Anharmonic Research Articles

On the photon antibunching and amplitude squared squeezing of coherent light coupled to a periodically driven anharmonic oscillator

On the photon antibunching and amplitude squared squeezing of coherent light coupled to a periodically driven anharmonic oscillator

High energy asymptotics for the perturbed anharmonic oscillator

In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Hölder continuous perturbation and investigate how the Hölder constant can affect the eigenvalues. More precisely, we derive several first terms in the asymptotic expansion for the eigenvalues.

Heat transport in long-ranged Fermi-Pasta-Ulam-Tsingou-type models.

We perform a detailed study of heat transport in one-dimensional long-ranged anharmonic oscillator systems, such as the long-ranged Fermi-Pasta-Ulam-Tsingou model. For these systems, the long-ranged anharmonic potential decays with distance as a power law, controlled by an exponent δ≥0. For such a nonintegrable model, one of the recent results that has captured quite some attention is the puzzling ballisticlike transport observed for δ=2, reminiscent of integrable systems. Here, we first employ the reverse nonequilibrium molecular dynamics simulations to look closely at the δ=2 transport in three long-ranged models and point out a few problematic issues with this simulation method. Next, we examine the process of energy relaxation, and find that relaxation can be appreciably slow for δ=2 in some situations. We invoke the concept of nonlinear localized modes of excitation, also known as discrete breathers, and demonstrate that the slow relaxation and the ballisticlike transport properties can be consistently explained in terms of a novel depinning of the discrete breathers that makes them highly mobile at δ=2. Finally, in the presence of quartic pinning potentials we find that the long-ranged model exhibits Fourier (diffusive) transport at δ=2, as one would expect from short-ranged interacting systems with broken momentum conservation. Such a diffusive regime is not observed for harmonic pinning.

Laser-Induced Electronic and Vibronic Dynamics in the Pyrene Molecule and Its Cation.

Among polycyclic aromatic hydrocarbons, pyrene is widely used as an optical probe thanks to its peculiar ultraviolet absorption and infrared emission features. Interestingly, this molecule is also an abundant component of the interstellar medium, where it is detected via its unique spectral fingerprints. In this work, we present a comprehensive first-principles study on the electronic and vibrational response of pyrene and its cation to ultrafast, coherent pulses in resonance with their optically active excitations in the ultraviolet region. The analysis of molecular symmetries, electronic structure, and linear optical spectra is used to interpret transient absorption spectra and kinetic energy spectral densities computed for the systems excited by ultrashort laser fields. By disentangling the effects of the electronic and vibrational dynamics via ad hoc simulations with stationary and moving ions, and, in specific cases, with the aid of auxiliary model systems, we rationalize that the nuclear motion is mainly harmonic in the neutral species, while strong anharmonic oscillations emerge in the cation, driven by electronic coherence. Our results provide additional insights into the ultrafast vibronic dynamics of pyrene and related compounds and set the stage for future investigations on more complex carbon-conjugated molecules.

Thermal rectification in three-dimensional mass-graded anharmonic oscillator lattices.

In this work we study the thermal rectification efficiency, i.e., asymmetric heat flow, of a three-dimensional mass-graded anharmonic lattice of length N and width W by means of nonequilibrium molecular dynamics simulations. The obtained rectification, which is of the same order of magnitude as that of the corresponding one-dimensional lattice, saturates at low values of the aspect ratio W/N, consistent with the already known behavior of the corresponding heat fluxes of the homogeneous system under analogous conditions. The maximum rectification is obtained in the temperature range wherein no rectification could be obtained in other one-dimensional systems, as well as in the corresponding one-dimensional instance of the model studied herein.

Quantum Anharmonic Oscillators: A Truncated Matrix Approach

This study aims at implementing a truncated matrix approach based on harmonic oscillator eigenfunctions to calculate energy eigenvalues of anharmonic oscillators containing quadratic, quartic, sextic, octic, and decic anharmonicities. The accuracy of the matrix method is also tested. Using this method, the wave functions of the anharmonic oscillators were written as a linear combination of some finite number of harmonic oscillator basis states. Results showed that calculation with 100 basis states generated accurate energies of oscillators with relatively small coupling constants, with computation time less than 1 minute. Including more basis states could result in more correct digits. For instance, using 300 harmonic oscillator basis states in a simple Mathematica code in about 8 minutes, highly accurate energies of the oscillators were obtained for relatively small coupling constants, with up to 15 correct digits. Reasonable accuracy was also found for much larger coupling constants with at least three correct digits for some low lying energies of the oscillators reported in this study. Some of our results contained more correct digits than other results reported in the literature.

