By a simulation study of three-dimensional (3D) and two-dimensional (2D) disordered lattice models in the chiral symplectic class, we show that one-dimensional (1D) weak topology universally induces an intermediate quasi-localized (QL) phase between metal and Anderson-localized phases, in which the localization length of wave functions is divergent only along the spatial direction associated with the weak topological index. Our numerical evaluation of the critical exponents of the metal-to-QL transition and the Anderson transition (in the absence of the weak topology) demonstrates that they belong to different universality classes. We also confirm that the critical exponents of these two transitions in the chiral symplectic class significantly differ from those in the chiral unitary and chiral orthogonal classes, highlighting the impact of Kramers time-reversal symmetry on quantum critical behavior.

We investigate the fate of a many-body localized phase in a non-Hermitian quasiperiodic model of hardcore bosons subjected to periodic driving. While in general, the many-body localized system is known to thermalize with increasing driving period due to Floquet heating, in this case, we demonstrate that the initially localized system first delocalizes and then localizes again, resulting in a re-entrant many-body localization (MBL) transition as a function of the driving period. Strikingly, further increase in the driving period results in a series of localization-delocalization transitions leaving behind traces of extended regimes (islands) in between MBL phases. Furthermore, non-Hermiticity renders the extended islands boundary-sensitive, resulting in a Floquet many-body skin effect under open boundaries. We present numerical evidence from spectral and dynamic studies, confirming these findings. Our study opens new pathways for understanding the interplay between non-Hermiticity and quasiperiodicity in driven systems.

We present a detailed analysis of the sixth-order Pais-Uhlenbeck oscillator and construct three-dimensional ghost-free representations through a Tri-Hamiltonian framework. We identify a six-dimensional Abelian Lie algebra of the PU model's dynamical flow and derive a hierarchy of conserved Hamiltonians governed by multiple compatible Poisson structures. These structures enable the realisation of a complete Tri-Hamiltonian formulation that generates identical dynamical flows. Positive-definite Hamiltonians are constructed, and their relation to the full Tri-Hamiltonian hierarchy is analysed. Furthermore, we develop a mapping between the PU model and a class of three-dimensional coupled second-order systems, revealing explicit conditions for ghost-free equivalence. We also explore the consequences of introducing interaction terms, showing that the multi-Hamiltonian structure is generally lost in such cases.

Exceptional points (EPs) are non-Hermitian spectral degeneracies marking a simultaneous coalescence of eigenvalues and eigenvectors. Despite the fact that multiband n-fold EPs (EPns) generically emerge as special points on manifolds of EPms, where m<n, EPns as well as their topological properties have hitherto been studied as isolated objects. In this work we address this issue and carefully map out the emerging properties of multifold exceptional structures in three and four dimensions under the influence of one or multiple generalized similarities, revealing diverse combinations of EPms in direct connection to EPns. We find that simply counting the number of constraints defining the EPns is not sufficient in the presence of similarities; the constraints can also be satisfied by the EPm-manifolds obeying certain spectral symmetries in the complex eigenvalue plane, reducing their dimension beyond what is expected from counting the number of constraints. Furthermore, the induced spectral symmetries not always allow for any EPm-manifold to emerge in n-band systems, making the plethora of exceptional structures deviate further from naive expectations. We illustrate our findings in simple periodic toy models. By relying on similarity relations instead of the less general symmetries, we simultaneously cover several physically relevant scenarios, ranging from optics and topolectrical circuits, to open quantum systems. This makes our predictions highly relevant and broadly applicable in modern research, as well as experimentally viable within various branches of physics.

Waveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are structured aperiodically according to the deterministic Fibonacci-Lucas substitution rule. These "Fibonacci waveguides" lack translational invariance and are characterized by a singular continuous energy spectrum and critical eigenstates, representing a deterministic intermediate between ordered and disordered systems. We demonstrate how to achieve decoherence-free, coherent interactions in this unique setting. We analyze two paradigmatic cases: (i) Giant emitters resonantly coupled to the simplest aperiodic version of a standard waveguide. For these, we show that atom photon bound states form only for specific coupling configurations dictated by the aperiodic sequence, leading to an effective atomic Hamiltonian, which itself inherits the Fibonacci structure; and (ii) emitters locally and off-resonantly coupled to the aperiodic version of the Su-Schrieffer-Heeger waveguide. In this case the mediating bound states feature aperiodically modulated profiles, resulting in an effective Hamiltonian with multifractal properties. Our work establishes Fibonacci waveguides as a versatile platform, which is experimentally feasible, demonstrating that the deterministic complexity of aperiodic structures can be directly engineered into the interactions between quantum emitters.

