Shortly after Schrödinger’s wave mechanics in terms of complex wave functions was published, Madelung formulated this theory in terms of two real hydrodynamic-like equations. This version is also the formal basis of Bohmian mechanics, albe...
For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency
In a recent paper, we have shown how in Madelung’s hydrodynamic formulation of quantum mechanics, the uncertainties are related to the phase and amplitude of the complex wave function. Now we include a dissipative environment via a nonlinear mo...
Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled....
For time dependent Hamiltonians like the parametric oscillator with time-dependent frequency, the energy is no longer a constant of motion. Nevertheless, in 1880, Ermakov found a dynamical invariant for this system using the corresponding Newtonian e...
In this paper, we introduce (at least formally) a diffusion effect that is based on an axiom postulated by Werner Heisenberg in the early days of quantum mechanics. His statement was that—in quantum mechanics—kinematical quantities such a...
Just as non-relativistic fluids, oftentimes we find relativistic fluids in situations where random fluctuations cannot be ignored, with thermal and turbulent fluctuations being the most relevant examples. Because of the theory’s inherent nonlin...
Symmetries play paramount roles in dynamics of physical systems. All theories of quantum physics and microworld including the fundamental Standard Model are constructed on the basis of symmetry principles. In classical physics, the importance and wei...
This article begins with an interdisciplinary review of a hydrodynamic approach to understanding the origins and nature of macroscopic quantum phenomena in high-temperature superconductivity, superfluidity, turbulence and biological systems. Building...
Complex systems of classical physics in certain situations are characterized by intensive fluctuations of the quantities governing their dynamics. These include important phenomena such as (continuous) second-order phase transitions, fully developed...
In this paper, we review and compare the stochastic quantum mechanics of Nelson and the scale relativity theory of Nottale. We consider both nonrelativistic and relativistic frameworks and include the electromagnetic field. These theories propose a d...
It is shown that lattice kinetic theory based on short-lived quasiparticles proves very effective in simulating the complex dynamics of strongly interacting fluids (SIF). In particular, it is pointed out that the shear viscosity of lattice fluids is...
Feraheme, is a recently FDA-cleared superparamagnetic iron oxide nanoparticle (SPION)-based MRI contrast agent that is also employed in the treatment of iron deficiency anemia. Feraheme nanoparticles have a hydrodynamic diameter of 30 nm and consist...
Strong magnetic fields impact quantum-chromodynamics (QCD) properties in several situations; examples include the early universe, magnetars, and heavy-ion collisions. These examples share a common trait—time evolution. A prominent QCD property impact...
Research shows that neurodegenerative processes do not develop from a single “broken” biochemistry process; rather, they develop when a complex multi-physics environment gradually loses its ability to stabilize the neuron via a collective...
We recently proposed the use of engineered irregularly shaped zinc oxide nanoparticles (ZnO NPs) coated with oleylamine (OAm), as photosynthetic biostimulants, to enhance crop yield. In the current research, we tested newly engineered rod-shaped ZnO...