Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

On the doubly anharmonic oscillator in an elastic environment in the presence of a point-like defect

R. L. L. Vitória, Kleber Anderson T. da Silva

Published Apr 1, 2023• 10 citations
Publisher

Abstract

Abstract We have investigated a doubly anharmonic oscillator in an elastic medium characterized by the presence of a point-like defect, where we obtain analytically your solution of bound states. We show that it is not possible to obtain a unique expression for the energy profile of the quantum system, but rather an expression corresponding to each radial mode of the system. Furthermore, an interesting quantum effect is presented: the three parameters that characterize the doubly anharmonic oscillator are quantized, that is, they depend on the quantum numbers of the system.

DOI
10.1209/0295-5075/accb0a

Related papers

Lennard-Jones Oscillations in an Elastic Environment

José E. S. Bezerra, R. L. L. Vitória, F. M. O. Moucherek

In this purely analytical analysis, we have investigated the effects of a point-like defect in a continuous medium on a diatomic molecule under the influence of small oscillations arising from the Lennard-Jones potential. In the search for bound-state solutions, we have shown that the allowed values for the lowest energy state of the molecule are influenced by the presence of the defect. Furthermore, another quantum effect was observed: the stability radial point of the diatomic molecule depends on the system’s quantum numbers; it is quantized.

AppliedMath•Sep 30, 2025•1 citation

Analytic ground state energy and wave function of a quantum system in an exponential-form anharmonic interaction potential

Israel B Babalola, Oluwole Emmanuel Oyewande, Idowu H Latok +1 more

Abstract An anharmonic oscillator with a perturbed quadratic potential which is coupled with an exponential term is being investigated in this paper by isolating an anharmonic oscillator interaction potential from the actual interaction experienced by the quantum system studied, and using standard perturbative techniques. The anharmonic potential considered is of interest because of its usefulness in the study of non-centrosymmetric materials which have applications in piezoelectricity. The ground state energy eigenvalue and its associated eigenstates were calculated for the quantum system using an analytical approach. Results obtained are compared to those of quantised harmonic oscillator to show the effect of the perturbation.

IOP Conference Series Earth and Environmental Science•Feb 1, 2021•0 citations

An analysis of states in the phase space: the anharmonic oscillator

Sebastiano Tosto

The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the properties of quantum systems exploiting the uncertainty principle only. For clarity the anharmonic oscillator is described having in mind the lattice oscillations of atoms/ions, yet quantum formalism of the model and approach have general character and can be extended to any oscillating system. The results show that the harmonic energy levels split into a complex system of energy levels dependent upon the number of anharmonic terms that characterize the oscillator.

arXiv:1105.3615•May 18, 2011•2 citations

Wigner function for a driven anharmonic oscillator

Karen V. Kheruntsyan

We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state regime. This provides explicit phase-space images of the resulting state of the cavity mode, and allows us to understand how the quantum interference is built up into it. The photon number probability distribution is calculated and analysed as well. We monitor the transition from the semiclassical to extreme quantum regime of operation, and identify qualitative changes, where the conventional characteristics of the model, such as bistability or turning points, become meaningless.

Journal of Optics B Quantum and Semiclassical Optics•Jan 1, 1999•47 citations

Energy features of a loaded quantum anharmonic oscillator

V. L. Gilyarov, A. I. Slutsker

A quantum anharmonic oscillator in the ground state has been considered under the conditions of loading with an external force. The wave functions have been calculated for different forces, and the eigenvalues of the energy of the system have been determined as a function of the load. It has been established that the zero-point energy of the oscillator varies linearly with a variation in the force (decreases under tension and increases under compression) and that the average kinetic and potential components of the energy are also characterized by linear variations.

