Condensed Matter

We generalise the non-affine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic resolution, we propose an extension of the Kernel Polynomial Method (KPM) for the computation of the vibrational density of states (VDOS) and the eigenmodes, including the Γ -correlator of the affine force-field, which is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show that the results converge well to the solution obtained by direct diagonalization (DD) of the Hessian (dynamical) matrix. As is well known, the DD approach has prohibitively high computational requirements for systems with N= 10 4 atoms or larger. Instead, the KPM approach developed here allows one to scale up lattice dynamic calculations of real materials up to 10 6 atoms, with a hugely more favorable (linear) scaling of computation time and memory consumption with N .

In this letter we propose a general principle for how to build up a quantum neural network with high learning efficiency. Our stratagem is based on the equivalence between extracting information from input state to readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth, and by Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability for a given quantum neural network architectures, and argue this quantity is positively correlated with the learning efficiency of this architecture. As examples, we compute the averaged operator size for several different architectures, and we also consider two typical learning tasks, which are a regression task of a quantum problem and a classification task on classical images, respectively. In both cases, we find that, for the architecture with a larger averaged operator size, the loss function decreases faster or the prediction accuracy in the testing dataset increases faster as the training epoch increases, which means higher learning efficiency. Our results can be generalized to more complicated quantum versions of machine learning algorithms.

We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility χ (3) 3 from slightly below the usual glass transition temperature down to 10K . According to the mean field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then χ (3) 3 , which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature T G . We find instead that upon cooling | χ (3) 3 | decreases by several orders of magnitude and becomes roughly constant in the regime 100K−10K . We rationalize our findings by assuming that the low temperature physics is described by localized excitations weakly interacting via a spin-glass dipolar pairwise interaction in a random magnetic field. Our quantitative estimations show that the spin-glass interaction is twenty to fifty times smaller than the local random field contribution, thus rationalizing the absence of the spin-glass Gardner phase. This hints at the fact that a Gardner phase may be suppressed in standard molecular glasses, but it also suggests ways to favor its existence in other amorphous solids and by changing the preparation protocol.

We present a quantum field theoretical method for the characterization of disordered complex media with short laser pulses in an optical coherence tomography setup (OCT). We solve this scheme of coherent transport in space and time with weighted essentially nonoscillatory methods (WENO). WENO is preferentially used for the determination of highly nonlinear and discontinuous processes including interference effects and phase transitions like Anderson localization of light. The theory determines spatiotemporal characteristics of the scattering mean free path and the transmission cross section that are directly measurable in time-of-flight (ToF) and pump-probe experiments. The results are a measure of the coherence of multiple scattering photons in passive as well as in optically soft random media. Our theoretical results of ToF are instructive in spectral regions where material characteristics such as the scattering mean free path and the diffusion coefficient are methodologically almost insensitive to gain or absorption and to higher-order nonlinear effects. Our method is applicable to OCT and other advanced spectroscopy setups including samples of strongly scattering mono- and polydisperse complex nano- and microresonators.

We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. Demarcating boundaries between localised and extended states in the space of system parameters and energy, mobility edges are generic in quasiperiodic systems which lack the energy-independent self-duality of the commonly studied Aubry-André-Harper model. The potentials in such systems are strongly and infinite-range correlated, reflecting their deterministic nature and rendering the problem distinct from that of disordered systems. Importantly, the underlying theoretical framework introduced is model-independent, thus allowing analytical extraction of mobility edge trajectories for arbitrary quasiperiodic systems. We exemplify the theory using two families of models, and show the results to be in very good agreement with the exactly known mobility edges as well numerical results obtained from exact diagonalisation.

Non-interacting spinless electrons in one-dimensional quasicrystals, described by the Aubry-André-Harper (AAH) Hamiltonian with nearest neighbour hopping, undergoes metal to insulator transition (MIT) at a critical strength of the quasi-periodic potential. This transition is related to the self-duality of the AAH Hamiltonian. Interestingly, at the critical point, which is also known as the self-dual point, all the single particle wave functions are multifractal or non-ergodic in nature, while they are ergodic and delocalized (localized) below (above) the critical point. In this work, we have studied the one dimensional quasi-periodic AAH Hamiltonian in the presence of spin-orbit (SO) coupling of Rashba type, which introduces an additional spin conserving complex hopping and a spin-flip hopping. We have found that, although the self-dual nature of AAH Hamiltonian remains unaltered, the self-dual point gets affected significantly. Moreover, the effect of the complex and spin-flip hoppings are identical in nature. We have extended the idea of Kohn's localization tensor calculations for quasi-particles and detected the critical point very accurately. These calculations are followed by detailed multifractal analysis along with the computation of inverse participation ratio and von Neumann entropy, which clearly demonstrate that the quasi-particle eigenstates are indeed multifractal and non-ergodic at the critical point. Finally, we mapped out the phase diagram in the parameter space of quasi-periodic potential and SO coupling strength.

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point of a dynamical phase transition. Here, we study a minimal neural network model that exhibits self-organized criticality in the presence of stochastic noise using a rewiring rule which only utilizes local information. For network evolution, incoming links are added to a node or deleted, depending on the node's average activity. Based on this rewiring-rule only, the network evolves towards a critcal state, showing typical power-law distributed avalanche statistics. The observed exponents are in accord with criticality as predicted by dynamical scaling theory, as well as with the observed exponents of neural avalanches. The critical state of the model is reached autonomously without need for parameter tuning, is independent of initial conditions, is robust under stochastic noise, and independent of details of the implementation as different variants of the model indicate. We argue that this supports the hypothesis that real neural systems may utilize similar mechanisms to self-organize towards criticality especially during early developmental stages.

The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behaviour is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation can be too restrictive by indicating that the self-correlation imposes a constraint on the spectral form factor integrated over time. More generally, we indicate that each expansion coefficient of the two-point correlation function imposes a constraint on the properly weighted time-integrated spectral form factor. We discuss how these constraints can affect the interpretation of the spectral form factor as a probe for ergodicity. We propose a new probe, which eliminates the effect of the constraint imposed by the self-correlation. The use of this probe is demonstrated for a model of randomly incomplete spectra and a Floquet model supporting many-body localization.

We analyze conformational properties of branched polymer structures, formed on the base of Erdös-Rényi random graph model. We consider networks with N=5 vertices and variable parameter c , that controls graph connectedness. The universal rotationally invariant size and shape characteristics, such as averaged asphericity ⟨ A 3 ⟩ and size ratio g of such structures are obtained both numerically by application of Wei's method and analytically within the continuous chain model. In particular, our results quantitatively indicate an increase of asymmetry of polymer network structure when its connectedness c decreases.

We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index needs to be adjusted to achieve perfect beam transmission, despite the presence of disorder. Remarkably, the effects of both diagonal and off-diagonal disorder in the waveguides and their couplings can be efficiently eliminated by our non-Hermitian design. Waveguide arrays thus provide an ideal platform for the experimental realization of non-Hermitian phenomena in the context of discrete photonics.