Quantum Darwinism in quantum Brownian motion.

Demystifying decoherence and the master equation of quantum Brownian motion

Relativistic Brownian Motion

We solve the problem of formulating Brownian motion in a relativistically covariant framework in 1 + 1 and 3 + 1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of invariant d'Alembert form. Treating the spacelike and timelike fluctuations separately, we show that it is essential to take into account the analytic continuation of " un...

Diffusion Equation and Complementary Schrodinger’s Equation from Brownian Motion

Diffusion Equation and classical Schrödinger Equation have been derived from Brownian motion and the quantum limits have been derived, which transform the classical Schrödinger equation in to usual quantum equation without any formal analytic continuation and waveparticle duality. These quantum limits have been shown to lead to Heisenberg uncertainty relation between position and momentum of th...

Brownian Motion: the Quantum Perspective

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

The geometry of Brownian surfaces

Motivated by Segal’s axiom of conformal field theory, we do a survey on geometrical random fields. We do a history of continuous random fields in order to arrive at a field theoretical analog of Klauder’s quantization in Hamiltonian quantum mechanic by using infinite dimensional Airault-Malliavin Brownian motion. AMS 2000 subject classifications: Primary 60G60; secondary 81T40.