Related papers: Smilansky-Solomyak model with a $\delta'$-interact…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
Synthetic nonconservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting…
We analyze two-dimensional Schr\"odinger operators with the potential $|xy|^p - \lambda (x^2+y^2)^{p/(p+2)}$ where $p\ge 1$ and $\lambda\ge 0$, which exhibit an abrupt change of its spectral properties at a critical value of the coupling…
We study the structure and the dynamics in the formation of irreversible gels by means of molecular dynamics simulation of a model system where the gelation transition is due to the random percolation of permanent bonds between neighboring…
We study the quantum criticality of the phase transition between the Dirac semimetal and the excitonic insulator in two dimensions. Even though the system has a semimetallic ground state, there are observable effects of excitonic pairing at…
We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…
The dynamics of an interface between the normal and superconducting phases under nonstationary external conditions is studied within the framework of the time-dependent Ginzburg-Landau equations of superconductivity, modified to include…
We address the intervention of classical-like behavior, well documented in experimental studies of strongly correlated electron systems of solids that emerges at temperatures $T$ far below the Debye temperature $T_D$. We attribute this…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
We systematically investigate the intricate interplay between short-range fermion-fermion interactions and disorder scatterings beneath the superconducting dome of noncentrosymmetric nodal-line superconductors. Employing the renormalization…
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…
We review recent theoretical progress in understanding spatially uniform $s$-wave superconductivity which arises from a fermion-fermion interaction, which is repulsive on the Matsubara axis, where it is real, but does depend on the…
Dark radiation (DR) is generally predicted in new physics scenarios that address fundamental puzzles of the Standard Model or tensions in the cosmological data. Cosmological data has the sensitivity to constrain not only the energy density…
A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasi-continuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be…
In this paper we describe the resonances of the singular perturbation of the Laplacian on the half space $\Omega =\mathbb R^3_+$ given by the self-adjoint operator named $\delta$-interaction. We will assume Dirichlet or Neumann boundary…
We investigate the cosmological dynamics of interacting dark energy models in which the interaction function is a nonlinear in terms of the energy densities. Considering explicitly the interaction between a pressureless dark matter and a…
This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at…
The construction of Dirac delta type potentials has been achieved with the use of the theory of self adjoint extensions of non-self adjoint formally Hermitian (symmetric) operators. The application of this formalism to investigate the…
We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that…
We study spectral and transport properties of one-dimensional tight-binding $\mathcal{PT}$-symmetric chains with alternating couplings. Based on the transfer matrix method, we have analytically developed the expressions for the transmission…