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In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration…
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions…
Models of simple excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This subject is a topic of practical relevance to diverse fields, ranging from neuroscience to…
The Higgs-Dilaton cosmological model is able to describe simultaneously an inflationary expansion in the early Universe and a dark energy dominated stage responsible for the present day acceleration. It also leads to a non-trivial relation…
Electrical circuits offer a unique platform to explore physical phenomena, from topology to non-Hermitian effects. Investigations of the fundamental properties of this metamaterial platform are crucial to distinguish observed/measured…
Salient features of vortex dynamics in super media are summarized. Recent examples are: the demonstration of prominent role of topology in vortex dynamics; the solution to the Hall anomaly which once bothered Bardeen, de Gennes and many…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
We theoretically investigate the motion of a domain wall and a vortex in type-II superconductors driven by inhomogeneities of temperature or spin density. The model consists of the time-dependent Ginzburg-Landau equation and the…
We compute the two-particle matrix element and Josephson tunneling amplitude in a two-dimensional model of topological superconductivity which captures the physics of the doped Mott insulator. The hydrodynamics of topological electronic…
We investigate the effect of higher-dimensional marginal operators on the thermodynamics of cosmological phase transitions. Focusing on the Abelian Higgs model, we systematically match these operators, which arise at higher orders in the…
We give an overview of the current theory of collective modes in trapped atomic gases at finite temperatures, when the dynamics of the condensate and non-condensate must both be considered. A simple introduction is given to the quantum…
In this series of papers, we study a Hamiltonian model for 3+1d topological phases, based on a generalisation of lattice gauge theory known as "higher lattice gauge theory". Higher lattice gauge theory has so called "2-gauge fields"…
Condensation of quantum loops naturally leads to topological phases with Abelian excitations. Here, I propose that non-Abelian topological phases can arise from merging two (or several) identical Abelian quantum loop condensates. I define…
Gravity can play a role in critical phenomena. Topological singularities induce ground state degeneracy and break the continuum symmetry of the vacuum. They also generate momenta oscillations about an average momentum and a positive…
We consider a two-dimensional array of ultra-small superconducting grains, weakly coupled by Josephson junctions with large charging energy. We start from an effective action based on a microscopic tunneling Hamiltonian, which includes…
The Kosterlitz-Thouless and the Hexatic phase transitions are celebrated examples of dipole (vortex, dislocation) induced transitions in condensed matter physics. For very clear reasons, these important ``topological" transitions are…
We investigate the mechanism by which topological defects form in first order phase transitions with a charged order parameter. We show how thick superconductor vortices and heavy cosmic strings form by trapping of magnetic flux. In an…
Motivated by the superconductivity of $M_x$Bi$_2$Se$_3$, we study topological excitations in a nematic superconductor using Ginzburg-Landau theory. An isolated excitation at low field is shown to be either a distorted phase vortex or a…
We study some functionals that describe the density of vortex lines in superconductors subject to an applied magnetic field, and in Bose-Einstein condensates subject to rotational forcing, in quite general domains in 3 dimensions. These…
In phase transitions, mesoscale structures such as topological defects, vortex strings, and domain walls control the path towards equilibrium, and thus the functional properties of many active devices. In photoinduced phase transitions…