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The general static solutions of the scalar field equation for the potential $V(\phi)= -1/2 M^2\phi^2 + \lambda/4 \phi^4$ are determined for a finite domain in $(1+1)$ dimensional space-time. A family of real solutions is described in terms…
We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the…
A scalar Higgs field can be repeatedly switched on and off when it couples to a classically oscillating scalar modulus field. The modulus flips the Higgs mass term between stable and tachyonic values. We study a cosmological scenario in…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as…
We establish the existence of homoclinic solutions for suitable systems of nonlocal equations whose forcing term is of gradient type. The elliptic operator under consideration is the fractional Laplacian and the potentials that we take into…
We investigate an influence of virtual particles on the classical motion of a system in Minkowski and Euclidean spaces. Our results indicate that fluctuations of fields different from the main field decelerate significantly its motion at…
In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable…
The quasi-static solutions of the matter density perturbation in various dark energy models and modified gravity models have been investigated in numerous papers. However, the oscillating solutions in those models have not been investigated…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
Li\'{e}nard-type nonlinear oscillators with linear and nonlinear damping terms exhibit diverse dynamical behavior in both the classical and quantum regimes. In this paper, we consider examples of various one-dimensional Li\'{e}nard type-I…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by…
A quasi-Gaussian quantum superposition of Ho\v{r}ava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
We study oscillatory universes within the context of Loop Quantum Cosmology. We make a comparative study of flat and positively curved universes sourced by scalar fields with either positive or negative potentials. We investigate how…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and…
According to the inflationary scenario for the very early Universe, all inhomogeneities in the Universe are of genuine quantum origin. On the other hand, looking at these inhomogeneities and measuring them, clearly no specific quantum…