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In this paper we study the existence and the instability of standing waves with prescribed $L^2$-norm for a class of Schr\"odinger-Poisson-Slater equations in $\R^{3}$ %orbitally stable standing waves with arbitray charge for the following…
The basic concepts of classical mechanics are given in the operator form. Then, the hybrid systems approach, with the operator formulation of both quantum and classical sector, is applied to the case of an ideal nonselective measurement. It…
The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordstr\"om domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational…
Spontaneously symmetry-broken (SSB) phases are locally ordered states of matter characterizing a large variety of physical systems. Because of their specific ordering, their presence is usually witnessed by means of local order parameters.…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
Ever since we have been in the possession of quantum theories without observers, such as Bohmian mechanics or the Ghirardi-Rimini-Weber (GRW) theory of spontaneous wave function collapse, a major challenge in the foundations of quantum…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…
The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual…
We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the…
We devise a stochastic Hamiltonian formulation of the water wave problem. This stochastic representation is built within the framework of the modelling under location uncertainty. Starting from restriction to the free surface of the general…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just…
From classical stochastic equations of motion we derive the quantum Schr\"odinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function $\phi$ are proportional to the coordinates and…
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the…
The change with time of the system consisting of the quantum object and the macroscopic measuring instrument is described on the base of the uniform dynamic law, which is suitable both evolution and reduction processes description. It is…
We study the focusing inhomogeneous nonlinear Schr\"odinger equation $$ i\partial_t u + \Delta u = -|x|^b |u|^{p-1}u ,\quad (t,x)\in (0,\infty)\times\mathbb{R}^N, $$ with $b>0$ and $p>1$. Due to the spatial growth of the nonlinearity,…
Schroedinger's wave function shows many aspects of a state of incomplete knowledge or information ("bit"): (1) it is usually defined on a space of classical configurations, (2) its generic entanglement is, therefore, analogous to…
A new approach to the stochastic theory of turbulence is suggested. The coloured noise that is present in the stochastic Navier-Stokes equation is generated from the delta-correlated noise allowing us to avoid the nonlocal field theory as…
Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…