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In this article we consider the initial value problem for the Chern-Simons-Schrodinger model in two space dimensions. This is a covariant NLS type problem which is L^2 critical. For this equation we introduce a so-called heat gauge, and…
In the standard model of cosmology, the Universe began its expansion with an anomalously low entropy, which then grew dramatically to much larger values consistent with the physical conditions at decoupling, roughly 380,000 years after the…
We consider the stochastic heat equation of the following form \frac{\partial}{\partial t}u_t(x) = (\sL u_t)(x) +b(u_t(x)) + \sigma(u_t(x))\dot{F}_t(x)\quad \text{for}t>0, x\in \R^d, where $\sL$ is the generator of a L\'evy process and…
Relative Locality is a recent approach to the quantum-gravity problem which allows to tame nonlocality effects which may rise in some models which try to describe Planck-scale physics. I here explore the effect of Relative Locality on basic…
In this paper, we study the localization phenomena in a slender cylinder composed of an incompressible hyperelastic material subjected to axial tension. We aim to construct the analytical solutions based on a three-dimensional setting and…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
The cosmological dynamics of multiple scalar/pseudoscalar fields are difficult to solve, especially when the field-space metric is curved. This presents a challenge in determining whether a given model can support cosmic acceleration,…
In this article, we investigate the asymptotic behavior of the solution to a one-dimensional stochastic heat equation with random nonlinear term generated by a stationary, ergodic random field. We extend the well-known central limit theorem…
We here discuss the emergence of Quasi Stationary States (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian Mean Field (HMF) model, numerical simulations are performed based on both the…
A theory of local temperature measurement of an interacting quantum electron system far from equilibrium via a floating thermoelectric probe is developed. It is shown that the local temperature so defined is consistent with the zeroth,…
We study the existence of stable axially and spherically symmetric plasma structures on the basis of the new nonlinear Schrodinger equation (NLSE) accounting for nonlocal electron nonlinearities. The numerical solutions of NLSE having the…
Why is thermalisation a universal phenomenon? How does a quantum system reach thermodynamical equilibrium? These questions are not new, dating even from the very birth of quantum theory and have been the subject of a renewed interest over…
At least one dimensionless physical constant (i.e., a physically observable) must change for the cosmic time to make the varying speed of light (VSL) models phenomenologically feasible. Various physical constants and quantities also should…
Quantum correlations, like entanglement, represent the characteristic trait of quantum mechanics, and pose essential issues and challenges to the interpretation of this pillar of modern physics. Although quantum correlations are largely…
We study the stochastic cubic nonlinear Schr\"odinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLS when the noise is almost space-time white…
We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration…
Nonlocal gravity (NLG), a classical extension of Einstein's theory of gravitation, has been studied mainly in linearized form. In particular, nonlinearities have thus far prevented the treatment of cosmological models in NLG. In this essay,…
In this work we examine what are the cosmological implications of allowing the geometrical curvature density to behave independently from the energy density contents. Using the full data extracted by Planck mission from CMB, combined with…
The standard model of cosmology ($\Lambda$CDM) is facing a serious crisis caused by the inconsistencies in the measurements of some fundamental cosmological parameters (Hubble constant $H_{0}$ and cosmic curvature parameter $\Omega_{k}$ for…
Experimental tests of Bell-type inequalities distinguishing between quantum mechanics and local realistic theories remain of considerable interest if performed on massive particles, for which no conclusive result has yet been obtained. Only…