arXiv subjects

Alexandre Gondran

Publications and source records attributed to Alexandre Gondran.

24 records · Page 2Linked to original sources

arXiv2009

Energy flow lines and the spot of Poisson-Arago

We show how energy flow lines answer the question about diffraction phenomena presented in 1818 by the French Academy: "deduce by mathematical induction, the movements of the rays during their crossing near the bodies". This provides a complementary answer to Fresnel's wave theory of light. A numerical simulation of these energy flow lines proves that they can reach the bright spot of Poisson-Arago in the shadow center of a circular opaque disc. For a monochromatic wave in vacuum, these energy flow lines correspond to the diffracted rays of Newton's Opticks.

physics.optics↗

arXiv2009

A New Causal Interpretation of EPR-B Experiment

In this paper we study a two-step version of EPR-B experiment, the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time enables us to refute the classic "impossibility" to decompose a pair of entangled atoms into two distinct states, one for each atom. We propose a new causal interpretation of the EPR-B experiment where each atom has a position and a spin while the singlet wave function verifies the two-body Pauli equation. In conclusion we suggest a physical explanation of non-local influences, compatible with Einstein's point of view on relativity.

quant-ph↗

arXiv2007

Numerical Simulation of the Double Slit Interference with Ultracold Atoms

We present a numerical simulation of the double slit interference experiment realized by F. Shimizu, K. Shimizu and H. Takuma with ultracold atoms. We show how the Feynman path integral method enables the calculation of the time-dependent wave function. Because the evolution of the probability density of the wave packet just after it exits the slits raises the issue of the interpreting the wave/particle dualism, we also simulate trajectories in the de Broglie-Bohm interpretation.

quant-ph↗

arXiv2006

A Crucial Experiment To Test The Broglie-Bohm Trajectories For Indistinguishable Particles

The standard quantum theory has not taken into account the size of quantum particles, the latter being implicitly treated as material points. The recent interference experiments of Zeilinger [3] with large molecules like fullerenes and the thought experiments of Bozic et al [7] with asymmetrical Young slits make it possible today to take into account the particle size. We present here a complete study of this phenomenon where our simulations show differences between the particles density after the slits and the modulus square of the wave function. Then we propose a crucial experiment that allows us to reconsider the wave-particle duality and to test the existence of the Broglie-Bohm trajectories for indistinguishable particles.

quant-ph↗

arXiv2005

A complete analysis of the Stern-Gerlach experiment using Pauli spinors

The Stern-Gerlach experiment is the fundamental experiment in order to exhibit the quantization of spin and understand the measurement problem in quantum mechanics. However, although the Stern-Gerlach experiment plays an essential role in the teaching of quantum mechanics, no complete analysis of this experiment using Pauli spinors is presented in the pedagogical literature. This paper presents such an analysis and develops implications for the theory of quantum measurement. We first propose an analytic expression of both the wave function and the probability density in the Stern-Gerlach experiment. Our explicit solution is obtained via a complete integration of the Pauli equation over time and space. The probability density evolution describes a slipping of the wave packet into two separate packets due to the measurement device, but it cannot account for impacts. We therefore calculate the de Broglie-Bohm trajectories, which not only explain impacts naturally, but also accounts for the spin quantization following the magnetic field gradient. It is then possible to propose a clear explanation of measurement effects in the Stern-Gerlach experiment.

quant-ph↗

arXiv2003

Revisiting the Schrodinger probability current

We revisit the definition of the probability current for the Schrodinger equation. First, we prove that the Dirac probability currents of stationary wave functions of the hydrogen atom and of the isotrop harmonic oscillator are not nil and correspond to a circular rotation of the probability. Then, we recall how it is necessary to add to classical Pauli and Schrodinger currents, an additional spin-dependant current, the Gordan current. Consequently, we get a circular probability current in the Schrodinger approximation for the hydrogen atom and the isotrop harmonic oscillator.

quant-ph↗