Related papers: A general algebraic model for molecular vibrationa…
We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…
We propose an extension of the Ellipsoidal-Statistical BGK model to account for discrete levels of vibrational energy in a rarefied polyatomic gas. This model satisfies an H-theorem and contains parameters that allow to fit almost arbitrary…
The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the…
We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the hydrogen chromophore's vibrational motion in the molecule $CF_3CHFI$. The original model has 4 degrees of freedom, three positions and one representing…
We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a…
Two-dimensional (2D) vibrational spectroscopy is a powerful means of investigating the structure and dynamics of complex molecules in condensed phases. However, even in theory, analysis of 2D spectra resulting from complex inter- and…
High-order harmonic generation by a bicircular field, which consists of two coplanar counter-rotating circularly polarized fields of frequency $r\omega$ and $s\omega$ ($r$ and $s$ are integers), is investigated for a polyatomic molecule.…
A novel approach is introduced for obtaining precise solutions of the pairing Hamiltonian for tetraquarks, which utilizes an algebraic technique in infinite dimensions. The parameters involved in the transition phase are calibrated based on…
Understanding the molecular vibrations underlying each of the unknown infrared emission (UIE) bands (such as those found at 3.3, 3.4, 3.5, 6.2, 6.9, 7.7, 11.3, 15.8, 16.4, 18.9 mm) observed in or towards astronomical objects is a vital link…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
A general algorithm for computing the quadrupole-hyperfine effects in the rovibrational spectra of polyatomic molecules is presented for the case of ammonia (NH$_3$). The method extends the general variational approach TROVE by adding the…
We study excitations of atomic vibrations in the reciprocal space for amorphous solids. There are two kinds of excitations we obtained, collective excitation and local excitation. The collective excitation is the collective vibration of…
The spontaneous symmetry breaking in a vibro-fluidized low-density granular gas in three connected compartments is investigated. When the total number of particles in the system becomes large enough, particles distribute themselves…
We study a model problem describing vibrational resonance by means of a high-order averaging technique based on so-called word series. With the tech- nique applied here, the tasks of constructing the averaged system and the associ- ated…
We investigate cooperative phenomena and superradiance for vibrational transitions in polar molecule spectroscopy when a high optical-depth (OD) sample is studied. Such cooperativity comes from the build-up of inter-particle coherence…
We introduce an improved semiclassical dynamics approach to quantum vibrational spectroscopy. In this method, a harmonic-based phase space sampling is preliminarily driven toward non-harmonic quantization by slowly switching on the actual…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
Quantum computing has recently been emerging in theoretical chemistry as a realistic avenue meant to offer computational speedup to challenging eigenproblems in the context of strongly-correlated molecular systems or extended materials.…
A numerical simulation of vibrational excitation of molecules was devised, and used to excite computational models of common molecules into a prescribed, pure, normal vibration mode in the ground electronic state, with varying, controlable…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…