Related papers: Evolution to symmetry
Spontaneous symmetry-breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation, but the equilibrium states observed in nature are not. Here, we prove that when a discrete symmetry is…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
We consider a time-dependent small quantum system weakly coupled to an environnement, whose effective dynamics we address by means of a Lindblad equation. We assume the Hamiltonian part of the Lindbladian is slowly varying in time and the…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
The ghost-free theory of massive gravity with two dynamical metrics has been shown to produce viable cosmological expansion, where the late-time acceleration of the Universe is due to the finite range of the gravitational interaction rather…
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait,…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…
We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…
We consider the evolution of perturbations to a flat FRW universe that arise from a ``stiff source,'' such as a self-ordering cosmic field that forms in a global symmetry-breaking phase transition and evolves via the Kibble mechanism.…
We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from $\hat{H}_0$ to $\hat{H}_1$ in a…
In this paper, we present a model describing the time evolution of two dimensional surface waves in gravity and infinite depth. The model of six interacting modes derives from the normal form of the system describing the dynamics of surface…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…
In the Hamiltonian formulation, it is not a priori clear whether a symmetric configuration will keep its symmetry during evolution. In this paper, we give precise requirements of when this is the case and propose a symmetry restriction to…