Sergej Flach

The unidirectional Hatano–Nelson chain serves as the fundamental non-Hermitian building block of the Su–Schrieffer–Heeger (SSH) model. We investigate its Anderson localization properties under diagonal binary disorder. For weak disorder, the complex eigenvalue spectrum forms a single closed loop, which bifurcates into two distinct loops at a critical disorder threshold. Correspondingly, the spectral winding number ν undergoes a transition from ν = 1 in the weak-disorder regime, through ν = 1/2 at the critical point, to ν = 0 in the strong-disorder limit. We show that the eigenstates are subexponentially localized, with a localization length that varies analytically as a function of the momentum-like quantum number q . Notably, at weak and critical disorder, the spectrum hosts two completely delocalized states with diverging localization lengths. This divergence is directly correlated with the non-trivial spectral winding number. These findings remain robust under various boundary conditions, with the exception of strictly open boundaries.

We study universal aspects of thermalization induced by Trotterization, a procedure routinely used in gate-based quantum computation. We use the reduced-Bardeen-Cooper-Schrieffer model-quantum integrable with a classically integrable mean-field limit-where the effects of Trotter chaos are expected to be particularly stark. The resulting Trotterized chaotic dynamics is characterized by its Lyapunov spectrum and rescaled Kolmogorov-Sinai entropy. The chaos quantifiers depend on the Trotterization time step τ. We observe a Trotter transition at a finite step value τ_{c}≈sqrt[N]. While the dynamics is weakly chaotic for time steps τ≪τ_{c}, the regime of large Trotterization steps is characterized by short temporal correlations. We derive two different scaling laws for the two different regimes by numerically fitting the maximum Lyapunov exponent data. The scaling law of the large τ limit agrees well with the one derived from the kicked top map. Beyond its relevance to current quantum computers, our work opens other directions-such as probing observables like the Loschmidt echo, which lie beyond standard mean-field description--across the Trotter transition we uncover.

We develop a systematic framework for constructing all-bands-flat (ABF) lattice Hamiltonians that explicitly break time-reversal symmetry (TRS). By threading magnetic flux through disconnected polygonal plaquettes and applying local entangling unitary transformations, we map plaquettes onto families of ABF models in one, two, and three dimensions. This procedure preserves the flux configuration while converting semi-detangled geometries into ABF lattices with nontrivial hopping structure. The resulting flat bands admit compact localized states (CLSs) whose support includes both the flux-threaded plaquettes and auxiliary sites introduced by the unitary transformations. In these TRS-broken constructions, the CLSs host localized circulatory currents whose magnitude depends on the applied flux. We further extend the framework to lattices with coexisting flat and dispersive bands, illustrating cases with both orthogonal and non-orthogonal CLSs. Our results provide a controlled route for generating dispersionless lattices supporting flux-induced local currents.

We assess the ergodic properties of the Fermi–Pasta–Ulam–Tsingou-α model for generic initial conditions using a Toda integral. It serves as an adiabatic invariant for the system and a suitable observable to measure its equilibrium time. Over this time scale, the onset of action diffusion results in ergodic temporal fluctuations. We compare this time scale with the inverse of the maximum Lyapunov exponent λ and its saturation time, which are systematically shorter. The Toda integral ergodization/equilibrium time is system size independent for long chains but show dramatic growth when the system size is smaller than a critical one, whose value depends on the energy density. We measure the dependence of energy density on the critical system size and relate this observation to the possible emergence of a Kolmogorov–Arnold–Moser regime. We numerically determine the critical energy density of this regime, finding that it approximately decays as 1/N2 with the number of particles N.

On-site potentials are ubiquitous in physical systems and strongly influence their heat transport and energy localization. These potentials will inevitably affect the dynamical properties of q breathers (QBs), defined as periodic orbits exponentially localized in normal mode space. By integrating on-site terms into the Fermi-Pasta-Ulam-Tsingou-β system, this work utilizes numerical simulations and Floquet analysis to systematically explore the influence of on-site potentials on QB stability. For most QBs, except those at the phonon band edges, the instability is primarily governed by parametric resonance and effectively described by coupled Mathieu equations. This approach provides a theoretical expression for the instability thresholds, which aligns well with numerical results. The instability threshold is highly sensitive to the seed mode, in stark contrast to systems without on-site potentials. In addition, a systematic stability analysis across three-dimensional parameter space shows that quartic intersite nonlinearity monotonically enhances QB instability, while quartic on-site nonlinearity yields nonmonotonic effects, in particular, an initial destabilization followed by restabilization at high amplitudes. The quadratic on-site potential uniformly promotes stability. Furthermore, these instability phase diagrams highlight both the individual contributions and combined effects of each possible component in regulating the QB dynamics. These findings offer valuable insights into QB stability and the manipulation of localized excitations in diverse physical systems with on-site potentials.

The observation of the Fermi-Pasta-Ulam-Tsingou (FPUT) paradox, namely the lack of equipartition in the evolution of a normal mode in a nonlinear chain on unexpectedly long times, is arguably the most famous numerical experiment in the history of physics. Seventy years after the original publication, most studies in FPUT chains still focus on long wavelength initial states similar to the original paper. It is shown here that all characteristic features of the FPUT paradox are rendered even more striking if modes with short(er) wavelengths are evolved instead. Since not every normal mode leads to equipartition, we also provide a simple technique to predict which modes, and in what perturbation order, are excited starting from an initial mode (root) in α-FPUT chains. The excitation sequences associated with a root are then numerically shown to spread energy at different speeds, leading to prethermalization regimes that become longer as a function of mode excitation number. This effect is visible in observables such as mode energies and spectral entropies and, surprisingly, also in the time evolution of invariant quantities such as Lyapunov times and Kolmogorov-Sinai entropies. Our findings generalize the original FPUT experiment, provide an original look at the paradox's source, and enrich the vast literature dedicated to studying equipartition in classical many-body systems.