Related papers: The vibrational modes of simplicial molecules
A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the…
Amorphous solids tend to present an abundance of soft elastic modes, which diminish their transport properties, generate heterogeneities in their elastic response, and affect non-linear processes like thermal activation of plasticity. This…
The influence of multiple vibrational modes on current fluctuations in electron transport through single-molecule junctions is investigated. Our analysis is based on a generic model of a molecular junction, which comprises a single…
We demonstrate, using examples from $2$ and $3$-dimensions, a systematic method of finding all possible periodic arrangements of a given molecule or molecules such that the arrangements have the symmetry of a given space group. The…
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…
In a simple model of a continuous random walk a particle moves in one dimension with the velocity fluctuating between V and -V. If V is associated with the thermal velocity of a Brownian particle and allowed to be position dependent, the…
The vibrations of a coupled pair of isotropic silver spheres are investigated and compared with the vibrations of the single isolated spheres. Situations of both strong coupling and also weak coupling are investigated using continuum…
We review the theory of nuclear collective vibrations evolved over decades from phenomenological quasiclassical picture to sophisticated microscopic approaches. The major focus is put on the underlying microscopic mechanisms of emergent…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…
We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton through one cell of…
Circularly-polarized (CP) vibrations are the nuclear-motion analog of CP light, emerging in molecules with non-Abelian point-group symmetry that support orthogonal and degenerate vibrational normal modes. Here, we explore the optical…
Molecules constitute compact hybrid quantum optical systems that can interface photons, electronic degrees of freedom, localized mechanical vibrations and phonons. In particular, the strong vibronic interaction between electrons and nuclear…
We propose a simple mathematical model that describes a pairing-induced motion of active and passive particles in a two-dimensional system, which is motivated by our previous paper [Ishikawa et al., Phys. Rev. E \textbf{106} (2022) 024604].…
A method is developed to construct the solutions of one and many variable, linear differential equations of arbitrary order. Using this, the $N$-particle Sutherland model, with pair-wise inverse sine-square interactions among the particles,…
Two complementary methods to describe the collective motion, RPA and Wigner function moments method, are compared on an example of a simple model - harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they…
We use combinatorial group theory methods to extend the definition of a classical James-Hopf invariant to a simplicial group setting. This allow us to realize certain coalgebra idempotents at sSet -level and obtain a functorial…
A geometrical model for tri-nuclear molecules is presented. An analytical solution is obtained provided the nuclei, which are taken to be prolately deformed, are connected in line to each other. Furthermore, the tri-nuclear molecule is…
We study the spectrum of vibrational modes in metal nanoparticles with a dielectric core. Vibrational modes are excited by the rapid heating of the particle lattice that takes place after laser excitation, and can be monitored by means of…
We introduce a new `geometric realization' of an (abstract) simplicial complex, inspired by probability theory. This space (and its completion) is a metric space, which has the right (weak) homotopy type, and which can be compared with the…