Related papers: Exactly solvable dynamical models with a minimal l…
In this work we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal…
Using a non-perturbative classical approach, we study the dynamics of a mobile particle interacting with an infinite one-dimensional (1D) chain of harmonic oscillators. This minimal system is an effective model for many 1D transport…
Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
In this work a classical linear harmonic oscillator, evolving during a small time interval (so that simple non-linear, second order Taylor approximation of the dynamics is satisfied) and restarting (by a mechanism) in a strictly chosen…
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…
For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
In this paper, we study the effect of the minimal length on neutrino oscillation in a static magnetic field. In the framework of the generalized uncertainty principle, we reformulate the Hamiltonian for a relativistic neutrino moving in a…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…
We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation,…
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes…
We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…
In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the…
Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of non-linear field theories. With an eye towards their cosmological implications, we…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
In this paper we consider a one-dimensional Mindlin model describing linear elastic behaviour of isotropic materials with micro-structural effects. After introducing the kinetic and the potential energy, we derive a system of equations of…
It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential…
Cooling methods and particle slowers as well as accelerators are basic tools for fundamental research and applications in different fields and systems. We put forward a generic mechanism to scale the momentum of a particle, regardless of…