Related papers: Nonlinear Constraints from Non-Abelian Internal Sy…
We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified (2+1)-dimensional dissipative nonlinear parabolic differential equation, given field moduli over three…
Continuous symmetries lead to universal slow relaxation of correlation functions in quantum many-body systems. In this work, we study how local symmetry-breaking impurities affect the dynamics of these correlation functions using Brownian…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
How might systematic left-right (L/R) asymmetry of the body plan originate in multicellular animals (and plants)? Somehow, the microscopic handedness of biological molecules must be brought up to macroscopic scales. Basic symmetry…
Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to…
We consider nonequilibrium time evolution in quantum spin chains after a global quench. Usually a nonequilibium quantum many-body system locally relaxes to a (generalised) Gibbs ensemble built from conserved operators with quasilocal…
Gravity in nonlinear and dynamical regimes underpins spectacular astrophysical phenomena and observable consequences, from the early universe to black hole collisions. In these extreme environments, inverse energy cascades - mediated by…
There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, full controllability is not possible, and controllability has…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
The mean-field thermodynamic limit is studied for a class of isolated Newtonian N-body systems whose Hamiltonian admits several invariants of motion. It is shown that the macrostates of individual members of a statistical equilibrium…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
In quantum many-body systems with kinetically constrained dynamics, the Hilbert space can split into exponentially many disconnected subsectors, a phenomenon known as Hilbert-space fragmentation. We study the interplay of such fragmentation…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…
The dynamics of irreversible relaxation of non-equilibrium macroscopic systems is discussed. Arguments are developed showing that the general process is supported by two independent successive mechanisms. One is mixing and it follows pure…
A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For…
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 consider the evolution of a network of strings in an expanding universe, allowing for the formation of junctions between strings of different tensions. By explicitly including, in the velocity-dependent evolution equations for the…