*Phys Rev E ; 105(1-1): 014109, 2022 Jan.*

##### RESUMO

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in midspectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the midspectrum eigenstates.

*Phys Rev Lett ; 124(20): 200602, 2020 May 22.*

##### RESUMO

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 Page [Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291] to the case of sparse random pure states (SRPS). These SRPS living in a Hilbert space of size N are defined as normalized vectors with only N^{D} (0≤D≤1) random nonzero elements. For D=1, these states used by Page represent ergodic states at an infinite temperature. However, for 0

*Phys Rev E ; 100(3-1): 032117, 2019 Sep.*

##### RESUMO

Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size. However, the approach to the limiting behavior is remarkably slow. Thus, an understanding of the scaling and finite-size properties of fractal dimensions is essential. We present such a study for random matrix ensembles, and compare with two chaotic quantum systems-the kicked rotor and a spin chain. For random matrix ensembles we analytically obtain the finite-size dependence of the mean behavior of the multifractal dimensions, which provides a lower bound to the typical (logarithmic) averages. We show that finite statistics has remarkably strong effects, so that even random matrix computations deviate from analytic results (and show strong sample-to-sample variation), such that restoring agreement requires exponentially large sample sizes. For the quantized standard map (kicked rotor) the multifractal dimensions are found to follow the random matrix predictions closely, with the same finite statistics effects. For a XXZ spin-chain we find significant deviations from the random matrix prediction-the large-size scaling follows a system-specific path towards unity. This suggests that local many-body Hamiltonians are "weakly ergodic," in the sense that their eigenfunction statistics deviate from random matrix theory.

*Phys Rev Lett ; 122(23): 230602, 2019 Jun 14.*

##### RESUMO

We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of electrons transferred between two metallic islands in the Coulomb blockade regime. Our experimental results are in excellent agreement with numerical calculations based on a recent theory describing the exact first-passage-time distributions for any nonequilibrium stationary Markov process. We also derive a simple analytical approximation for the first-passage-time distribution, which takes into account the non-Gaussian statistics of the electron transport, and show that it describes the experimental distributions with high accuracy. This universal approximation describes a wide class of stochastic processes, and can be used beyond the context of mesoscopic charge transport. In addition, we verify experimentally a fluctuation relation between the first-passage-time distributions for positive and negative thresholds.

*Phys Rev Lett ; 122(7): 070601, 2019 Feb 22.*

##### RESUMO

The eigenstate thermalization hypothesis (ETH) is one of the cornerstones of contemporary quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this Letter. We report on the construction of highly nonlocal operators, behemoths, that are building blocks for various kinds of local and nonlocal operators. The behemoths have a singular distribution and width wâ¼D^{-1} (D being the Hilbert space dimension). From there, one may construct local operators with the ordinary Gaussian distribution and wâ¼D^{-1/2} in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with wâ¼D^{-Î´}, 0<Î´<1/2. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of nonintegrable many-body systems.

*Beilstein J Nanotechnol ; 9: 1184-1193, 2018.*

##### RESUMO

We study the influence of the inverse proximity effect on the superconductivity nucleation in hybrid structures consisting of semiconducting nanowires placed in contact with a thin superconducting film and discuss the resulting restrictions on the operation of Majorana-based devices. A strong paramagnetic effect for electrons entering the semiconductor together with spin-orbit coupling and van Hove singularities in the electronic density of states in the wire are responsible for the suppression of superconducting correlations in the low-field domain and for the reentrant superconductivity at high magnetic fields in the topologically nontrivial regime. The growth of the critical temperature in the latter case continues up to the upper critical field destroying the pairing inside the superconducting film due to either orbital or paramagnetic mechanism. The suppression of the homogeneous superconducting state near the boundary between the topological and non-topological regimes provides the conditions favorable for the Fulde-Ferrel-Larkin-Ovchinnikov instability.