Topological materials are of interest to both fundamental science and advanced technologies because topological states are robust with respect to perturbations and dissipation. Experimental detection of topological invariants is thus in great demand but remains extremely challenging. Ultrafast laser-matter interactions, and in particular high-harmonic generation, meanwhile, were proposed several years ago as tools to explore the structural and dynamical properties of various matter targets. Here we show that the high-harmonic emission signal produced by a circularly polarized laser contains signatures of topological phases and transitions in the paradigmatic Haldane model. In addition to clear shifts of the overall emissivity and harmonic cutoff, the high-harmonic emission shows a unique circular dichroism, which exhibits clear changes in behavior at the topological phase boundary. Our findings pave the way to understand fundamental questions about the ultrafast electron-hole pair dynamics in topological materials via nonlinear high-harmonic generation spectroscopy.

We obtain exact solutions for kinks in ${\varphi }^8$, ${\varphi }^{10}$, and ${\varphi }^{12}$ field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order ${\varphi }^4$ and ${\varphi }^6$ theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the coexistence of up to three distinct kinks (for a ${\varphi }^{12}$ potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the ${\varphi }^{10}$ field theory, which is a quasiexactly solvable model akin to ${\varphi }^6$, we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.

Based on the completeness relation for the squared solutions of the Lax operator L, we show that a subset of nonlocal equations from the hierarchy of nonlocal nonlinear Schrödinger equations (NLS) is a completely integrable system. The spectral properties of the Lax operator indicate that there are two types of soliton solutions. The relevant action-angle variables are parametrized by the scattering data of the Lax operator. The notion of the symplectic basis, which directly maps the variations of the potential of L to the variations of the action-angle variables has been generalized to the nonlocal case. We also show that the inverse scattering method can be viewed as a generalized Fourier transform. Using the trace identities and the symplectic basis, we construct the hierarchy Hamiltonian structures for the nonlocal NLS equations.

The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.

We explore a variant of the ϕ⁶ model originally proposed in Phys. Rev.D 12 (1975) 1606 as a prototypical, so-called, “bag” model in which domain walls play the role of quarks within hadrons. We examine the steady state of the model, namely an apparent bound state of two kink structures. We explore its linearization, and we find that, as a function of a parameter controlling the curvature of the potential, an effectively arbitrary number of internal modes may arise in the point spectrum of the linearization about the domain wall profile. We explore some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, and how they depend on the principal parameter of the model. We find that the critical velocity exhibits a non-monotonic dependence on the parameter controlling the curvature of the potential. For the multi-bounce windows, we find that their range and complexity decrease as the relevant parameter decreases (and as the number of internal modes in the model increases). We use a modified collective coordinates method [in the spirit of recent works such as Phys. Rev.D 94 (2016) 085008] in order to capture the relevant phenomenology in a semi-analytical manner.

One of the most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In the present work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. The results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.