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When a symmetry gets spontaneously broken in a phase transition, topological defects are typically formed. The theoretical picture of how this happens in a breakdown of a global symmetry, the Kibble-Zurek mechanism, is well established and…
We analyze the evolution of scalar and gauge fields during first order phase transitions and show how the Kibble mechanism for the formation of topological defects emerges from the underlying dynamics, paying particular attention to…
Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in…
In superconductors, and in other systems with a local U(1) gauge invariance, there are two mechanisms that form topological defects in phase transitions. In addition to the standard Kibble mechanism, thermal fluctuations of the magnetic…
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…
We review recent simulations of the formation of a particular class of non-topological defects known as semilocal strings during a phase transition. Semilocal strings have properties that are intermediate between topological cosmic strings…
Topological defects such as cosmic strings may have been formed at early-universe phase transitions. Direct tests of this idea are impossible, but the mechanism can be elucidated by studying analogous processes in low-temperature…
The control of condensed matter systems out of equilibrium by laser pulses allows us to investigate the system trajectories through symmetry-breaking phase transitions. Thus the evolution of both collective modes and single particle…
The Kibble-Zurek mechanism describes the formation of topological defects during spontaneous symmetry breaking for quite different systems. Shortly after the big bang, the isotropy of the Higgs-field is broken during the expansion and…
We consider the number distribution of topological defects resulting from the finite-time crossing of a continuous phase transition and identify signatures of universality beyond the mean value, predicted by the Kibble-Zurek mechanism.…
Formation of topological defects during symmetry breaking phase transitions via the {\it Kibble mechanism} is extensively used in systems ranging from condensed matter physics to the early stages of the universe. Kibble mechanism uses…
We demonstrate a novel mechanism for the formation of topological defects in a first order phase transition for theories in the presence of small explicit symmetry breaking terms. We carry out numerical simulations of collisions of two…
Systems passing through quantum critical points at finite rates have a finite probability of undergoing transitions between different eigenstates of the instantaneous Hamiltonian. This mechanism was proposed by Kibble as the underlying…
The gauge symmetry of the Ginzburg-Landau theory for two-gap superconductors is analyzed in this letter. We argue that the existence of two different phases, associated with the two independent scalar Higgs fields, explicitly breaks the…
The association of broken symmetries with phase transitions is ubiquitous in condensed matter physics: crystals break translational symmetry, magnets break rotational symmetry, and superconductors break gauge symmetry. However, despite the…
A growing number of superconducting materials display evidence for spontaneous time-reversal symmetry breaking (TRSB) below their critical transition temperatures. Precisely what this implies for the nature of the superconducting ground…
In magnetic systems, electronic bands often acquire nontrivial topological structure characterized by gauge flux distribution in momentum (k)-space. It sometimes follows that the phase of the wavefunctions cannot be defined uniquely over…
The Kibble-Zurek mechanism provides a description of the topological structure occurring in the symmetry breaking phase transitions, which may manifest as the cosmological strings in the early universe or vortex lines in the superfulid. A…
In supersymmetric theories, topological defects can have nontrivial behaviors determined purely by whether or not supersymmetry is restored in the defect core. A well-known example of this is that some supersymmetric cosmic strings are…
Inspired by the appearance of split-complex structures in the dimensional reduction of string theory, and in the theories emerging as byproducts, we study the hyper-complex formulation of Abelian gauge field theories, by incorporating a new…