of invariant polynomials under the reflections groups W after a localization. Then we study the polynomials representation of the ring of invariant differential operators under the reflections groups. We use the higher Specht polynomials associated with the representation of the reflections group W to exhibit the generators of its simple components.

We report a detailed ab initio molecular dynamics (AIMD) study of the structural and vibrational properties of aqueous [Fe(tpy)2]2+ (tpy = 2,2':6',2''-ter-pyridine) in the low-spin (LS) and high-spin (HS) states, which extends our previous work on aqueous [Fe(bpy)3]2+ (bpy = 2,2'-bipyridine) [L. M. Lawson Daku and A. Hauser, J. Phys. Chem. Lett., 2010, 1, 1830-1835; L. M. Lawson Daku, Phys. Chem. Chem. Phys., 2018, 20, 6236-6253]. Upon the LS → HS change of states, the axial and distal Fe-N bonds of aqueous [Fe(tpy)2]2+ are predicted to lengthen by 0.226 Å and 0.206 Å, respectively, in excellent agreement with experiments [X. Zhang et al., J. Phys. Chem. C, 2015, 119, 3312-3321; G. Vankó et al., J. Phys. Chem. C, 2015, 119, 5888-5902]. The lengthening of the Fe-N bonds results from their weakening, which also gives rise to an increased thermal fluctuation of the molecular structure. As with [Fe(bpy)3]2+, the first hydration shell of [Fe(tpy)2]2+ consists in a chain of hydrogen-bonded water molecules wrapped around the ligands. The predicted hydration number of [Fe(tpy)2]2+ in both spin states is ≈15 while it was found for [Fe(bpy)3]2+ to increase from ≈15 to ≈17 on passing from the LS to the HS state. Due to the ≈0.2 Å lengthening of the Fe-N bonds in both complexes upon the LS → HS transition, the water molecules can get closer to the Fe atom: by ≈0.4 Å for [Fe(tpy)2]2+ and by ≈0.2 Å for [Fe(bpy)3]2+. This difference is ascribed to the fact that the bpy ligands with their trigonal coordination motif provides a bulkier environment to the Fe atom than the tpy ligands with their tetragonal coordination motif. In other words, upon the tpy → bpy substitution, the bulkier environment provided by the bpy ligands repels the hydration shell, the displacement being greater in the HS state than in the LS state. As a consequence of their chemical similarity, the calculated LS and HS IR spectra of aqueous [Fe(tpy)2]2+ closely resemble those of aqueous [Fe(bpy)3]2+, the LS → HS transition translating into a global increase in intensity. The present work taken with the one on aqueous [Fe(bpy)3]2+ enhances our understanding of the spin-state dependence of the structural and vibrational properties of Fe(ii) polypyridyl complexes in water, highlighting the strong interpenetration between their coordination sphere and their hydration shell.

In this paper we study a two-dimensional [2D] rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient of friction. At the quantum level, we use the Lewis-Riesenfeld procedure of invariants to construct exact solutions for the corresponding time-dependent Schr\"{o}dinger equations. The eigenfunctions obtained are in terms of the generalized Laguerre polynomials. By mean of the solutions we verify a generalization version of the Heisenberg's uncertainty relation and derive the generators of the $su(1,1)$ Lie algebra. Based on these generators, we construct the coherent states $\grave{\textrm{a}}$ la Barut-Girardello and $\grave{\textrm{a}}$ la Perelomov and respectively study their properties., Comment: 27 pages

The accurate description of transition metal complexes in liquid solutions is a challenging fundamental research problem, which must be tackled when it comes to understanding the role of the solvent in the photoinduced low-spin (LS) → high-spin (HS) transition in solvated Fe(ii) complexes. We report an in-depth ab initio molecular dynamics (AIMD) study of the spin-state dependence of the structural and vibrational properties of the prototypical [Fe(bpy)

In this paper we consider two kinds of noncommutative space-time commutation relations in two-dimensional configuration space and feature the absolute value of the minimal length from the generalized uncertainty relations associated to the particular commutation relations. We study the problem of the two-dimensional gravitational quantum well in the new Hermitian variables and confront the experimental results for the first lowest energy state of the neutrons in the Earth's gravitational field to estimate the upper bounds on the noncommutativity parameters. The absolute value of the minimum length is smaller than a few nanometers., 12 pages

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.