Related papers: Cyclically deformed defects and topological mass c…
We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically…
We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to dimension…
The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by…
Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and accessing information encoded in quantum-mechanical systems. Among the informationally complete sets of quantum measurements, the…
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…
This paper presents a new approach to distributed nonlinear control for formation acquisition and maintenance, inspired by recent results on cyclic topologies and based on tools from contraction theory. First, simple nonlinear control laws…
An innovative technique, called conversion, is introduced to model circumferential cracks in thin cylindrical shells. The semi-analytical finite element method is applied to investigate the modal deformation of the cylinder. An element…
We develop a unified mathematical theory of defect condensations for topological orders in all dimensions based on higher categories, higher algebras and higher representations. A k-codimensional topological defect $A$ in an n+1D…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
In this paper an approach to generate multi-dimensionally consistent $N$-component systems is proposed. The approach starts from scalar multi-dimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained…
Disordered magnets, martensitic mixed crystals, and glassy solids can be irreversibly deformed by subjecting them to external deformation. The deformation produces a smooth, reversible response punctuated by abrupt relaxation "glitches".…
In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay…
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
Dynamical chiral symmetry breaking is described within the linear sigma model of QCD coupled to quarks. The main technical tool used for this intrinsically non--perturbative problem is an exact renormalization group equation for the quantum…
A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as…
We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The…
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they…
The deformed energy method has shown to be a good option for dimensional synthesis of mechanisms. In this paper the introduction of some new features to such approach is proposed. First, constraints fixing dimensions of certain links are…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
Cyclic models of the universe have the advantage of avoiding initial conditions problems related to postulating any sort of beginning in time. To date, the only known viable examples of cyclic models have been ekpyrotic. In this paper, we…