Investigation of the anharmonic EXAFS oscillation of distorted HCP crystals based on extending quantum anharmonic correlated Einstein model

In this work, we have expanded and developed an efficient model to calculate and analyze the extended X-ray absorption fine structure (EXAFS) oscillation of distorted hexagonal close-packed (HCP) crystals with non-ideal axial ratio c/a in the wavenumber and temperature dependencies. The analysis procedure is performed by evaluating the influence of EXAFS cumulants on the amplitude reduction and phase shift of the anharmonic EXAFS oscillation that is described in terms of the Debye–Waller factor using the cumulant expansion approach. The calculation model of the anharmonic EXAFS cumulants is expanded and developed from the correlated Einstein model using the anharmonic effective potential and the first-order perturbation. The numerical results for crystalline zinc agree well with those obtained from other theoretical methods and experiments at various temperatures. The obtained results show that the present theoretical model is necessary to analyze experimental EXAFS signals of distorted HCP crystals under the effect of non-ideal axial ratio c/a.

Moyal equation—Wigner distribution functions for anharmonic oscillators

We investigate the structure of Wigner distribution functions of energy eigenstates of quartic and sextic anharmonic oscillators. The corresponding Moyal equations are shown to be solvable, revealing new properties of Schrödinger eigenfunctions of these oscillators. In particular, they provide alternative approaches to their determination and corresponding eigenenergies, away from the conventional differential equation method, which usually relies on the not so widely known bi- and tri-confluent Heun functions.

The Stationary Optomechanical Entanglement Between an Optical Cavity Field and a Cubic Anharmonic Oscillator

The Stationary Optomechanical Entanglement Between an Optical Cavity Field and a Cubic Anharmonic Oscillator

Diagrammatic approach to classical coherent two-dimensional infrared spectroscopy

The authors develop a diagrammatic theory for the classical description of nonlinear response functions of anharmonic oscillators. Based on the theory, the authors demonstrate that the third-order response of a weakly anharmonic system can be qualitatively described using classical dynamics, clarifying the boundary of classical and purely quantum phenomena in relation to observations of molecular coherence.

Mathieu-state reordering in periodic thermodynamics

Abstract A periodically driven, moderately anharmonic oscillator constitutes an ideal model system for investigating quantum resonances, which are amenable to a quantum pendulum approximation. In the present paper, I study the quasi-stationary Floquet-state occupation probabilities which emerge when such a resonantly driven system is coupled to a heat bath. It is demonstrated that the Floquet state which is associated with the ground state of the pendulum turns into an effective ground state, carrying the highest population in the strong-driving regime. Moreover, the population of this effective Floquet ground state can even exceed that of the undriven system’s true ground state at the same bath temperature. These effects can be optimized by suitably engineering the properties of the bath.

Suppression of Superconductivity by Anharmonic Oscillations in Zn- or Ni-doped Cu0.5Tl0.5Ba2(CaMg)Cu1.5M1.5O10-δ (M=Zn, Ni) Superconductors; Evident by Magnetic Measurements

Suppression of Superconductivity by Anharmonic Oscillations in Zn- or Ni-doped Cu0.5Tl0.5Ba2(CaMg)Cu1.5M1.5O10-δ (M=Zn, Ni) Superconductors; Evident by Magnetic Measurements

Энергетические характеристики системы квантовых ангармонических осцилляторов

Энергетические характеристики системы квантовых ангармонических осцилляторов

Active Thermochemical Tables: the thermophysical and thermochemical properties of methyl, CH3, and methylene, CH2, corrected for nonrigid rotor and anharmonic oscillator effects

The thermophysical properties (isobaric heat capacity, entropy, enthalpy increment) of two prominent radicals, methyl, CH3, and methylene, CH2, were computed using the Nonrigid Rotor Anharmonic Oscillator (NRRAO) approach and compared to their RRHO counterparts, demonstrating significant differences between the results from the two approaches. Methylene presents a typical case in which the NRRAO thermophysical properties have significantly higher values than their RRHO counterparts at higher temperatures. In the case of methyl, the positive anharmonicity of the umbrella motion causes an opposite effect, and the NRRAO corrected thermophysical properties have lower values than their RRHO counterparts. The NRRAO corrected thermophysical properties, in turn, affect the resulting thermochemical properties. Two reactions important in combustion modelling were tested: the recombination of methyl radical with hydrogen atoms to form methane, and the recombination of two methyl radicals to form ethane. The related NRRAO equilibrium constants differ significantly from their RRHO analogs, and the consequences for chemical modelling are discussed. Also reported are the most current ATcT enthalpies of formation for CHn (n = 4-0) species and for C2H6, together with the tightly related sequential bond dissociation enthalpies along with the CHn series.

Effect of the non-ideal axial ratio c/a on anharmonic EXAFS oscillation of h.c.p. crystals.

