We investigate how brain activity can be supported by a turbulent regime based on the deviations of a self-similar scaling of high-order structure functions within the phenomenological Kolmogorov's theory. By analyzing a large neuroimaging data set, we establish the relationship between scaling exponents and their order, showing that brain activity has more than one invariant scale, and thus orders higher than 2 are needed to accurately describe its underlying statistical properties. Furthermore, we build whole-brain models of coupled oscillators to show that high-order information allows for a better description of the brain's empirical information transmission and reactivity.

Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schrödinger equation (HSE), which can be promising in simulating three-dimensional turbulent flows in various engineering applications. The HSE is derived by generalizing the Madelung transform to compressible or incompressible flows with finite vorticity and dissipation. Since the HSE is expressed as a unitary operator on a two-component wave function, it is more suitable than the NSE for quantum computing. The flow governed by the HSE can resemble a turbulent flow consisting of tangled vortex tubes with the five-thirds scaling of energy spectrum. We develop a prediction-correction quantum algorithm to solve the HSE. This algorithm is implemented for simple flows on the quantum simulator Qiskit with partial exponential speedup.

Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models, they remain an open question for interacting bosonic systems. In this work, we present a precise definition of quantum phases for non-Hermitian systems and propose a family of phases referred to as composite quantum phases. We demonstrate the existence of these phases in a one-dimensional spin-1 system and show their robustness against perturbations through numerical simulations. Furthermore, we investigate the phase diagram of our model, indicating the extensive presence of these phases in non-Hermitian systems. Our work establishes an alternate framework for studying and constructing quantum phases in non-Hermitian interacting systems, revealing exciting possibilities beyond the single-particle picture.

The flow of electric current through a two-dimensional material in a magnetic field gives rise to the family of Hall effects. The quantum versions of these effects accommodate robust electronic edge channels and fractional charges. Recently, the Hall effect of skyrmions, classical magnetic quasiparticles with a quantized topological charge, has been theoretically and experimentally reported, igniting ideas on a quantum version of this effect. To this end, we perform dynamical mean-field-theory calculations on localized $f$ electrons coupled to itinerant $c$ electrons in the presence of spin-orbit interaction and a magnetic field. Our calculations reveal localized quantum nanoskyrmions that start moving transversally when a charge current in the itinerant electrons is applied. The results show the time-transient buildup of the quantum skyrmion Hall effect, accompanied by an Edelstein effect and a magnetoelectric effect that rotate the spins. This work motivates studies about the steady state of the quantum skyrmion Hall effect, looking for eventual quantum skyrmion edge channels and their transport properties.

Complex interactions among a large number of individuals lead to multiple patterns of collective human behavior. However, the theoretical prediction of pattern transitions has not been empirically confirmed. This is because in previous empirical studies, different patterns were observed in different systems, and the coexistence of multiple patterns in the same system was rarely found. By investigating nearly 10 million messages in 252 QQ groups, we find rich distribution patterns of interevent time for human collective behavior, including the transitions between bimodal distribution, double-power-law distribution, and single-power-law distribution. The model developed in this paper suggests that human physiological rhythms and the high collective activity play key roles in the presentation of the single-power-law distribution. These results enhance the empirical research in the field of human dynamics, and are helpful for understanding many complex socioeconomic phenomena.

In this work we develop the theory of the Loschmidt echo and dynamical phase transitions in noninteracting strongly disordered Fermi systems after a quench. In finite systems the Loschmidt echo displays zeros in the complex time plane that depend on the random potential realization. Remarkably, the zeros coalesce to form a 2D manifold in the thermodynamic limit, atypical for 1D systems, crossing the real axis at a sharply defined critical time. We show that this dynamical phase transition can be understood as a transition in the distribution function of the smallest absolute value of the eigenvalues of the Loschmidt matrix and develop a finite-size scaling theory. Contrary to expectations, the notion of dynamical phase transitions in disordered systems becomes decoupled from the equilibrium Anderson localization transition. Our results highlight the striking qualitative differences of quench dynamics in disordered and nondisordered many-fermion systems.

Neuronal systems need to process temporal signals. Here, we show how higher-order temporal (co)fluctuations can be employed to represent and process information. Concretely, we demonstrate that a simple biologically inspired feedforward neuronal model can extract information from up to the third-order cumulant to perform time series classification. This model relies on a weighted linear summation of synaptic inputs followed by a nonlinear gain function. Training both the synaptic weights and the nonlinear gain function exposes how the nonlinearity allows for the transfer of higher-order correlations to the mean, which in turn enables the synergistic use of information encoded in multiple cumulants to maximize the classification accuracy. The approach is demonstrated both on synthetic and real-world datasets of multivariate time series. Moreover, we show that the biologically inspired architecture makes better use of the number of trainable parameters than a classical machine-learning scheme. Our findings emphasize the benefit of biological neuronal architectures, paired with dedicated learning algorithms, for the processing of information embedded in higher-order statistical cumulants of temporal (co)fluctuations.

