Terms Of Harmonic Oscillators Research Articles

GeTe2 Phase Change Material for Terahertz Devices with Reconfigurable Functionalities Using Optical Activation.

The phenomenon of phase change transition has been a fascinating research subject over decades due to a possibility of dynamically controlled materials properties, allowing the creation of optical devices with unique features. The present paper unravels the optical characteristics and terahertz (THz) dielectric permittivity of a novel phase change material (PCM), GeTe2, prepared by pulsed laser deposition (PLD) and their remarkable contrast in crystalline and amorphous states, in particular, a difference of 7 orders of magnitude in conductivity. The THz spectra were analyzed using the harmonic oscillator and Drude term. Using GeTe2 PLD films, we designed and prepared a THz metasurface in the form of periodic structure and revealed a possibility of tuning the THz resonance either by a thermal control or light-induced crystallization response, thus achieving the dynamic and tunable functionality of the metastructure. We propose controlling the state of metasurface by observing the intensity characteristics of the Raman peak of 155 cm-1. Density functional theory (DFT) modeling demonstrates that in the process of crystallization the mode intensity of 155 cm-1 assigned to Te-Te stretching in amorphous chain fragments decreases and disappears at full crystallization.

Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature

The so-called Darboux III oscillator is an exactly solvable N-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This oscillator can be interpreted as a smooth (super)integrable deformation of the usual N-dimensional harmonic oscillator in terms of a non-negative parameter λ which is directly related to the curvature of the underlying space. In this paper, a detailed study of the Shannon information entropy for the quantum version of the Darboux III oscillator is presented, and the interplay between entropy and curvature is analysed. In particular, analytical results for the Shannon entropy in the position space can be found in the N-dimensional case, and the known results for the quantum states of the N-dimensional harmonic oscillator are recovered in the limit of vanishing curvature λ→0. However, the Fourier transform of the Darboux III wave functions cannot be computed in exact form, thus preventing the analytical study of the information entropy in momentum space. Nevertheless, we have computed the latter numerically both in the one and three-dimensional cases and we have found that by increasing the absolute value of the negative curvature (through a larger λ parameter) the information entropy in position space increases, while in momentum space it becomes smaller. This result is indeed consistent with the spreading properties of the wave functions of this quantum nonlinear oscillator, which are explicitly shown. The sum of the entropies in position and momentum spaces has been also analysed in terms of the curvature: for all excited states such total entropy decreases with λ, but for the ground state the total entropy is minimized when λ vanishes, and the corresponding uncertainty relation is always fulfilled.

Oscillator Laser Model

AbstractA laser model is formulated in terms of quantum harmonic oscillators. Emitters in the low lasing states are usual harmonic oscillators, and emitters in the upper states are inverted harmonic oscillators. Diffusion coefficients, consistent with the model and necessary for solving quantum nonlinear laser equations analytically, are found. Photon number fluctuations of the lasing mode and fluctuations of the population of the lasing states are calculated. Collective Rabi splitting peaks are predicted in the intensity fluctuation spectra of the superradiant lasers. Population fluctuation mechanisms in superradiant lasers and lasers without superradiance are discussed and compared with each other.

Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems

The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of nuclear models bearing the SU(3) symmetry are reviewed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation (irrep), which corresponds to the maximal spatial overlap among the fermions. The consideration of the highest weight (hw) irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid–shell region. Subsequently, the consequences of the use of the hw irreps on the binding energies and two-neutron separation energies in the rare earth region are discussed within the proxy-SU(3) scheme, by considering a very simple Hamiltonian, containing only thethree dimensional (3D) isotropic harmonic oscillator (HO) term and the quadrupole-quadrupole interaction. This Hamiltonian conserves the SU(3) symmetry and treats the nucleus as a rigid rotator.

