We construct microscopical models of one-dimensional noninteracting topological insulators in all of the chiral universality classes. Specifically, we start with a deformation of the Su-Schrieffer-Heeger (SSH) model that breaks time-reversal symmetry, which is in the AIII class. We then couple this model to its time-reversal counterpart in order to build models in the classes BDI, CII, DIII, and CI. We find that the $Z$ topological index (the winding number) in individual chains is defined only up to a sign. This comes from noticing that changing the sign of the chiral symmetry operator changes the sign of the winding number. This freedom to choose the sign of the chiral symmetry operator on each chain independently allows us to construct two distinct possible chiral symmetry operators when the chains are weakly coupled—in one case, the total winding number is given by the sum of the winding number of individual chains, while in the second case, the difference is taken. We also find that the chiral models that belong to $Z$ classes, AIII, BDI, and CII are topologically equivalent, so they can be adiabatically deformed into one another without the change of topological invariant, so long as the chiral symmetry is preserved. We study the properties of the edge states in the constructed models and prove that topologically protected edge states must all be localized on the same sublattice (on any given edge). We also discuss the role of particle-hole symmetry on the protection of edge states and explain how it manages to protect edge states in $Z_2$ classes, where the integer invariant vanishes and chiral symmetry alone does not protect the edge states anymore. We generalize our results to the case of an arbitrary number of coupled chains, by constructing possible chiral symmetry operators for the multiple chain case, and briefly discuss the applications to any odd number of dimensions.

Disorder-induced feedback makes random lasers very susceptible to any changes in the scattering medium. The sensitivity of the lasing modes to perturbations in the disordered systems has been utilized to map the regions of perturbation. A tracking parameter that takes into account the cumulative effect of changes in the spatial distribution of the lasing modes of the system has been defined to locate the region in which a scatterer is displaced by a few nanometers. We show numerically that the precision of the method increases with the number of modes. The proposed method opens up the possibility of application of random lasers as a tool for monitoring locations of nanoscale displacement, which can be useful for single-particle detection and monitoring.

We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than the periodicity of the potential, the packet of spreading particles, all starting from a common origin, converges to a normal distribution centered at the origin with a mean-squared displacement that grows as $2D^{*}t$, with an effective diffusion constant that is smaller than that of a freely diffusing particle. We examine the interplay between this coarse-grained description and the fine structure of the density, which is given by the Boltzmann-Gibbs (BG) factor $e^{-V\left(x\right)/k_{B}T}$, the latter being nonnormalizable. We explain this result and construct a theory of observables using the Fokker-Planck equation. These observables are classified as those that are related to the BG fine structure, like the energy or occupation times, while others, like the positional moments, for long times, converge to those of the large-scale description. Entropy falls into a special category as it has a coarse-grained and a fine structure description. The basic thermodynamic formula $F=TS-E$ is extended to this far-from-equilibrium system. The ergodic properties are also studied using tools from infinite ergodic theory.

Possible routes for intra-cluster bond formation (ICBF) in protonated serine dimers have been studied. We found no evidence of ICBF following low energy collision induced dissociation (in correspondence with previous works), however, we do observe clear evidence for ICBF following photon absorption in the $4.6-14$ eV range. Moreover, the comparison of photon induced dissociation measurements of the protonated serine dimer to those of a protonated serine dipeptide provides evidence that ICBF, in this case, involves peptide bond formation (PBF). The experimental results are supported by {\it ab initio} molecular dynamics and exploration of several excited state potential energy surfaces, unravelling a pathway for PBF following photon absorption. The combination of experiments and theory provides insight into the PBF mechanisms in clusters of amino acids, and reveals the importance of electronic excited states reached upon UV/VUV light excitation.

Lasers and Bose-Einstein condensates (BECs) exhibit macroscopic quantum coherence in seemingly unrelated ways. Lasers possess a well-defined global phase while the number of photons fluctuates. In BECs of atoms, instead, the number of particles is conserved and the global phase is undefined. Here, we use gate-based quantum circuits to create a unified framework that connects lasers and BEC states. Our approach relies on a scalable circuit that measures the total number of particles without destroying long-range coherence. We introduce two complementary probes of global and relative phase coherence, study how they are affected by measurements of the particle number, and implement them on a superconducting quantum computer by Rigetti. We find that particle conservation enhances long-range phase coherence, highlighting a mechanism used by superfluids and superconductors to gain phase stiffness.

