Classical electromagnetic radiation from quantum currents and densities are calculated. For the free Schrodinger equation with no external force it's found that the classical radiation is zero to all orders of the multipole expansion. This is true of mixed or pure states for the charged particle. It is a non-trivial and surprising result. A similar result is found for the Klein-Gordon currents when the wave function consists of only positive energy solutions. For the Dirac equation it is found that radiation is suppressed at lower frequencies but is not zero at all frequencies. Implications of these results for the interpretation of quantum mechanics are discussed.
We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial (based on Kullback-Leibler distances between phase-space attractors) and temporal (Lyapunov exponent-based) complexity metrics, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. Remarkably, we find that a parametrically invariant meta-attractor emerges at a speci…
It is shown here how the semiclassical theory of electrical susceptibility can be extended to the case in which both radiation and matter are quantized. This is done specifically for the cases of linear and second order susceptibilities. The expressions derived allow to determine a set of conditions for the validity of the semiclassical approximation and predict interesting new phenomena such as photon number dependent susceptibility.
Here we present a semiclassical analysis of spontaneous and stimulated radiative emission from unmodulated and optically-modulated electron quantum wavepackets. We show that the radiative emission/absorption and corresponding deceleration/acceleration of the wavepackets depend on the controllable 'history-dependent' wavepacket size. The characteristics of the radiative interaction when a wavepacket of size (duration) is short relative to the radiation wavelength, are close to the predictions of the classical point-particle modeling. On the other hand, in the long-sized wavepacket limit, the in…
We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, $Z…
The semiclassical Kepler-Coulomb problem and the quantum-mechanical Schrödinger-Coulomb problem are compared for their predictions of quadrupole E2 transitions. The semiclassical treatment involves an extension of previous work for the electric dipole transitions (Physical Review A 71, 020501), and rates are derived for $Δ\ell= 0, \pm 2$ transitions on the basis of the multipolar properties of the emitted radiation. For the quantum case a derivation is presented within the Schrödinger framework without reference to spin. Comparison of the E2 rates shows reasonable agreement, but not as good as…
Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations
In a recent work, we provided a standardized and exact analytical formalism for computing in the semiclassical regime the radiation force experienced by a two-level atom interacting with any number of plane waves with arbitrary intensities, frequencies, phases, and propagation directions [J. Opt. Soc. Am. B \textbf{35}, 127-132 (2018)]. Here, we extend this treatment to the multilevel atom case, where degeneracy of the atomic levels is considered and polarization of light enters into play. A matrix formalism is developed to this aim.
We study the quantum cosmology of a flat Friedmann-Lemaître-Robertson-Walker universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the action, as in unimodular gravity. We study two versions of the quantum theory: the first is based on a time coordinate conjugate to the radiation/dark energy matter component, i.e., conformal time (for radiation) or unimodular time. As shown by Gryb and Thébault, this quantum theory achieves a type of singularity resolution; we illustrate this and other properties…
