Related papers: A general algebraic model for molecular vibrationa…
Using the Wigner-Heisenberg algebra for bosonic systems in connection with oscillators we find a new representation for the Virasoro algebra.
We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electron Volts. Using our recently…
We construct a generalisation of the three-dimensional Poincar\'e algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincar\'e gravity in three space-time dimensions as well as to study…
A generalized equation is constructed for a class of classical oscillators with strong anharmonicity which are not exactly solvable. Aboodh transform based homotopy perturbation method (ATHPM) is applied to get the approximate analytical…
An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of…
The role of discrete (or point-group) symmetries in alpha-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the alpha-particles. Particular attention is paid to the discrete…
The generation of high harmonics (HHG) in atomic systems by the highly non-linear response to an intense laser field is a prominent pathway to the synthesis of ever shorter laser pulses at increasingly higher photon energies. Extensions of…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
Vibrational spectroscopy is a key technique to elucidate microscopic structure and dynamics. Without the aid of theoretical approaches, it is however, often difficult to understand such spectra at a microscopic level. Ab initio molecular…
Alchemical transformations showed that perturbation theory can be applied also to changes in the atomic nuclear charges of a molecule. The alchemical path that connects two different chemical species involves the conceptualization of a…
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…
In this work, we present a proof-of-concept investigation of non-equilibrium chemical reaction dynamics at a molecule-electrode interface, driven out of equilibrium by an applied votage bias and mediated by a confined, enhanced vacuum…
We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to…
We demonstrate that the Dynamic Mode Decomposition technique can effectively reduce the amount of noise in Dispersive Fourier Transform dataset; and allow for finer quantitative analysis of the experimental data. We therefore were able to…
As pioneering experiments have shown, strong vibrational coupling between molecular vibrations and light modes in an optical cavity can significantly alter molecular properties and even affect chemical reactivity. However, the current…
The spectra (rotational, rotation-vibrational or electronic) of diatomic molecules due to transitions involving only closed-shell ($^1\Sigma$) electronic states follow very regular, simple patterns and their theoretical analysis is usually…
We derive an electron-vibration model Hamiltonian in a quantum chemical framework, and explore the extent to which such a Hamiltonian can capture key effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body operator, and…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…
We exploit the rich algebraic structure of the interacting boson model to explain the notion of partial dynamical symmetry (PDS), and present a procedure for constructing Hamiltonians with this property. We demonstrate the relevance of PDS…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…