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We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition (QPT) where the critical point exhibits an emergent enhanced symmetry. Such a transition…
Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…
We assume that $\Omega_1, \Omega_2 \subset \mathbb{R}^{n+1}$, $n \geq 1$ are two disjoint domains whose complements satisfy the capacity density condition and the intersection of their boundaries $F$ has positive harmonic measure. Then we…
Interaction of waves with point and line defects are usually described by $\delta$-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of point defects or parallel line defects…
A phase--field method is applied to the modeling of flow and breakup of droplets in a T--shaped junction in the hydrodynamic regime where capillary and viscous stresses dominate over inertial forces, which is characteristic of microfluidic…
Geometric phase shift associated with an electron propagating through a dimerized-disordered continuum is shown to be 0, or $\pm \pi$ (modulo 2$\pi$), according as the associated circuit traversed in the two-dimensional parameter space…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We discuss the features of a two-Higgs doublet model exhibiting a two stage phase transition. At finite temperatures electric charge violating stationary points are developed. In conjunction with {\em CP} violation in the Higgs or the…
We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in…
We present a new two dimensional model for elliptic (i.e., shape anisotropic) patchy colloids, where the impenetrable core of the particles is decorated on its co-)vertices by Kern-Frenkel type of patches. Using (i) well-documented criteria…
Liquid-gas equilibrium is considered using the global isomorphism with the Ising-like (lattice gas) model. Such an approach assumes the existence of the order parameter in terms of which the symmetry of binodal is restored not only in the…
We investigate the limit behaviour of the spectral measures of matrices following the Gibbs measure for the Ising model on random graphs, Potts model on random graphs, matrices coupled in a chain model or induced QCD model. For most of…
This research investigates the formation and stability of localized states, known as quantum droplets and bubbles, in the quadratic-cubic discrete nonlinear Schr\"odinger equation. Near a Maxwell point, these states emerge from two fronts…
We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling a rich range of behavior is…
This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. Introducing the model that describes two immiscible fluids…
The low-energy limits of models with disorder are frequently described by sigma models. In two dimensions, most sigma models admit either a Wess-Zumino-Witten or a theta term. When such a term is present the model can have a stable critical…
We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements using tensor network methods. The state is subjected to uniform measurements $M = \cos{\theta}Z+\sin{\theta}X$ on the…
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a…
Electron scattering in the monolayer graphene with short-range impurities modelled by the annular well with a band-asymmetric potential has been considered. Band-asymmetry of the potential resulted in the mass (gap) perturbation in the…
We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain…