Related papers: Time-dependent local-to-normal mode transition in …
We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT)…
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for…
This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a…
The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by using the frequency-dependent response function. It is shown how the source terms…
We report a quantum mechanical method for calculating the momentum distributions of constituent atoms of polyatomic molecules in rotational-vibrational eigenstates. Application of the present theory to triatomic molecules in the…
Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
We investigate transient nonlinear localization, namely the self-excitation of energy bursts in an atomic lattice at finite temperature. As a basic model we consider the diatomic Lennard-Jones chain. Numerical simulations suggest that the…
Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical…
General conditions are formulated that allow to determine which quantum phase transitions in itinerant electron systems can be described by a local Landau-Ginzburg-Wilson or LGW theory solely in terms of the order parameter. A crucial…
The correlation diagram of the vibrational energy spectra associated with the stretching modes of triatomic molecules such as CO$_2$ and H$_2$O is analyzed by means of two interacting Morse oscillators. By considering a linear dependence of…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
The cyclic motion of particles in a periodic potential under the influence of a constant external force is analyzed in an atom optical approach based on Landau-Zener transitions between two resonant states. The resulting complex picture of…
The change of the vibrational energy within a molecule after collisions with another molecule plays an essential role in the evolution of molecular internal energy distributions, which is also the limiting process in the relaxation of the…
In this paper, we present a detailed analysis of normal modes based on the Boltzmann equation within the mutilated relaxation time approximation (RTA). Using this linearized effective kinetic description, our analysis encompasses a complete…
We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy…
A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local "quasi-equilibrium" state a non-hydrodynamic dynamical…
The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds…
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…