Physics of the Solid State•Mar 1, 2010•7 citations

Dynamics and spectra of open quantum systems coupled to anharmonic environments

Kian Damezin, Brendon W. Lovett, Erik M. Gauger +1 more

In open quantum systems, the environment is typically modelled as a collection of harmonic oscillators, whereas realistic environments often exhibit unique non-Markovian effects due to the anharmonicity of the environment. Here we present a framework for modelling anharmonic environments in open quantum systems numerically exactly, in which, via a matching criterion, we map the anharmonic environment onto an effective harmonic one. This results in an effective spectral density that is a collection of shifted bare spectra arising from the non-equidistant energy gaps of the anharmonic environment, along with a unique zero-frequency term that effectively acts as static disorder on the system. This is due to the non-zero variance of the diagonal of the bath coupling operator. In tandem, we develop a framework for investigating the effects of environments comprising a few damped anharmonic modes where the matching criterion fails to work due to the non-Gaussianity of the environment. For both continuous and discrete damped anharmonic environments, this work investigates their unique influence on the system's dynamics, including enhanced non-Markovianity compared to a harmonic approximation, novel effects in the absorption spectrum, and the potential for anharmonic environments to enhance energy transport.

quant-pharXiv:2608.27163•Aug 28, 2026•0 citations
Abstract We have investigated a doubly anharmonic oscillator in an elastic medium characterized by the presence of a point-like defect, where we obtain analytically your solution of bound states. We show that it is not possible to obtain a unique expression for the energy profile of the quantum system, but rather an expression corresponding to each radial mode of the system. Furthermore, an interesting quantum effect is presented: the three parameters that characterize the doubly anharmonic oscillator are quantized, that is, they depend on the quantum numbers of the system.
In this purely analytical analysis, we have investigated the effects of a point-like defect in a continuous medium on a diatomic molecule under the influence of small oscillations arising from the Lennard-Jones potential. In the search for bound-state solutions, we have shown that the allowed values for the lowest energy state of the molecule are influenced by the presence of the defect. Furthermore, another quantum effect was observed: the stability radial point of the diatomic molecule depends on the system’s quantum numbers; it is quantized.
Abstract An anharmonic oscillator with a perturbed quadratic potential which is coupled with an exponential term is being investigated in this paper by isolating an anharmonic oscillator interaction potential from the actual interaction experienced by the quantum system studied, and using standard perturbative techniques. The anharmonic potential considered is of interest because of its usefulness in the study of non-centrosymmetric materials which have applications in piezoelectricity. The ground state energy eigenvalue and its associated eigenstates were calculated for the quantum system using an analytical approach. Results obtained are compared to those of quantised harmonic oscillator to show the effect of the perturbation.
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the properties of quantum systems exploiting the uncertainty principle only. For clarity the anharmonic oscillator is described having in mind the lattice oscillations of atoms/ions, yet quantum formalism of the model and approach have general character and can be extended to any oscillating system. The results show that the harmonic energy levels split into a complex system of energy levels dependent upon the number of anharmonic terms that characterize the oscillator.
We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state regime. This provides explicit phase-space images of the resulting state of the cavity mode, and allows us to understand how the quantum interference is built up into it. The photon number probability distribution is calculated and analysed as well. We monitor the transition from the semiclassical to extreme quantum regime of operation, and identify qualitative changes, where the conventional characteristics of the model, such as bistability or turning points, become meaningless.
A quantum anharmonic oscillator in the ground state has been considered under the conditions of loading with an external force. The wave functions have been calculated for different forces, and the eigenvalues of the energy of the system have been determined as a function of the load. It has been established that the zero-point energy of the oscillator varies linearly with a variation in the force (decreases under tension and increases under compression) and that the average kinetic and potential components of the energy are also characterized by linear variations.
In open quantum systems, the environment is typically modelled as a collection of harmonic oscillators, whereas realistic environments often exhibit unique non-Markovian effects due to the anharmonicity of the environment. Here we present a framework for modelling anharmonic environments in open quantum systems numerically exactly, in which, via a matching criterion, we map the anharmonic environment onto an effective harmonic one. This results in an effective spectral density that is a collection of shifted bare spectra arising from the non-equidistant energy gaps of the anharmonic environment, along with a unique zero-frequency term that effectively acts as static disorder on the system. This is due to the non-zero variance of the diagonal of the bath coupling operator. In tandem, we develop a framework for investigating the effects of environments comprising a few damped anharmonic modes where the matching criterion fails to work due to the non-Gaussianity of the environment. For both continuous and discrete damped anharmonic environments, this work investigates their unique influence on the system's dynamics, including enhanced non-Markovianity compared to a harmonic approximation, novel effects in the absorption spectrum, and the potential for anharmonic environments to enhance energy transport.