Related papers: Dynamical systems with benign ghosts
We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex…
We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such…
Beings, animate or inanimate, are dynamical systems which continuously interact with the (external and /or internal) environment through the physical or physiologic interfaces of their Kantian (representational) realities. And the nature of…
In this paper, we present a collection of infinite-dimensional systems with nonholonomic constraints. In finite dimensions the two essentially different types of dynamics, nonholonomic or vakonomic ones, are known to be obtained by taking…
Dynamical descriptions and modeling of natural systems have generally focused on fixed points, with saddles and saddle-based phase-space objects such as heteroclinic channels/cycles being central concepts behind the emergence of…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
Dynamical universality is the observation that the dynamical properties of different systems might exhibit universal behavior that are independent of the system details. In this paper, we study the long-time dynamics of an one-dimensional…
Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
In this work, we study the dynamical systems analysis of phantom dark energy models considering a general potential. The stability analysis of the system shows that there is only one fixed point which could be the beginning of the universe…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…
Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is worked…
A class of non-compact billiards is introduced, namely the infinite step billiards, i.e., systems of a point particle moving freely in the domain $\Omega = \bigcup_{n\in\N} [n,n+1] \times [0,p_n]$, with elastic reflections on the boundary;…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
We obtain 21 two-dimensional natural Hamiltonian systems with sextic invariants, which are polynomial of the sixth order in momenta. Following to Bertrand, Darboux, and Drach these results of the standard brute force experiments can be…
As the first step to extend our understanding of higher-derivative theories, within the framework of analytic mechanics of point particles, we construct a ghost-free theory involving third-order time derivatives in Lagrangian. While…
We show the existence of drifting orbits for certain perturbations of non-convex Hamiltonian systems with several degrees of freedom. These orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes…
Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research as been enjoying, it is currently not known what…