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The classical and quantum dynamics of the Friedmann-Robertson-Walker Universe with massless scalar and massive fermion matter field as a source is discussed in the framework of the Dirac generalized Hamiltonian formalism. The Hamiltonian…
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely…
We develop a semi-classical approximation to electron spin resonance in quantum spin systems, based on the rotor or non-linear sigma model. The classical time evolution is studied using molec- ular dynamics while random initial conditions…
We investigate the dynamics of a strongly interacting spin system that is motivated by current experimental realizations of strongly interacting Rydberg gases in lattices. In particular we are interested in the temporal evolution of…
The evolution of spatially homogeneous and isotropic cosmological models containing a perfect fluid with equation of state p=w\rho\ and a cosmological constant \Lambda\ is investigated for arbitrary combinations of w and \Lambda, using…
Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…
Using the dynamical systems approach together with the cosmographic parameters, we present a model-independent dynamical system formulation for cosmology in f(R) gravity. The formulation is model-independent in the sense that one needs to…
We consider the long time semiclassical evolution for the linear Schr\"odinger equation. We show that, in the case of chaotic underlying classical dynamics and for times up to $\hbar^{-2+\epsilon},\ \epsilon>0$, the symbol of a propagated…
The intention of our paper is to provide a pedagogical application of geometric algebra to a particularly well-investigated system: We formulate the geometric and dynamical properties of Friedmann-Robertson-Walker spacetimes within the…
Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the…
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
We investigate the dynamics and the phase-space evolution for the scalar nonmetricity cosmology with a Chameleon mechanism. In particular, we consider a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry and within the…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
Specific internal self-interactions in gaseous cosmic fluids are shown to give rise to effective negative pressures which may violate the strong energy condition. On this basis we discuss the transition from an initial de Sitter phase to a…
We investigate how the quantum dynamics of gravitational models depends on the internal clock employed in quantisation. Our previous result on the quantum Friedmann-Lemaitre model demonstrates that almost all physical predictions from the…
A semiclassical mechanism which suppresses the weak anisotropies of an inhomogeneous cosmological model is developed. In particular, a wave function of this Universe having a meaningful probabilistic interpretation is obtained that is in…