A remarkable feature of the trimer Su-Schrieffer-Heeger (SSH3) model is that it supports localized edge states. However, in contrast to the dimer version of the model, a change in the total number of edge states in SSH3 without mirror-symmetry is not necessarily associated with a phase transition, i.e., a closing of the band gap. As such, the topological invariant predicted by the 10-fold way classification does not always coincide with the total number of edge states present. Moreover, although Zak's phase remains quantized for the case of a mirror-symmetric chain, it is known that it fails to take integer values in the absence of this symmetry and thus it cannot play the role of a well-defined bulk invariant in the general case. Attempts to establish a bulk-edge correspondence have been made via Green's functions or through extensions to a synthetic dimension. Here we propose a simple alternative for SSH3, utilizing the previously introduced sublattice Zak's phase, which also remains valid in the absence of mirror symmetry and for noncommensurate chains. The defined bulk quantity takes integer values, is gauge invariant, and can be interpreted as the difference of the number of edge states between a reference and a target Hamiltonian. Our derivation further predicts the exact corrections for finite open chains, is straightforwardly generalizable, and invokes a chiral-like symmetry present in this model.

Fermi acceleration in a Fermi-Ulam model, consisting of an ensemble of particles bouncing between two, infinitely heavy, stochastically oscillating hard walls, is investigated. It is shown that the widely used approximation, neglecting the displacement of the walls (static wall approximation), leads to a systematic underestimation of particle acceleration. An improved approximative map is introduced, which takes into account the effect of the wall displacement, and in addition allows the analytical estimation of the long term behavior of the particle mean velocity as well as the corresponding probability distribution, in complete agreement with the numerical results of the exact dynamics. This effect accounting for the increased particle acceleration—Fermi hyperacceleration—is also present in higher-dimensional systems, such as the driven Lorentz gas.

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behavior is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.

We look for fluctuations expected for the QCD critical point using an intermittency analysis in the transverse momentum phase space of protons produced around midrapidity in the 12.5 % most central...

Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian derived by subsystem partitioning. We provide an intuitive interpretation of such latent symmetries by relating them to corresponding local symmetries in the powers of the underlying Hamiltonian matrix. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-Abelian latent symmetry group. It is demonstrated that the rotational symmetries can be broken in a controlled manner while maintaining the underlying more fundamental latent symmetry. This opens up the perspective of investigating accidental degeneracies in terms of latent symmetries.

A semianalytical approach to atomic waveguide scattering for harmonic confinement is developed, taking into account all partial waves. As a consequence $\ell${}-wave confinement-induced resonances are formed, being coupled to each other due to the confinement. The corresponding resonance condition is obtained analytically using the K-matrix formalism. Atomic scattering is described by transition diagrams which depict all relevant processes the atoms undergo during the collision. Our analytical results are compared to corresponding numerical data and show very good agreement.