scholarly journals A criterion of integrability for perturbed nonresonant harmonic oscillators. ?Wick ordering? of the perturbations in classical mechanics and invariance of the frequency spectrum

1982 ◽  
Vol 87 (3) ◽  
pp. 365-383 ◽  
Author(s):  
Giovanni Gallavotti
Keyword(s):  
Frequency Spectrum ◽  
Classical Mechanics ◽  
Harmonic Oscillators ◽  
Wick Ordering

scholarly journals A note on the spectrum of the frequencies of a polar crystal lattice

1934 ◽  
Vol 147 (862) ◽  
pp. 594-599 ◽  
Keyword(s):  
Crystal Lattice ◽  
Frequency Spectrum ◽  
Elastic Waves ◽  
Characteristic Temperature ◽  
Classical Mechanics ◽  
Thermodynamical Properties ◽  
Polar Crystal ◽  
Infra Red ◽  
Theoretical Results ◽  
Polar Lattice

The following considerations deal with those vibrations of a polar crystal lattice in which the ions are moving as a whole. The frequencies of these vibrations extend from the slow macroscopic elastic waves to the infra-red region, and can be calculated by the methods of classical mechanics. (Higher frequencies occurring in optical phenomena are connected with excitations of electrons. They are not considered here.) The oldest problem, which depends on a knowledge of the lattice frequency spectrum, is that of the calculation of specific heat; other such problems are those of the calculation of thermal expansion and other thermodynamical properties of crystals. Very rough approximations (Debye’s method) are generally used, and give quite reasonable results. But a close comparison of theoretical results with experimental observations shows that the method is not completely satisfactory ( e. g. , Debye’s characteristic temperature, Θ, is not constant). The most important vibration in a binary polar lattice is that in which the vibrations of the two kinds of ions are in opposite phase—it gives rise to the infra-red absorption known as residual rays (reststrahlen). Recently the existence of secondary absorption maxima in the infra-red region has been discovered: their explanation depends on a knowledge of the whole frequency spectrum of the lattice.

scholarly journals The multi-faceted inverted harmonic oscillator: Chaos and complexity

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Arpan Bhattacharyya ◽  
Wissam Chemissany ◽  
S. Shajidul Haque ◽  
Jeff Murugan ◽  
Bin Yan
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Chaos ◽  
Classical Mechanics ◽  
Circuit Complexity ◽  
Physical Models ◽  
Harmonic Oscillators ◽  
Quantum Field ◽  
Displacement Operator ◽  
Non Gaussian ◽  
Full Quantum

The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends also to its inverted counterpart, in which the oscillator frequency is analytically continued to pure imaginary values. In this article we probe the inverted harmonic oscillator (IHO) with recently developed quantum chaos diagnostics such as the out-of-time-order correlator (OTOC) and the circuit complexity. In particular, we study the OTOC for the displacement operator of the IHO with and without a non-Gaussian cubic perturbation to explore genuine and quasi scrambling respectively. In addition, we compute the full quantum Lyapunov spectrum for the inverted oscillator, finding a paired structure among the Lyapunov exponents. We also use the Heisenberg group to compute the complexity for the time evolved displacement operator, which displays chaotic behaviour. Finally, we extended our analysis to N-inverted harmonic oscillators to study the behaviour of complexity at the different timescales encoded in dissipation, scrambling and asymptotic regimes.

scholarly journals CLASSICAL MECHANICS OF MANY PARTICLES DEFINED ON CANONICALLY DEFORMED NONRELATIVISTIC SPACETIME

2011 ◽  
Vol 26 (11) ◽  
pp. 819-832 ◽  
Author(s):  
MARCIN DASZKIEWICZ ◽  
CEZARY J. WALCZYK
Keyword(s):  
Gravitational Field ◽  
Classical Mechanics ◽  
Harmonic Oscillators ◽  
Many Particles

We provide the classical mechanics of many particles moving in canonically twist-deformed spacetime. In particular, we consider two examples of such noncommutative systems — the set of N particles moving in gravitational field as well as the system of N interacting harmonic oscillators.

Frequency Spectrum Evolution of Quasi-Optical Dielectric Resonators with Conducting Endplates

2002 ◽  
Vol 57 (12) ◽  
pp. 10 ◽  
Author(s):  
Nikolay T. Cherpak ◽  
A. A. Barannik ◽  
Yu.V. Prokopenko ◽  
Yu. F. Filippov ◽  
T.A. Smirnova
Keyword(s):  
Frequency Spectrum ◽  
Dielectric Resonators ◽  
Optical Dielectric

Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov
Keyword(s):  
Internal Energy ◽  
Hamiltonian Systems ◽  
Classical Mechanics ◽  
Motion Equation ◽  
Holonomic Constraints ◽  
Dissipative Processes ◽  
Motion Energy ◽  
Analytical Review ◽  
History Of ◽  
Material Points

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

Sound as a transverse wave

2017 ◽  
Vol 13 (1) ◽  
pp. 4522-4534
Author(s):  
Armando Tomás Canero
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Waves ◽  
Longitudinal Wave ◽  
Transverse Wave ◽  
Sound Propagation ◽  
Correspondence Principle ◽  
Classical Mechanics ◽  
Wave Model ◽  
Scientific Experiments

This paper presents sound propagation based on a transverse wave model which does not collide with the interpretation of physical events based on the longitudinal wave model, but responds to the correspondence principle and allows interpreting a significant number of scientific experiments that do not follow the longitudinal wave model. Among the problems that are solved are: the interpretation of the location of nodes and antinodes in a Kundt tube of classical mechanics, the traslation of phonons in the vacuum interparticle of quantum mechanics and gravitational waves in relativistic mechanics.

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