Related papers: Evolution to symmetry
We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with…
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…
The time evolution of a class of completely integrable discrete Lotka-Volterra s ystem is shown not unique but have two different ways chosen randomly at every s tep of generation. This uncertainty is consistent with the existence of…
It has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic material freely through massive horizontal gene transfer…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
We study the quantum dynamics of a time reparametrization invariant system with a vanishing Hamiltonian. The evolution of the physical degrees of freedom of the system is described, both at the classical and at the quantum level, in…
We study the space-time evolution of the fine structure constant, $\alpha$, inside evolving spherical overdensities in a lambda-CDM Friedmann universe using the spherical infall model. We show that its value inside virialised regions will…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…
Any positive-energy state of a free Dirac particle that is initially highly-localized, evolves in time by spreading at speeds close to the speed of light. This general phenomenon is explained by the fact that the Dirac evolution can be…
A time dependent variational approach is considered to derive the equations of movement for the $\lambda \phi^4$ model. The temporal evolution of the model is performed numerically in the frame of the Gaussian approximation in a lattice of…
The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…
We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a…
The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group…
Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Tidal forces acting on galaxies in clusters lead to a strong dynamical evolution. In order to quantify the amount of evolution, I run self-consistent N-body simulations of disk galaxies for a variety of models in the hierarchically forming…
A new class of random quantum--dynamical systems in continuous space is introduced and studied in some detail. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic,…
We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total…