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Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the…
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 classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the…
For zero energy, $E=0$, we derive exact, classical and quantum solutions for {\em all} power-law oscillators with potentials $V(r)=-\gamma/r^\nu$, $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions…
A new thermodynamic analysis is presented for the intimate connections between blackbody radiation and zero-point radiation within classical physics. First, using the thermodynamic behavior of an oscillator under an adiabatic change of…
A nonlinear oscillator with an abruptly inhomogeneous restoring force driven by an uniform oscillating force exhibits stochastic properties under specific resonance conditions. This behaviour elucidates the elementary mechanism of the…
We consider the global thermal state of classical and quantum harmonic oscillators that interact with a reservoir. Ohmic damping of the oscillator can be exactly treated with a 1D scalar field reservoir, whereas general non-Ohmic damping is…
The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and…
It is proved that a classical (respec. quantum) system consisting of a particle in a constant magnetic field is canonically (respec. unitarily) equivalent to a 2-dimensional harmonic oscillator plus a free particle. It is also shown that…
Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is…
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
The classical and quantum oscillator model on Lie-algebraically deformed nonrelativistic space-time is introduced and analyzed. The corresponding equations of motions are studied using mostly numerical methods. The time-dependent energy…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
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…
The initial states which minimize the predictability loss for a damped harmonic oscillator are identified as quasi-free states with a symmetry dictated by the environment's diffusion coefficients. For an isotropic diffusion in phase space,…
In this work we further advance theoretical investigation of radiation by the electric dipole under the assumption that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a…
This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has the natural frequency $\omega_j$ and is described by the Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}\omega_j^2x_j^2$. The…
We report on the generic classical electric circuit modeling that describes standard single-tone microwave optomechanics. Based on a parallel RLC circuit in which a mechanical oscillator acts as a movable capacitor, derivations of…