Related papers: Peacock's Principle as a Conservative Strategy
It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…
In this paper, we study four-strategy conservative replicator dynamics induced by constant payoff matrices. We establish necessary and sufficient conditions for permanence to occur by associating the payoff matrix with its digraph,…
Liouville's theorem -- the preservation of phase-space volume -- is often presented as a corollary of Hamilton's canonical equations. Here we adopt an ensemble-first viewpoint in which the starting point is local probability conservation on…
We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set…
We prove that the recently developed semiexplicit symplectic integrators for non-separable Hamiltonian systems preserve any linear and quadratic invariants possessed by the Hamiltonian systems. This is in addition to being symmetric and…
150 years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex numbers in both classical and…
We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation $AHA^\dagger$ that leaves the Hamiltonian $H$…
We give a proof of the KAM theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is…
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…
A common way of stating the non-cloning theorem -- one of distinguishing characteristics of quantum theory -- is that one cannot make a copy of an arbitrary unknown quantum state. Even though this theorem is an important part of the ongoing…
A self-consistent quadratic theory is presented to account for nonlinear contributions in quantum dynamics. Evolution equations are shown to depend on higher-order gradients of the Hamiltonian, which are incorporated via their equations of…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important…
We present a cut elimination argument that witnesses the conservativity of the compositional axioms for truth (without the extended induction axiom) over any theory interpreting a weak subsystem of arithmetic. In doing so we also fix a…
The modified Hunter--Saxton equation models the propagation of short capillary-gravity waves. As it involves a mixed derivative, its initial value problem on the periodic domain is much more complicated than the standard evolutionary…
A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws…
Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode…
The Boris algorithm for integrating charged particle trajectories in electric and magnetic fields is popular due to its simple implementation, rapid iteration, and observed long-term numerical fidelity. The underlying cause of this…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
The rotation-two-component Camassa--Holm system, which possesses strongly nonlinear coupled terms and high-order differential terms, tends to have continuous nonsmooth solitary wave solutions, such as peakons, stumpons, composite waves and…