Related papers: Generalization of Uncertainty Relation for Quantum…
We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
Recently two generalized nonlinear Schr\"{o}dinger equations have been proposed by Chavanis [Eur. Phys. J. Plus 132 (2017) 286] by applying Nottale's theory of scale relativity relying on a fractal space-time to describe dissipation in…
In this work, we derive a generalization of the so-called Schr\"odinger-Langevin or Kostin equation for a Brownian particle interacting with a heat bath. This generalization is based on a nonlinear interaction model providing a…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
This paper derives the stochastic homogenization for two dimensional Navier--Stokes equations with random coefficients. By means of weak convergence method and Stratonovich--Khasminskii averaging principle approach, the solution of two…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
For fluctuating currents in non-equilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…
We consider the uncertainty relation between position and momentum of a particle on $ S^1 $ (a circle). Since $ S^1 $ is compact, the uncertainty of position must be bounded. Consideration on the uncertainty of position demands delicate…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by the postulate of finite transmission speed of light and information . The theory shows…
The phenomenon of universality is one of the most striking in many-body physics. Despite having sometimes wildly different microscopic constituents, systems can nonetheless behave in precisely the same way, with only the variable names…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
A small quantum scattering system (the microsystem) is studied in interaction with a large quantum system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem…
In the spirit of Sakharov's `metric elasticity' proposal, we draw a loose analogy between general relativity and the hydrodynamic state of a quantum gas. In the `top-down' approach, we examine the various conditions which underlie the…