Related papers: Topological interface states mediated by spontaneo…

Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there…

In this introductory lecture, some basic features of the spontaneous symmetry breaking are discussed. More specifically, $\sigma $-model, non-linear realization, and some examples of spontaneous symmetry breaking in the non-relativistic…

We describe spontaneous symmetry breaking in the powers of two optical modes coupled into a ring resonator, using a pair of coupled Lorentzian equations, featuring tunable self- and cross-phase modulation terms. We investigate a wide…

We study three dimensional systems where strong repulsion leads to an insulating state via spontaneously generated spin-orbit interactions. We discuss a microscopic model where the resulting state is topological. Such topological `Mott'…

Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However,…

Topological phase transition is accompanied with a change of topological numbers. It has been believed that the gap closing and the breakdown of the adiabaticity at the transition point is necessary in general. However, the gap closing is…

We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of…

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology and energetics, we show that for a generic normal state band…

We show that in a system of one dimensional spinless fermions a topological phase and phase transition can emerge only through interaction. By allowing a dimerized or bond-alternating nearest neighbour interaction we show that the system…

Nonreciprocal interactions-- where forces between entities are asymmetric-- govern a wide range of nonequilibrium phenomena, yet their role in structural transitions in living and active systems remains elusive. Here, we demonstrate a…

The collective dynamics of a many-body system is described as a special case of low-energy quantum dynamics, occurring when the ground state breaks a continuous symmetry of the Hamiltonian. This approach is applied to the spontaneous…

For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent…

We perform a theoretical study of nonlinear optical isolator devices based on coupled microcavities with gain and loss. Using coupled-mode theory, we derive a correspondence between the boundary of asymptotic stability in the nonlinear…

Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…

Topological phononic crystals (PCs) are periodic artificial structures which can support nontrivial acoustic topological bands, and their topological properties are linked to the existence of topological edge modes. Most previous studies…

Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…

Topologically nontrivial states are common in symmetry broken phases at macroscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as single particles. The earliest and latest applications are…

Time-dependent systems have recently been shown to support novel types of topological order that cannot be realised in static systems. In this paper, we consider a range of time-dependent, interacting systems in one dimension that are…

In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…