Condensed Matter

A major challenge in network science is to determine parameters governing complex network dynamics from experimental observations and theoretical models. In complex chemical reaction networks, for example, such as those describing processes in internal combustion engines and power generators, rate constant estimates vary significantly across studies despite substantial experimental efforts. Here, we examine the possibility that variability in measured constants can be largely attributed to the impact of missing network information on parameter estimation. Through the numerical simulation of measurements in incomplete chemical reaction networks, we show that unaccountability of network links presumed unimportant (with local sensitivity amounting to less than two percent of that of a measured link) can create apparent rate constant variations as large as one order of magnitude even if no experimental errors are present in the data. Furthermore, the correlation coefficient between the logarithmic deviation of the rate constant estimate and the cumulative relative sensitivity of the neglected reactions was less than 0.5 in all cases. Thus, for dynamical processes on complex networks, iteratively expanding a model by determining new parameters from data collected under specific conditions is unlikely to produce reliable results.

We study the mobility edges in a variety of one-dimensional tight binding models with slowly varying quasi-periodic disorders. It is found that the quasi-periodic disordered models can be approximated by an ensemble of periodic models. The mobility edges can be determined by the overlaps of the energy bands of these periodic models. We demonstrate that this method provides an efficient way to find out the precise location of mobility edge in qusi-periodic disordered models. Based on this approximate method, we also propose an index to indicate the degree of localization of each eigenstate.

The rapid spreading of SARS-CoV-2 and its dramatic consequences, are forcing policymakers to take strict measures in order to keep the population safe. At the same time, societal and economical interactions are to be safeguarded. A wide spectrum of containment measures have been hence devised and implemented, in different countries and at different stages of the pandemic evolution. Mobility towards workplace or retails, public transit usage and permanence in residential areas constitute reliable tools to indirectly photograph the actual grade of the imposed containment protocols. In this paper, taking Italy as an example, we will develop and test a deep learning model which can forecast various spreading scenarios based on different mobility indices, at a regional level. We will show that containment measures contribute to "flatten the curve" and quantify the minimum time frame necessary for the imposed restrictions to result in a perceptible impact, depending on their associated grade.

We study the evolution of multi-region bipartite entanglement entropy under locally scrambled quantum dynamics. We show that the multi-region entanglement can significantly modify the growth of single-region entanglement, whose effect has been largely overlooked in the existing literature. We developed a novel theoretical framework, called the entanglement feature formalism, to organize all the multi-region entanglement systematically as a sign-free many-body state. We further propose a two-parameter matrix product state (MPS) ansatz to efficiently capture the exponentially many multi-region entanglement features. Using these tools, we are able to study the multi-region entanglement dynamics jointly and represent the evolution in the MPS parameter space. By comparing the dynamical constraints on the motion of entanglement cuts, we are able to identify different quantum dynamics models in a unifying entanglement feature Hamiltonian. Depending on the quantum dynamics model, we find that multi-region effects can dominate the single region entanglement growth and only vanish for Haar random circuits. We calculate the operator-averaged out-of-time-order correlator based on the entanglement feature Hamiltonian and extract the butterfly velocity from the result. We show that the previously conjectured bound between the entanglement velocity and the butterfly velocity holds true even under the influence of multi-region entanglement. These developments could enable more efficient numerical simulations and more systematic theoretical understandings of the multi-region entanglement dynamics in quantum many-body systems.

We study numerically the population transfer protocol on the Quantum Random Energy Model and its relation to quantum computing, for system sizes of n≤20 quantum spins. We focus on the energy matching problem, i.e. finding multiple approximate solutions to a combinatorial optimization problem when a known approximate solution is provided as part of the input. We study the delocalization process induced by the population transfer protocol by observing the saturation of the Shannon entropy of the time-evolved wavefunction as a measure of its spread over the system. The scaling of the value of this entropy at saturation with the volume of the system identifies the three known dynamical phases of the model. In the non-ergodic extended phase, we observe that the time necessary for the population transfer to complete follows a long-tailed distribution. We devise two statistics to quantify how effectively and uniformly the protocol populates the target energy shell. We find that population transfer is most effective if the transverse-field parameter Γ is chosen close to the critical point of the Anderson transition of the model. In order to assess the use of population transfer as a quantum algorithm we perform a comparison with random search. We detect a "black box" advantage in favour of PT, but when the running times of population transfer and random search are taken into consideration we do not see strong indications of a speedup at the system sizes that are accessible to our numerical methods. We discuss these results and the impact of population transfer on NISQ devices.

