Related papers: Time-metric equivalence and dimension change under…

We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific…

Refraction, interference, and diffraction serve as distinguishing features for wave-like phenomena. While they are normally associated only with a purely spatial wave-propagation pattern, analogs to interference and diffraction involving…

We study the long-range, long-time behavior of the reactive-telegraph equation and a related reactive-kinetic model. The two problems are equivalent in one spatial dimension. We point out that the reactive-telegraph equation, meant to model…

Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…

We investigate the recurrence properties of the time series of quantum mechanical expectation values, in terms of two representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence-time…

Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to…

On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum…

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…

Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…

Materials with unusual optical properties are central to advanced control of light. Yet, in nature, such materials may be exceedingly rare and often difficult to obtain. To overcome this limitation, here we introduce the concept of temporal…

Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell…

The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…

Time-reversal symmetry plays an essential role in the thermodynamic uncertainty relations, which bound the fluctuations of observables in terms of the associated dissipation. In fact, thermodynamic uncertainty relations are typically…

Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is "traded" for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a…

We demonstrate that non-convex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise…

In the event symmetric approach to quantum gravity it is assumed that the fundamental laws of physics must be invariant under exchange of any two space-time events. The fact that this symmetry if obviously not observed is attributed to the…

After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…

We propose to use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. This time redefinition acts like a microscope which blows up the inner details of seemingly instantaneous…

We settle the open question concerning the Harnack inequality for globally positive solutions to non-local in time diffusion equations by constructing a counter-example for dimensions $d\ge\beta$, where $\beta\in(0,2]$ is the order of the…

The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…