Some remarks on few recent results on the damped quantum harmonic oscillator

In a recent paper, Deguchi et al. (2019), the authors proposed an analysis of the damped quantum harmonic oscillator in terms of ladder operators. This approach was shown to be partly incorrect in Bagarello et al. (2019), via a simple no-go theorem. More recently, (Deguchi and Fujiwara, 2019), Deguchi and Fujiwara claimed that our results in Bagarello et al. (2019) are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistakes in Deguchi et al. (2019) and Deguchi and Fujiwara (2019). We also propose a very simple example clarifying the core of the problem.

Regarding Nonstationary Quadratic Quantum Systems

With the help of the evolution operator method, we have established unitary connection between quadratic systems, namely between a free particle with variable mass M(t) , a particle with variable mass M(t) in a variable homogeneous field, and a harmonic oscillator with variable mass M(t) and frequency ω(t) , on which a variable force F(t) acts. Knowledge of the unitary connection allowed us to express easily in general form the propagators, invariants, wave functions, and other functions of a linear potential and a harmonic oscillator in terms of the corresponding quantities for a free particle. We have analyzed the linear and quadratic invariants in detail. Results known in the literature follow as particular cases from the general results obtained here.

Approximate Hamiltonian for baryons in heavy-flavor QCD

Aiming at relativistic description of gluons in hadrons, the renormalization group procedure for effective particles (RGPEP) is applied to baryons in QCD of heavy quarks. The baryon eigenvalue problem is posed using the Fock-space Hamiltonian operator obtained by solving the RGPEP equations up to second order in powers of the coupling constant. The eigenstate components that contain three quarks and two or more gluons are heuristically removed at the price of inserting a gluon-mass term in the component with one gluon. The resulting problem is reduced to the equivalent one for the component of three quarks and no gluons. Each of the three quark–quark interaction terms thus obtained consists of a spin-dependent Coulomb term and a spin-independent harmonic oscillator term. Quark masses are chosen to fit the lightest spin-one quarkonia masses most accurately. The resulting estimates for bbb and ccc states match estimates obtained in lattice QCD and in quark models. Masses of ccb and bbc states are also estimated. The corresponding wave functions are invariant with respect to boosts. In the ccb states, charm quarks tend to form diquarks. The accuracy of our approximate Hamiltonian can be estimated through comparison by including components with two gluons within the same method.

A Quantum Field Approach for Advancing Optical Coherence Tomography Part I: First Order Correlations, Single Photon Interference, and Quantum Noise.

Optical coherence tomography has become an important imaging technology in cardiology and ophthalmology, with other applications under investigations. Major advances in optical coherence tomography (OCT) imaging are likely to occur through a quantum field approach to the technology. In this paper, which is the first part in a series on the topic, the quantum basis of OCT first order correlations is expressed in terms of full field quantization. Specifically first order correlations are treated as the linear sum of single photon interferences along indistinguishable paths. Photons and the electromagnetic (EM) field are described in terms of quantum harmonic oscillators. While the author feels the study of quantum second order correlations will lead to greater paradigm shifts in the field, addressed in part II, advances from the study of quantum first order correlations are given. In particular, ranging errors are discussed (with remedies) from vacuum fluctuations through the detector port, photon counting errors, and position probability amplitude uncertainty. In addition, the principles of quantum field theory and first order correlations are needed for studying second order correlations in part II.

Renormalized quark–antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD

In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space–time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit–Fermi spin couplings in the effective quark–antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.

Parametric Symmetry Breaking in a Nonlinear Resonator.

Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far-from-equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work unveils that the double hysteresis is a manifestation of an out-of-equilibrium symmetry breaking between parametric phase states. Such a fundamental phenomenon, in the most ubiquitous building block of nature, paves the way for the investigation of new dynamical phases of matter in parametrically driven many-body systems and motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.

On the quantum mechanical solutions with minimal length uncertainty

In this paper, we study two generalized uncertainty principles (GUPs) including [Formula: see text] and [Formula: see text] which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.