With the help of scanning tunneling microscopy (STM) it has become possible to address single magnetic impurities on superconducting surfaces and to investigate the peculiar properties of the in-gap states known as Yu-Shiba-Rusinov (YSR) states. These systems are an ideal playground to investigate multiple aspects of superconducting bound states, such as the occurrence of quantum phase transitions or the interplay between Andreev transport physics and the spin degree of freedom, with profound implications for disparate topics like Majorana modes or Andreev spin qubits. However, until very recently YSR states were only investigated with conventional tunneling spectroscopy, missing the crucial information contained in other transport properties such as shot noise. In this paper we adapt the concept of full counting statistics (FCS) to provide the deepest insight thus far into the spin-dependent transport in these hybrid atomic-scale systems. We illustrate the power of FCS by analyzing different situations in which YSR states show up including single-impurity junctions with a normal and a superconducting STM tip, as well as double-impurity systems where one can probe the tunneling between individual YSR states [Nat. Phys. 16, 1227 (2020)]. The FCS concept allows us to unambiguously identify every tunneling process that plays a role in these situations and to classify them according to the charge transferred in them. Moreover, FCS provides all the relevant transport properties, including current, shot noise, and all the cumulants of the current distribution. In particular, our approach is able to reproduce the experimental results recently reported on the shot noise of a single-impurity junction with a normal STM tip [Phys. Rev. Lett. 128, 247001 (2022)]. We also predict the signatures of resonant (and nonresonant) multiple Andreev reflections in the shot noise and Fano factor of single-impurity junctions with two superconducting electrodes and show that the FCS approach allows us to understand conductance features that have been incorrectly interpreted in the literature. In the case of double-impurity junctions we show that the direct tunneling between YSR states is characterized by a strong reduction of the Fano factor that reaches a minimum value of $7/32$, a significant result in quantum transport. The FCS approach presented here can be naturally extended to investigate the spin-dependent superconducting transport in a variety of situations, such as atomic spin chains on surfaces or superconductor-semiconductor nanowire junctions, and it is also suitable to analyze multiterminal superconducting junctions, irradiated contacts, and many other basic situations.

Quantum entanglement phase transitions have provided new insights into quantum many-body dynamics. Both disorders and measurements are found to induce similar entanglement transitions. Here, we provide a theoretical framework that unifies these two seemingly disparate concepts and discloses their internal connections. Specifically, we analytically analyze a $d$-dimensional free-fermion gas subject to continuous projective measurements. By mapping the Lindblad master equation to the functional Keldysh field theory, we develop an effective theory termed as the time-local Keldysh nonlinear sigma model, which enables us to analytically describe the physics of the monitored system. Our effective theory resembles that used to describe the disordered fermionic systems. As an application of the effective theory, we study the transport property and obtain a Drude-form conductivity where the elastic scattering time is replaced by the inverse measurement strength. According to these similarities, two different concepts, measurements and disorders, are unified in the same theoretical framework. A numerical verification of our theory and predictions is also provided.

We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial state. After examining adiabatic versions of certain keystone circuit-based quantum algorithms, this technique is applied to adiabatic quantum algorithms with undetermined speedup. In particular, we analytically obtain lower bounds on adiabatic algorithms for finding $k$-clique in random graphs. Additionally, for a particular class of Hamiltonian, it is straightforward to prove the equivalence between our framework and the conventional approach based on spectral gap analysis.

We study an atom-cavity hybrid system where fermionic atoms in a one-dimensional lattice are subject to a cavity-induced dynamic gauge potential. The gauge coupling leads to highly degenerate steady states in which the fermions accumulate to one edge of the lattice under an open boundary condition. Such a phenomenon originates from the many-body Liouvillian superoperator of the system, which, being intrinsically non-Hermitian, is unstable against boundary perturbations and manifests the non-Hermitian skin effect. Contrary to the single-body case, the steady state of a multiatom system is approached much slower under the open boundary condition, as the long-time damping of the cavity mode exhibits distinct rates at different times. This stagewise slowdown is attributed to the competition between light-assisted hopping and the dynamic gauge coupling, which significantly reduces the steady-state degeneracy under the open boundary condition, as distinct hosts of quasisteady states dominate the dynamics at different timescales.

