Condensed Matter

We investigate the quantum dynamics of Two-Level Systems (TLS) in glasses at low temperatures (1 K and below). We study an ensemble of TLSs coupled to phonons. By integrating out the phonons within the framework of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we derive analytically the explicit form of the interactions among TLSs, and of the dissipation terms. We find that the unitary dynamics of the system shows clear signatures of Many-Body Localization physics. We study numerically the time behavior of the concurrence, which measures pairwise entanglement also in non-isolated systems, and show that it presents a power-law decay both in the absence and in the presence of dissipation, if the latter is not too large. These features can be ascribed to the strong, long-tailed disorder characterizing the distributions of the model parameters. Our findings show that assuming ergodicity when discussing TLS physics might not be justified for all kinds of experiments on low-temperature glasses.

Amorphous solids are yield stress materials that flow when a sufficient load is applied. Their flow consists of periods of elastic loading interrupted by rapid stress drops, or avalanches, coming from microscopic rearrangements known as shear transformations (STs). Here we show that the spatial extent of avalanches in a steadily sheared amorphous solid has a profound effect on the distribution of local residual stresses x . We find that in this distribution, the most unstable sites are located in a system size dependent plateau. While the entrance into the plateau is set by the lower cutoff of the mechanical noise produced by individual STs, the departure from the usually assumed power-law (pseudogap) form P(x)??x θ comes from far field effects related to spatially extended rearrangements. Interestingly, we observe that the average value of weakest sites ??x min ??is located in an intermediate power law regime between the pseudogap and the plateau regimes, whose exponent decreases with system size. Our findings imply a new scaling relation linking the exponents characterizing the avalanche size and residual stress distributions.

Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of pairwise interactions and to capture the many-body interactions between two or more nodes strongly affecting dynamical processes. In fact, the simplicial complexes topology allows to assign a dynamical variable not only to the nodes of the interacting complex systems but also to links, triangles, and so on. Here we show evidence that the dynamics defined on simplices of different dimensions can be significantly different even if we compare dynamics of simplices belonging to the same simplicial complex. By investigating the spectral properties of the simplicial complex model called "Network Geometry with Flavor" we provide evidence that the up and down higher-order Laplacians can have a finite spectral dimension whose value increases as the order of the Laplacian increases. Finally we discuss the implications of this result for higher-order diffusion defined on simplicial complexes.

The entropy stabilized oxide Mg 0.2 Co 0.2 Ni 0.2 Cu 0.2 Zn 0.2 O exhibits antiferromagnetic order and magnetic excitations, as revealed by recent neutron scattering experiments. This observation raises the question of the nature of spin wave excitations in such disordered systems. Here, we investigate theoretically the magnetic ground state and the spin-wave excitations using linear spin-wave theory in combination with the supercell approximation to take into account the extreme disorder in this magnetic system. We find that the experimentally observed antiferromagnetic structure can be stabilized by a rhombohedral distortion together with large second nearest neighbor interactions. Our calculations show that the spin-wave spectrum consists of a well-defined low-energy coherent spectrum in the background of an incoherent continuum that extends to higher energies.

We show that the distribution of elements H in the Hessian matrices associated with amorphous materials exhibit singularities P(H)∼ |H| γ with an exponent γ<0 , as |H|→0 . We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that γ depends only on the degree of smoothness n of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix.

We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size ( s ) and the corresponding energy burst ( E ) in this version of the model have a non-linear relation ( E??s γ ). Numerical results indicate that γ??.5 universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of ??γ+1) .

Unlike their Hermitian counterparts, non-Hermitian (NH) systems may display an exponential sensitivity to boundary conditions and an extensive number of edge-localized states in systems with open boundaries, a phenomena dubbed the "non-Hermitian skin effect." The NH skin effect is one of the primary challenges to defining a topological theory of NH Hamiltonians, as the sensitivity to boundary conditions invalidates the traditional bulk-boundary correspondence. The NH skin effect has recently been connected to the winding number, a topological invariant unique to NH systems. In this paper, we extend the definition of the winding number to disordered NH systems by generalizing established results on disordered Hermitian topological insulators. Our real-space winding number is self-averaging, continuous as a function of the parameters in the problem, and remains quantized even in the presence of strong disorder. We verify that our real-space formula still predicts the NH skin effect, allowing for the possibility of predicting and observing the NH skin effect in strongly disordered NH systems. As an application we apply our results to predict a NH Anderson skin effect where a skin effect is developed as disorder is added to a clean system, and to explain recent results in optical funnels.

We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and time scales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder W c (L,d) as a function of length L and width d . In the quasi-1D case W c has a finite large- L limit at fixed d , which increases strongly with d . In the 2D case W c (L,L) grows with L . The results are consistent with the avalanche picture of the many-body localization transition.

We study the dynamics of a two-site model in which the tunneling amplitude between the sites is not constant but rather a high-frequency noise. Obviously, the population imbalance in this model decays exponentially with time. Remarkably, the decay is modified dramatically when the level asymmetry fluctuates in-phase with fluctuations of the tunneling amplitude. For particular type of these in-phase fluctuations, namely, the telegraph noise, we find the exact solution for the average population dynamics. It appears that the population imbalance between the sites starting from 1 at time t=0 approaches a constant value in the limit t→∞ . At finite bias, the imbalance goes to zero at t→∞ , while the dynamics of the decay governed by noise acquires an oscillatory character.

Correlation inequalities have played an essential role in the analysis of ferromagnetic models but have not been established in spin glass models. In this study, we obtain some correlation inequalities for the Ising models with quenched randomness, where the distribution of the interactions is symmetric. The acquired inequalities can be regarded as an extension of the previous results, which were limited to the local energy for a spin set, to the local energy for a pair of spin sets. Besides, we also obtain some correlation inequalities for asymmetric distribution.