Multitrace approach to noncommutativeΦ24theory

In this article we provide a multitrace analysis of the theory of noncommutative $\Phi^4$ in two dimensions on the fuzzy sphere ${\bf S}^2_{N,\Omega}$, and on the Moyal-Weyl plane ${\bf R}^{2}_{\theta, \Omega}$, with a non-zero harmonic oscillator term added. The doubletrace matrix model symmetric under $M\longrightarrow -M$ is solved in closed form. An analytical prediction for the disordered-to-non-uniform-ordered phase transition and an estimation of the triple point, from the termination point of the critical boundary, are derived and compared with previous Monte Carlo measurement.

Progress towards an effective non-Markovian description of a system interacting with a bath

We analyze a system coupled to a bath of independent harmonic oscillators. We transform the bath in chain structure by solving an inverse eigenvalue problem. We solve the equations of motion for the collective variables defined by this transformation, and we derive the exact dynamics for an harmonic oscillator in terms of the microscopic motion of the environmental modes. We compare this approach to the well-known Generalized Langevin Equation and we show that our dynamics satisfies this equation.

Superconformal mechanics inSU(2|1)superspace

Using the worldline $SU(2|1)$ superfield approach, we construct $\mathcal{N}=4$ superconformally invariant actions for the $d=1$ multiplets ($\mathbf{1},\mathbf{4},\mathbf{3}$) and ($\mathbf{2},\mathbf{4},\mathbf{2}$). The $SU(2|1)$ superfield framework automatically implies the trigonometric realization of the superconformal symmetry and the harmonic oscillator term in the corresponding component actions. We deal with the general $\mathcal{N}=4$ superconformal algebra $D(2,1;\ensuremath{\alpha})$ and its central-extended $\ensuremath{\alpha}=0$ and $\ensuremath{\alpha}=\ensuremath{-}1$ $psu(1,1|2)\ensuremath{\bigoplus}su(2)$ descendants. We capitalize on the observation that $D(2,1;\ensuremath{\alpha})$ at $\ensuremath{\alpha}\ensuremath{\ne}0$ can be treated as a closure of its two $su(2|1)$ subalgebras, one of which defines the superisometry of the $SU(2|1)$ superspace, while the other is related to the first one through the reflection of $\ensuremath{\mu}$, the parameter of contraction to the flat $\mathcal{N}=4,d=1$ superspace. This closure property and its $\ensuremath{\alpha}=0$ analog suggest a simple criterion for the $SU(2|1)$ invariant actions to be superconformal: they should be even functions of $\ensuremath{\mu}$. We find that the superconformal actions of the multiplet ($\mathbf{2},\mathbf{4},\mathbf{2}$) exist only at $\ensuremath{\alpha}=\ensuremath{-}1,0$ and are reduced to a sum of the free sigma-model-type action and the conformal superpotential yielding, respectively, the oscillator potential $\ensuremath{\sim}{\ensuremath{\mu}}^{2}$ and the standard conformal inverse-square potential in the bosonic sector. The sigma-model action in this case can be constructed only on account of nonzero central charge in the superalgebra $su(1,1|2)$.

Quantization of the electromagnetic field in nondispersive polarizable moving media above the Cherenkov threshold

We quantize the macroscopic electromagnetic field in a system of non-dispersive polarizable bodies moving at constant velocities possibly exceeding the Cherenkov threshold. It is shown that in general the quantized system is unstable and neither has a ground state nor supports stationary states. The quantized Hamiltonian is written in terms of quantum harmonic oscillators associated with both positive and negative frequencies, such that the oscillators associated with symmetric frequencies are coupled by an interaction term that does not preserve the quantum occupation numbers. Moreover, in the linear regime the amplitudes of the fields may grow without limit provided the velocity of the moving bodies is enforced to be constant. This requires the application of an external mechanical force that effectively pumps the system.