While great progress has been achieved in developing optical methods for measuring fast changes in membrane potential (like action potentials) in excitable cells, less progress has been made in precise (and calibrated) measurements of steady state resting membrane potentials (RMPs) and small changes in RMPs (in excitable or non-excitable cells). In excitable cells, small changes in RMPs are associated with multiple physiological processes such as sub-threshold events in neuronal signaling and in synaptic plasticity.

According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of earthquakes. Moreover, according to the so-called inverse Omori law, the rate of earthquakes should also increase prior to a mainshock -- this law has received much less attention due to its large uncertainty. Here, we mainly study the inverse Omori law based on a highly detailed Southern California earthquake catalog, which is complete for magnitudes larger than M>0.3. First, we develop a technique to identify mainshocks, foreshocks, and aftershocks. We then find, based on a statistical procedure we developed, that the rate of earthquakes is higher a few days prior to a mainshock. We find that this increase is much smaller for a catalog with a magnitude threshold of m over 2.5 and for the Epidemic-Type Aftershocks Sequence (ETAS) model catalogs, even when used with a small magnitude threshold. We also analyze the rate of aftershocks after mainshocks and find that the Omori-Utsu law does not hold for many individual mainshocks and that it may be valid only statistically when considering many mainshocks together. Yet, the analysis of the ETAS model based on the Omori-Utsu law exhibits similar behavior as that of the real catalogs, indicating the validity of this law.

Dynamical processes on complex networks, ranging from biological, technological and social systems, show phase transitions (PTs) between distinct global states of the system. Often, such transitions rely upon the interplay between the structure and dynamics that takes place on it, such that weak connectivity, either sparse network or frail interactions, might lead to global activity collapse, while strong connectivity leads to high activity. Here, we show that controlling dynamics of a fraction of the nodes in such systems acts as an external field in a continuous PT. As such, it defines corresponding critical exponents, both at equilibrium and of the transient time. We find the critical exponents for a general class of dynamics using the leading orders of the dynamic functions. By applying this framework to three examples, we reveal distinct universality classes.

Phase transitions (PT) have attracted tremendously broad research ranging from states of matter through superconductivity to ferromagnetism and many other systems [1–3]. Particularly, a special focus has been given to the behavior near the transition, revealing various critical phenomena including critical exponents and universality classes [1–3]. In the field of complex networks, a percolation PT has been widely explored where the order parameter is the relative size of the giant component while the tuning parameter is the occupation probability [4–8]. In this PT, the network is regarded as failed only when it completely loses its connectivity.

Chaos, namely exponential sensitivity to initial conditions, is generally considered a nuisance, inasmuch as it prevents long-term predictions in physical systems. Here, an easily accessible approach to undo deterministic chaos and tailor ray trajectories in arbitrary 2D optical billiards by introducing spatially varying refractive index therein is presented. A new refractive index landscape is obtained by a conformal mapping, which makes the trajectories of the chaotic billiard fully predictable and the billiard fully integrable. Moreover, trajectory rectification can be pushed a step further by relating chaotic billiards with non-Euclidean geometries. Two examples are illustrated by projecting billiards built on a sphere as well as the deformed spacetime outside a Schwarzschild black hole, which respectively lead to all periodic orbits and spiraling trajectories remaining away from the boundaries of the transformed 2D billiards/cavities. An implementation of this method is proposed, which enables real-time control of chaos and can further contribute to a wealth of potential applications in the domain of optical microcavities.

Unconventional superconductivity was realized in systems comprising a monolayer of magnetic adatoms adsorbed on conventional superconductors, forming Shiba-bands. Another approach to induce unconventional superconductivity and 2D Shiba-bands was recently introduced, namely, by adsorbing chiral molecules (ChMs) on conventional superconductors, which act in a similar way to magnetic impurities as verified by conductance spectroscopy. However, the fundamental effect ChMs have on the strength of superconductivity has not yet been directly observed and mapped. In this work, local magnetic susceptometry is applied on heterostructures comprising islands of ChMs (α-helix L-polyalanine) monolayers adsorbed on Nb. It is found that the ChMs alter the superconducting landscape, resulting in spatially-modulated weaker superconductivity. Surprisingly, the reduced diamagnetic response is located along the perimeter of the islands with respect to both their interior and the bare Nb. The authors suggest that topological edge-states forming at the edges are the source of the reduced superconductivity, akin to the case of magnetic islands. The results pave new paths for the realization of topological-superconductivity-based devices with changing order parameter.