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We discuss the problem of the stability of the isotropy of the universe in the space of ever-expanding spatially homogeneous universes with a compact spatial topology. The anisotropic modes which prevent isotropy being asymptotically stable…
An Anderson impurity in a Hubbard model on chains with finite length is studied using the density-matrix renormalization group (DMRG) technique. In the first place, we analyzed how the reduction of electron density from half-filling to…
The effects of impurities in spin-1/2 Heisenberg chains are recently experiencing a renewed interest due to experimental realizations in solid state systems and ultra-cold gases. The impurities effectively cut the chains into finite…
We prove compactness and hence existence for solutions to a class of non linear transport equations. The corresponding models combine the features of linear transport equations and scalar conservation laws. We introduce a new method which…
Zero modes, understood here as degrees of freedom with vanishing confining frequency, play a central role in the nonequilibrium dynamics of bosonic systems. In Gaussian models, however, they lead to an unbounded, logarithmic growth of…
Flat band (FB) systems, featuring dispersionless energy bands, have garnered significant interest due to their compact localized states (CLSs). However, a detailed account on how local impurities affect the physical properties of…
In this work, we investigate probe scalar field models preserving covariance on fixed, static background geometries that present hyperscaling violation properties. We develop a first-order framework that rises from restrictions on the…
In this paper, the positive solutions of a diffusive competition model with saturation are mainly discussed. Under certain conditions, the stability and multiplicities of coexistence states are analyzed. And by using the topological degree…
Two integrable spin ladder systems with different types of impurities are proposed. The impurities are introduced in such a way that the integrability of the models is not violated. The models are solved exactly and the Bethe ansatz…
Topological insulators are typically characterized by particularly stable properties, such as global invariants, and can be identified by probing their robust surface states. A recently discovered novel form of band topology, delicate…
We present the first complete (i.e., ambiguity-free) derivation of the equations of motion of two non-spinning compact objects up to the 4PN order, based on the Fokker action of point particles in harmonic coordinates. The last ambiguity…
A Kondo model for three spin-one-half impurities placed at the vertices of an equilateral triangle is studied using the numerical renormalization-group method. The impurity spins can form two frustrated doublets which, because of the…
We find analytical vacuum stability or bounded below conditions for general scalar potentials of a few fields. After a brief review of copositivity we go beyond it. We discuss the vacuum stability conditions of the general potential of two…
We show that the elasticity Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…
A scalar potential of the form $\lambda_{ab} \phi_a^2 \phi_b^2$ is bounded from below if its matrix of quartic couplings $\lambda_{ab}$ is copositive -- positive on non-negative vectors. Scalar potentials of this form occur naturally for…
Local configurational symmetry in lattice structures may give rise to stationary, compact solutions, even in the absence of disorder and nonlinearity. These compact solutions are related to the existence of flat dispersion curves (bands).…
The electronic structure of cuprate superconductors is studied within the kinetic energy driven superconducting mechanism in the presence of the out-of-plane impurities. With increasing the impurity concentration, although both…
The effect of impurities in a two-dimensional lattice of coupled nonlinear chaotic oscillators and their ability to control the dynamical behavior of the system are studied. We show that a single impurity can produce synchronized…
In a number of systems, including certain semiconductors and unconventional superconductors, the effective density of states varies near the Fermi energy like $|E-E_F|^r$. The behavior of dilute magnetic impurities in such systems is…
We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account…