Coupled second-quantized oscillators

Second quantization is a powerful technique for describing quantum mechanical processes in which the number of excitations of a single particle is not conserved. A textbook example of second quantization is the presentation of the simple harmonic oscillator in terms of creation and annihilation operators, which, respectively, represent addition or removal of quanta of energy from the oscillator. Our aim in this article is to bolster this textbook example. Accordingly, we explore the physics of coupled second-quantized oscillators. These explorations are phrased as exactly solvable eigenvalue problems, the mathematical structure providing a framework for the physical understanding. The examples we present can be used to enhance the discussion of second-quantized harmonic oscillators in the classroom, to make a connection to the classical physics of coupled oscillators, and to acquaint students with systems employed at the frontiers of contemporary physics research.

Scalar Charged Particle in Presence of Magnetic and Aharonov–Bohm Fields Plus Scalar–Vector Killingbeck Potentials

The generalized form of Killingbeck potential is an attractive Coulomb term plus a linear term and a harmonic oscillator term, i.e. −a/r + br + λr2, which has a useful application in quarkonium spectroscopy. The ground state energy with the corresponding wave function are obtained for any arbitrary m-state in two-dimensional Klein–Gordon equation with equal mixture of scalar–vector Killingbeck potentials in the presence of constant magnetic and singular Ahoronov–Bohm flux fields perpendicular to the plane where the interacting charged particle is confined. The analytical exact iteration method is used in our solution. We obtain the energy eigensolutions for particle and antiparticle corresponding to S(r) = V(r) and S(r) = −V(r) cases, respectively. Some special cases like the Coulomb, harmonic oscillator potentials and the nonrelativistic limits are found in presence and absence of external fields.

Single charm and beauty baryon masses in the hypercentral approach

Heavy flavour baryons containing one charm (beauty) quark with light flavour combinations are studied using the hypercentral approach. The considered potential is a combination of Coulombic, linear confining and harmonic oscillator terms. An improved form of the hyperfine interaction and isospin-dependent quark potential is introduced. The ground-state masses ( \( J^p=1/2^+\) and \( 3/2^+\) of heavy baryons are computed. Also the magnetic moments of heavy baryons with \( J^p=3/2^+\) using the effective mass of the confined quarks are computed. The obtained results are close to the ones obtained in experiments or in the other works.

9D nonadiabatic quantum dynamics through a four-state conical intersection: Investigating the homolysis of the O–O bond in anthracene-9,10-endoperoxide

The excited state dynamics of anthracene-9,10-endoperoxide is investigated using quantum wavepacket dynamics. APO is an aromatic endoperoxide which, upon excitation to S(1), shows a cleavage of the oxygen-oxygen bond, leading to rearrangement products. It was shown that the dynamics of the O-O cleavage is modulated by a four-state degeneracy [D. Mollenhauer, I. Corral, and L. González, J. Phys. Chem. Lett. 1, 1036 (2010)]. The most important mode to describe the O-O cleavage is the opening of the O-O bond. Excitation to higher excited states S(n) (n ≥ 2) leads to the release of singlet molecular oxygen. For this release, the twist of the oxygen atoms around the molecular axis is an important mode. These two degrees of freedom were employed to calculate two-dimensional potential energy surfaces for the four singlet states which become degenerate. Further modes were included in terms of harmonic oscillators. Using the multiconfigurational time-dependent Hartree method, quantum dynamic simulations were performed in up to nine degrees of freedom. Moreover, the nine branching space vectors, which prove the degeneracy to be a four-state conical intersection (4CI), were calculated and included in the wavepacket propagations. The resulting dynamics show that the 4CI is reached very fast (in less than 30 fs after excitation) and the wavepacket distributes over all states. The degree of distribution into the states is very much dependent on which modes are included in the simulation.

MASSES OF CHARM AND BEAUTY BARYONS IN THE CONSTITUENT QUARK MODEL

The masses of the ground state heavy baryons are studied using the hypercentral approach. The considered potential is a combination of Coulombic, linear confining and harmonic oscillator terms. An improved form of the hyperfine interaction and isospin dependent quark potential is introduced. By solving the Schrödinger equation for three particles system, we calculate the ground state masses of the baryons containing one, two and three heavy quarks. The obtained results are very close to the ones obtained in experiments or in the other works.