Related papers: Initial Time Singularities in Non-Equilibrium Evol…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the dynamics onto that…
Using a one-dimensional minisuperspace model with a dimensionless ratio $\frac{E}{E_{Pl}}$, we study the initial singularity problem at the quantum level for the closed rainbow cosmology with a homogeneous, isotropic classical space-time…
Spinor Bose-Einstein condensates provide a unique example in which the Bogoliubov theory fails to describe the metastability associated with first-order quantum phase transitions. This problem is resolved by developing the spinor Beliaev…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
We perform the first numerical three-dimensional studies of quantum field effects in the Bosenova experiment on collapsing condensates by E. Donley et al. [Nature 415, 39 (2002)] using the exact experimental geometry. In a stochastic…
It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…
The central problem of this chapter is temporal coherence of a three-dimensional spatially homogeneous Bose-condensed gas, initially prepared at finite temperature and then evolving as an isolated interacting system. A first theoretical…
We propose an evolutional scenario of the universe which starts from quantum states with conformal invariance, passing through the inflationary era, and then makes transition to the conventional Einstein space-time. The space-time dynamics…
We study solutions to the evolution equation $u_t=\Delta u-u +\sum_{k\geqslant 1}q_ku^k$, $t>0$, in $\mathbf{R}^d$. Here the coefficients $q_k\geqslant 0$ verify $ \sum_{k\geqslant 1}q_k=1< \sum_{k\geqslant 1}kq_k<\infty$. First, we deal…
Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville's theorem…
We present an equation-free dynamic renormalization approach to the computational study of coarse-grained, self-similar dynamic behavior in multidimensional particle systems. The approach is aimed at problems for which evolution equations…
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation…
We study an initial value problem for the one-dimensional non-stationary linear Schr\"odinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems…
We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special…
In this thesis, we discuss several instances in which non-linear behaviour affects cosmological evolution in the early Universe. We begin by reviewing the standard cosmological model and the tools used to understand it theoretically and to…
In recent years, numerical simulations with Gaussian initial states have demonstrated the existence of a quantum bounce in loop quantum cosmology in various models. A key issue pertaining to the robustness of the bounce and the associated…
We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum…
A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A…
We propose a novel approach to the problem of constraining cosmological initial conditions. Within the framework of effective field theory, we classify initial conditions in terms of boundary terms added to the effective action describing…