The temperature and wavenumber dependence of the extended X-ray absorption fine-structure (EXAFS) oscillation of hexagonal close-packed (h.c.p.) crystals have been calculated and analyzed under the effect of the non-ideal axial ratio c/a. The anharmonic EXAFS oscillation is presented in terms of the Debye-Waller factor using the cumulant expansion approach up to the fourth order. An effective calculation model is expanded and developed from the many-body perturbation approach and correlated Debye model using the anharmonic effective potential. This potential, depending on the non-ideal axial ratio c/a, is obtained from the first-shell near-neighbor contribution approach. A suitable analysis procedure is performed by evaluating the influence of EXAFS cumulants on the phase shift and amplitude reduction of the anharmonic EXAFS oscillation. The numerical results for crystalline zinc are found to be in good agreement with those obtained from experiments and other theoretical methods at various temperatures. The obtained results show that the present theoretical model is essential and effective in improving the accuracy for analyzing the experimental data of anharmonic EXAFS signals of h.c.p. crystals with a non-ideal axial ratio c/a.

Schatten-von Neumann classes of integral operators

In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting on the kernel. As applications we establish several criteria in terms of different types of differential operators and their spectral asymptotics in different settings: compact manifolds, operators on lattices, domains in Rn of finite measure, and conditions for operators on Rn given in terms of anharmonic oscillators. We also give examples in the settings of compact sub-Riemannian manifolds, contact manifolds, strictly pseudo-convex CR manifolds, and (sub-)Laplacians on compact Lie groups.

Proposal for a Nanomechanical Qubit

Mechanical oscillators have been demonstrated with very high quality factors over a wide range of frequencies. These also couple to a wide variety of fields and forces, making them ideal as sensors. The realization of a mechanically-based quantum bit could therefore provide an important new platform for quantum computation and sensing. Here we show that by coupling one of the flexural modes of a suspended carbon nanotube to the charge states of a double quantum dot defined in the nanotube, it is possible to induce sufficient anharmonicity in the mechanical oscillator so that the coupled system can be used as a mechanical quantum bit. This can however only be achieved when the device enters the ultrastrong coupling regime. We discuss the conditions for the anharmonicity to appear, and we show that the Hamiltonian can be mapped onto an anharmonic oscillator, allowing us to work out the energy level structure and how decoherence from the quantum dot and the mechanical oscillator are inherited by the qubit. Remarkably, the dephasing due to the quantum dot is expected to be reduced by several orders of magnitude in the coupled system. We outline qubit control, readout protocols, the realization of a CNOT gate by coupling two qubits to microwave cavity, and finally how the qubit can be used as a static force quantum sensor.

Harmonic and Anharmonic Oscillator Models for Pure Vibrational Infrared Spectroscopy of Diatomic Molecules

In molecular vibrational infrared spectroscopy, absorption spectra arise from molecular vibration and correspond to transitions between the vibrational energy levels associated with a given electronic state of the molecule. The vibrational transitions, which fall in the near infrared region, are induced through the interaction of the molecular electric dipole with the electric vector of the electromagnetic radiation. The near infrared region extends roughly from 1?m to ?10?^2 ?m. The article explains the pure vibrational absorption spectra of diatomic molecules such as HCl, HBr, HI, CO, … etc. In order to explain the vibrational spectra, diatomic molecules are treated as harmonic oscillator and anharmonic oscillator. In the harmonic oscillator model, we get only one absorption band at the wavenumber value? ?_osc corresponding to frequency of oscillation?_osc while in the actual experimental data, there are many absorption bands corresponding to wave numbers slightly lesser than ? ?_osc, 2? ?_osc, 3? ?_osc, ……..The occurrence of these additional bandsis attributed to the selection rule ?v=±2, ±3, ±4, ……The additional bands are having lesser intensity and are called overtone bands.

Stable solvers for real-time Complex Langevin

This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue of runaway solution moot, but they also allow us to simulate at comparatively large Langevin time steps, leading to lower computational cost. We compare different ways of regularizing the underlying path integral and estimate the errors introduced due to the finite Langevin time steps. Based on that insight, we implement benchmark (non-)thermal simulations of the quantum anharmonic oscillator on the canonical Schwinger-Keldysh contour of short real-time extent.

Conformable fractional Bohr Hamiltonian with Bonatsos and double-well sextic potentials

Using the conformable fractional calculus, a new formulation of the Bohr Hamiltonian is introduced. The conformable fractional energy spectra of free- and two- parameters anharmonic oscillator potentials are investigated. The energy eigenvalues and wave functions are calculated utilizing the finite-difference discretization method. It is proved that the conformable fractional spectra of the free-parameter Bonatsos potentials, close completely the gaps between the classical spectra of the vibrational dynamical symmetry, the models, and the critical point symmetry. The ground effective sextic potential, which generates both the ground state and the excited states is considered to have two degenerate minima. In this case, the conformable fractional spectra of sextic potentials show a change, as a function of barrier height, from -unstable energy level sequence to the spectrum of model and simultaneously provide new features. The shape coexistence phenomena in the ground band states are identified. The energy spectrum and shape coexistence with mixing phenomena in 96Mo nucleus are discussed in the framework of the conformable fractional Bohr Hamiltonian.