Non-Hermitian (NH) quantum systems have emerged as a powerful framework for describing open quantum systems, non-equilibrium dynamics, and engineered quantum optical materials. However, solving the ground-state properties of NH systems is challenging due to the exponential scaling of the Hilbert space, and exotic phenomena such as the emergence of exceptional points. Another challenge arises from the limitations of traditional methods like exact diagonalization (ED). For the past decade, neural networks (NN) have shown promise in approximating many-body wavefunctions, yet their application to NH systems remains largely unexplored. In this paper, we explore different NN architectures to investigate the ground-state properties of a parity-time-symmetric, one-dimensional NH, transverse field Ising model with a complex spectrum by employing a recurrent neural network (RNN), a restricted Boltzmann machine (RBM), and a multilayer perceptron (MLP). We construct the NN-based many-body wavefunctions and validate our approach by recovering the ground-state properties of the model for small system sizes, finding excellent agreement with ED. Furthermore, for larger system sizes, we demonstrate that the RNN outperforms both the RBM and MLP. However, we show that the accuracy of the RBM and MLP can be significantly improved through transfer learning, allowing them to perform comparably to the RNN for larger system sizes. These results highlight the potential of neural network-based approaches--particularly for accurately capturing the low-energy physics of NH quantum systems.

We investigate the Pais-Uhlenbeck (PU) model, a paradigmatic example of a higher time-derivative theory, by identifying the Lie symmetries of its associated fourth- order dynamical equation. Exploiting these symmetries in conjunction with the model’s Bi-Hamiltonian structure, we construct distinct Poisson bracket formulations that pre- serve the system’s dynamics. Amongst other possibilities, this allow us to recast the PU model in a positive definite manner, offering a solution to the long-standing problem of ghost instabilities. Furthermore, we systematically explore a family of transformations that reduce the PU model to equivalent first-order, higher-dimensional systems. Finally we examine the impact on those transformations by adding interaction terms of poten- tial form to the PU model and demonstrate how they usually break the Bi-Hamiltonian structure. Our approach yields a unified framework for interpreting and stabilizing higher time-derivative dynamics through a symmetry analysis in some parameter regime.

Spontaneous symmetry breaking (SSB) and exceptional points (EPs) are often assumed to be inherently linked. Here we investigate the intricate relationship between SSB and specific classes of EPs across three distinct, real-world scenarios in nonlinear optics. In these systems, the two phenomena do not<br>coincide for all classes of EPs; they can occur at dislocated points in parameter space. This recurring behavior across disparate platforms implies that such decoupling is not unique to these optical systems, but likely reflects a more general principle. Our results highlight the need for careful analysis of assumed correlations between SSB and EPs in both theoretical and applied contexts. They deepen our understanding of nonlinear dynamics in<br>optical systems and prompt a broader reconsideration of contexts where EPs and<br>SSB are thought to be interdependent.

We present several analytical approaches to the Dicke superradiance problem, which involves determining the time evolution of the density operator for an initially inverted ensemble of $N$ identical two-level systems undergoing collective spontaneous emission. This serves as one of the simplest cases of open quantum system dynamics that allows for a fully analytical solution. We explore multiple methods to tackle this problem, yielding a solution valid for any time and any number of spins. These approaches range from solving coupled rate equations and identifying exceptional points in non-Hermitian evolution to employing combinatorial and probabilistic techniques, as well as utilizing a quantum jump unraveling of the master equation. The analytical solution is expressed as a residue sum obtained from a contour integral in the complex plane, suggesting the possibility of fully analytical solutions for a broader class of open quantum system dynamics problems.