We present a method to constrain local charge multipoles within density-functional theory. Such multipoles quantify the anisotropy of the local charge distribution around atomic sites and can indicate potential hidden orders. Our method allows selective control of specific multipoles, facilitating a quantitative exploration of the energetic landscape outside of local minima. Thus, it enables a clear distinction between electronically and structurally driven instabilities. We demonstrate the effectiveness of this method by applying it to charge quadrupoles in the prototypical orbitally ordered material ${\mathrm{KCuF}}_3$. We quantify intersite multipole-multipole interactions as well as the energy-lowering related to the formation of an isolated local quadrupole. We also map out the energy as a function of the size of the local quadrupole moment around its local minimum, enabling quantification of multipole fluctuations around their equilibrium value. Finally, we study charge quadrupoles in the solid solution ${\mathrm{KCu}}_{1-x}{\mathrm{Zn}}_x{\mathrm{F}}_3$ to characterize the behavior across the tetragonal-to-cubic transition. Our method provides a powerful tool for studying symmetry breaking in materials with coupled electronic and structural instabilities and potentially hidden orders.

We present an approach to entanglement purification on complex quantum network architectures, that is, how a quantum network built from repeaters with limited processing fidelity can purify and distribute entanglement between users. In particular, we explore how noisy gates, depolarizing channels, and finite memory storage time influence the performance of entanglement purification in a quantum network. Finally, we apply the purification techniques we developed in the context of entanglement routing for different quantum network topologies in an effort to inform future design choices for quantum network configurations.

Waves propagating in certain one-dimensional quasiperiodic lattices are known to exhibit a sharp localization transition. We theoretically predict and experimentally observe that the localization of light in one-dimensional photonic quasicrystals is followed by a second delocalization transition for some states on increasing quasiperiodic modulation strength—an example of a reentrant transition. We further propose that this phenomenon can be qualitatively captured by a dimerized tight-binding model with long-range couplings. This work furthers our understanding of localization physics in complex systems and the impact of quasiperiodicity on light transport in photonic devices.

Inspired by the progress on the spin liquid candidates ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ where the Ce ions carry the dipole-octupole doublets, we analyze the distinction between the thermodynamic and spectroscopic measurements for the octupolar U(1) spin liquid. Due to the peculiar properties of octupolar U(1) spin liquid and the selective Zeeman coupling, both uniform susceptibility and the spectroscopic measurements only probe the spinon excitations, while the specific heat measures all excitations. After clarifying the contents in each measurement, we observe that, thermodynamics carries the information of single spinon, while the spectroscopy is associated with spinon pairs. Such distinction immediately leads to the multiplicity relation of the excitation gaps from different measurements that include the uniform susceptibility, Knight shift, and $1/T_1$ spin lattice relaxation of NMR and $\mu \mathrm{SR}$, and the inelastic neutron scattering measurements. We hope this work provides a useful recipe for the identification of fractionalization in the octupolar U(1) spin liquid and other spin liquids.

According to both Bohmian and stochastic quantum mechanics, the standard quantum mechanical kinetic energy can be understood as consisting of two hidden-variable components. One component is associated with the current (or Bohmian) velocity, while the other is associated with the osmotic velocity (or quantum potential), and they are identified with the phase and the amplitude, respectively, of the wave function. These two components are experimentally accessible through the real and imaginary parts of the weak value of the momentum postselected in position. In this paper, a kinetic energy equipartition is presented as a signature of quantum thermalization in closed systems. This means that the expectation value of the standard kinetic energy is equally shared between the expectation values of the squares of these two hidden-variable components. Such components cannot be reached from expectation values linked to typical Hermitian operators. To illustrate these concepts, numerical results for the nonequilibrium dynamics of a few-particle harmonic trap under random disorder are presented. Furthermore, the advantages of using the center-of-mass frame of reference for dealing with systems containing many indistinguishable particles are also discussed.

Quantum droplets are a quantum analog to classical fluid droplets in that they are self-bound and display liquid-like properties—such as incompressibility and surface tension—though their stability is the result of quantum fluctuations. One of the major systems for observing quantum droplets is two-component Bose gases. Two-component droplets are typically considered to be balanced, having a fixed ratio between the densities of the two components. This work goes beyond the fixed density ratio by investigating spherical droplets in imbalanced mixtures. With increasing imbalance, the droplet is able to lower its energy up to a limit, at which point the droplet becomes saturated with the atoms of the majority component and any further atoms added to this component cannot bind to the droplet. Analyzing the breathing mode dynamics of imbalanced droplets indicates that the droplet can emit particles, as in balanced mixtures, but the imbalance leads to an intricate superposition of multiple simultaneously decaying collective oscillations.