Related papers: On the Flux-Across-Surfaces Theorem
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
The Schr\"{o}dinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though…
The logarithmic superfluid theory of physical vacuum predicts that gravity is an induced phenomenon, which has a multiple-scale structure. At astronomical scales, as the distance from a gravitating center increases, gravitational potential…
A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics, describing both fluid flow and point mass trajectories. The familiar equations of energy, motion, and those of Lagrangian mechanics are…
We consider collisions of particles advected in a fluid. As already pointed out by Smoluchowski [Z. f. physik. Chemie XCII, 129-168, (1917)], macroscopic motion of the fluid can significantly enhance the frequency of collisions between the…
A well-known result by L. Markus, later extended by D. A. Neumann, states that two continuous flows on a surface are equivalent if and only if there is a surface homeomorphism preserving orbits and time directions of their separatrix…
We demonstrate the possibility of a turbulent flow of electrons in graphene in the hydrodynamic region, by calculating the corresponding turbulent probability density function. This is used to calculate the contribution of the turbulent…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Recently Bousso conjectured the entropy crossing a certain light-like hypersurface is bounded by the surface area. We point out a number of difficulties with this conjecture.
Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. Here, the energy cascade is approximated by a combined…
The quantum potential is shown to result from the presence of a subtle thermal vacuum energy distributed across the whole domain of an experimental setup. Explicitly, its form is demonstrated to be exactly identical to the heat distribution…
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are…
It is argued that any operational measure of time is inseparably bound to the presence of a periodic process in some medium. Since, as first formulated by Einstein's (1905) equation for the energy, all "particles" (neutrons, electrons,…
We consider the quantum traversal time of an incident wave packet across a potential well using the theory of quantum time of arrival (TOA)-operators. This is done by constructing the corresponding TOA-operator across a potential well via…
The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the…
Two quantum systems, each described as a random-matrix ensemble. are coupled to each other via a number of transition states. Each system is strongly coupled to a large number of channels. The average transmission probability is the product…
We derive an expression for the mean square displacement of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, $t$, and Planck's constant, $\hbar$, and allows a…
Gas permeation through nanoscale pores is ubiquitous in nature and plays an important role in a plethora of technologies. Because the pore size is typically smaller than the mean free path of gas molecules, their flow is conventionally…
The classical fluid dynamics boundary condition of no-slip suggests that variation in the wettability of a solid should not affect the flow of an adjacent liquid. However experiments and molecular dynamics simulations indicate that this is…
In a theoretical analysis, we generalise well known asymptotic results to obtain expressions for the rate of transfer of material from the surface of an arbitrary, rigid particle suspended in an open pathline flow at large P\'eclet number,…