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Writing / Irene Vega
An oscillator is any system (electrical, mechanical, pneumatic, etc.) that has the ability to reciprocate sustainably around a state of equilibrium. In quantum physics, the theory that governs the world on an atomic scale, a harmonic oscillator has no rest state, because the uncertainty principle prohibits a particle from having a perfectly specified position and velocity.
The professor of the area of Applied Physics at the Rey Juan Carlos University continues to develop a pioneering line of research related to the fundamentals of quantum physics, deriving fluctuations of the state of minimum energy of a harmonic oscillator from retarded potentials similar to those of electromagnetism classic. In this sense, the researcher Álvaro García López has designed a new and simple model that allows, through analytical and numerical considerations, to demonstrate the existence of quantized orbits - the only possible ones in which electrons can move and that have a value of energy given - in terms of entertaining oscillations, in which the maximum amplitude of the oscillation takes a certain value.
“Unlike the typical conservative systems of Newtonian mechanics, dissipative structures are characterized by absorbing and dissipating energy to their surroundings. In particular, we have studied a damped harmonic oscillator capable of self-excitation by delay feedback. In other words, the movement of the particle in present time is affected by its past states”, explains Professor Álvaro García López. However, unlike other previously studied systems, in this case the delay depends on the dynamic state of the particle. “The dynamics of these high-dimensional systems are terribly complex, since not only the evolution of the body in the past affects its present state, but how far into the past the effects of its memory extend depends on said present dynamic state. . This gives rise to a process in which history itself meddles in the present, creating chaos and instability. Something similar happens to human beings: depending on their current state of mind, they think more or less about their past”, highlights the professor.
More technically speaking, using a massive particle that loses energy by dissipation in a harmonic external potential and an internal potential with state-dependent retardation, it has been shown that the state of minimum energy of the oscillator loses stability through a very important phenomenon in nonlinear physics. known as the Hopf bifurcation, triggering a limit cycle type oscillation (in accordance with Liénard's theorem). As the effects of memory increase, another attractive orbit appears at a higher energy, forming a second quantized level. In addition, the system is sensitive to the initial conditions, which makes it impossible to guess at which of the two levels it will stop when the particle is externally perturbed. “Through the model developed, it has been possible to observe for the first time quasiperiodic and chaotic superposition orbits that intermittently go through degenerate orbits of the fundamental state”, points out the researcher.
It is hoped that these systems will allow us to explore other typical phenomena of quantum physics, such as particle entanglement, understood in terms of synchronization of non-linear oscillations, which causes two bodies to tremble at the same time. The results have been published in the prestigious magazine Chaos, Solitons & Fractals from the Elsevier group.