Finite-size effects have been a major and justifiable source of concern for studies of many-body localization, and several works have been dedicated to the subject. In this paper, however, we discuss yet another crucial problem that has received much less attention, that of the lack of self-averaging and the consequent danger of reducing the number of random realizations as the system size increases. By taking this into account and considering ensembles with a large number of samples for all system sizes analyzed, we find that the generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2 chain close to the transition point to localization are described remarkably well by an exact analytical expression derived for the non-interacting Fibonacci lattice, thus providing an additional tool for studies of many-body localization.

In this work we establish a relation between entanglement entropy and fractal dimension D of generic many-body wave functions, by generalizing the result of Don N. Page [Phys. Rev. Lett. 71, 1291] to the case of {\it sparse} random pure states (S-RPS). These S-RPS living in a Hilbert space of size N are defined as normalized vectors with only N D ( 0≤D≤1 ) random non-zero elements. For D=1 these states used by Page represent ergodic states at infinite temperature. However, for 0<D<1 the S-RPS are non-ergodic and fractal as they are confined in a vanishing ratio N D /N of the full Hilbert space. Both analytically and numerically, we show that the mean entanglement entropy S 1 (A) of a subsystem A , with Hilbert space dimension N A , scales as S 1 ¯ ¯ ¯ ¯ ¯ (A)∼DlnN for small fractal dimensions D , N D < N A . Remarkably, S 1 ¯ ¯ ¯ ¯ ¯ (A) saturates at its thermal (Page) value at infinite temperature, S 1 ¯ ¯ ¯ ¯ ¯ (A)∼ln N A at larger D . Consequently, we provide an example when the entanglement entropy takes an ergodic value even though the wave function is highly non-ergodic. Finally, we generalize our results to Renyi entropies S q (A) with q>1 and to genuine multifractal states and also show that their fluctuations have ergodic behavior in narrower vicinity of the ergodic state, D=1 .

We consider the quasiperiodic Aubry-André chain in the insulating regime with localised single-particle states. Adding local interaction leads to the emergence of extended correlated two-particle bound states. We analyse the nature of these states including their multifractality properties. We use a projected Green function method to compute numerically participation numbers of eigenstates and analyse their dependence on the energy and the system size. We then perform a scaling analysis. We observe multifractality of correlated extended two-particle bound states, which we confirm independently through exact diagonalisation.

We demonstrate the design of a neural network, where all neuromorphic computing functions, including signal routing and nonlinear activation are performed by spin-wave propagation and interference. Weights and interconnections of the network are realized by a magnetic field pattern that is applied on the spin-wave propagating substrate and scatters the spin waves. The interference of the scattered waves creates a mapping between the wave sources and detectors. Training the neural network is equivalent to finding the field pattern that realizes the desired input-output mapping. A custom-built micromagnetic solver, based on the Pytorch machine learning framework, is used to inverse-design the scatterer. We show that the behavior of spin waves transitions from linear to nonlinear interference at high intensities and that its computational power greatly increases in the nonlinear regime. We envision small-scale, compact and low-power neural networks that perform their entire function in the spin-wave domain.

An accurate description of electron-ion interactions in materials is crucial for our understanding of their equilibrium and non-equilibrium properties. Here, we assess the properties of frictional forces experienced by ions in non-crystalline metallic systems, including liquid metals and warm dense plasmas, that arise from electronic excitations driven by the nuclear motion due to the presence of a continuum of low-lying electronic states. To this end, we perform detailed ab-initio calculations of the full friction tensor that characterizes the set of friction forces. The nonadiabatic electron-ion interactions introduce hydrodynamic couplings between the ionic degrees of freedom, which are sizeable between nearest neigbors. The friction tensor is generally inhomogeneous, anisotropic and non-diagonal, especially at lower densities.