Experiments on chains of Rydberg atoms appear as a playground to study quantum phase transitions in 1D. As a natural extension, we report a quantitative ground-state phase diagram of Rydberg atoms arranged in a two-leg ladder interacting via van der Waals potential. We address this problem numerically, using the density matrix renormalization group algorithm. Our results suggest that, quite remarkably, ${\mathbb{Z}}_k$ crystalline phases, with the exception of the checkerboard phase, appear in pairs characterized by the same pattern of occupied rungs but distinguishable by a spontaneously broken ${\tilde{\mathbb{Z}}}_2$ symmetry between the two legs of the ladder. Within each pair, the two phases are separated by a continuous transition in the Ising universality class, which eventually fuses with the ${\mathbb{Z}}_k$ transition, whose nature depends on $k$. According to our results, the transition into the ${\mathbb{Z}}_2\otimes {\tilde{\mathbb{Z}}}_2$ phase changes its nature multiple times, including an Ashkin-Teller transition that is surprisingly stable over an extended interval, followed by the ${\mathbb{Z}}_4$-chiral transition, and finally in a two step-process mediated melting via the floating phase. The transition into the ${\mathbb{Z}}_3$ phase with resonant states on the rungs belongs to the three-state Potts universality class at the commensurate point, to the ${\mathbb{Z}}_3$-chiral Huse-Fisher universality class away from it, and eventually it is through an intermediate floating phase. The Ising transition between ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_3\otimes {\tilde{\mathbb{Z}}}_2$ phases, entering the floating phase, opens the possibility to realize lattice supersymmetry in Rydberg quantum simulators.

It is well known that simulating quantum circuits with low but nonzero hardware noise is more difficult than without noise. It requires either to perform density matrix simulations (coming with a space overhead) or to sample over “quantum trajectories” where Kraus operators are inserted randomly (coming with a runtime overhead). We propose a simulation technique based on a representation of hardware noise in terms of trajectories generated by operators that remain close to identity at low noise. We give explicit expressions for noise that can be represented by Pauli channels, as well as for certain non-Pauli channels. This representation significantly reduces the variance over the quantum trajectories, speeding up noisy simulations by factors around 10 to 100. As a by-product, we provide a formula to factorize generic Pauli channels into a concatenation of channels involving only one nontrivial Pauli string.

Electron scattering cross sections are essential for the quantitative description of electron-induced processes in nanoconfined aqueous systems. Here we report on energy- and size-dependent cross sections for water clusters with diameters between $\sim 1.0$ and 2.5 nm and electron energies below $\sim 32$ eV. The cross sections of the clusters are up to a factor of 2 larger than those of water, suggesting a reduced dielectric screening in nanoconfinement. The cross sections show no significant cluster size dependence. A slight increase of cross sections with increasing electron energy is attributed to the increasing contribution from electronic scattering channels. As the simplest form of nanoconfined water, nanoscale water clusters represent an important model system.

In the search for accurate approximate solutions of the many-body Schrödinger equation, reduced density matrices play an important role, as they allow one to formulate approximate methods with polynomial scaling in the number of particles. However, these methods frequently encounter the issue of $N$-representability, whereby in self-consistent applications of the methods, the reduced density matrices become unphysical. A number of algorithms have been proposed in the past to restore a given set of $N$-representability conditions once the reduced density matrices become defective. However, these purification algorithms either have ignored symmetries of the Hamiltonian related to conserved quantities or have not incorporated them in an efficient way, thereby modifying the reduced density matrix to a greater extent than is necessary. In this paper, we present an algorithm capable of efficiently performing all of the following tasks in the least invasive manner: restoring a given set of $N$-representability conditions, maintaining contraction consistency between successive orders of reduced density matrices, and preserving all conserved quantities. We demonstrate the superiority of the present purification algorithm over previous ones in the context of the time-dependent two-particle reduced density matrix method applied to the quench dynamics of the Fermi-Hubbard model.

A consistent treatment of inhomogeneous diffusion requires a fully Hamiltonian formalism to account for the underlying couplings between various degrees of freedom. We do so by adopting a well-established approach, whereby the cold atom can be modeled as an open system nonlinearly coupled to a heat bath which mimics the light fields. By analyzing the explicit equation of motion for the system obtained, we demonstrate that there is not a microscopic correspondence to non-Gaussian thermal noise, as well as the spatial and momentum-dependent frictions giving play to the novel effects on anomalous diffusion. For application to cold atoms diffusing in dissipative optical lattices, we provide that the Hamiltonian-Langevin dynamics needed to be used to study this issue, because the drift coefficient and the partial diffusion coefficient are the momentum dependence and satisfy the fluctuation-dissipation theorem, however, the current phenomenological models lack a few momentum and coordinate coupling terms. Our results reveal that the mechanism of the spatial Lévy-like distribution of cold atoms originates from an intrinsic stochastic metastable potential.

Problems in the field of open quantum systems often involve an environment that strongly influences the dynamics of excited states. Here we present a numerical method to model optical spectra of non-Markovian open quantum systems. The method employs a process tensor framework to efficiently compute multitime correlations in a numerically exact way. To demonstrate the efficacy of our method, we compare 2D electronic spectroscopy simulations produced through our method to Markovian master equation simulations in three different system-bath coupling regimes.

We introduce two methods for quantum process and detector tomography. In the quantum process tomography method, we develop an analytical procedure for projecting the linear inversion estimation of a quantum channel onto the set of completely positive trace-preserving matrices. By integrating this method with alternate projection techniques, we achieve a three-order-of-magnitude improvement in approximating the closest quantum channel to an arbitrary Hermitian matrix compared to existing methods without compromising computational efficiency. Our second method extends this approach to quantum detector tomography, demonstrating superior efficiency compared to current techniques. Through numerical simulations, we evaluate our protocols across channels of up to four qubits in quantum process tomography and systems of up to six qubits in quantum detector tomography, showcasing superior precision and efficiency.

Understanding the mechanisms to mitigate opinion polarization in our society is crucial to minimizing social division and ultimately strengthening democracy. Due to the challenge of collecting long-term reliable empirical data, researchers have been mostly focused on a theoretical understanding of the process of opinion depolarization. To this aim, realistic yet simple models prove valuable, especially when multiple topics are discussed at the same time, which may result in entangled opinion dynamics. In this paper, we propose the multidimensional social compass model, based on two competing key ingredients: DeGroot learning, driven by the social influence exerted across multiple topics, and the preference of individuals to maintain their initial opinions. The interplay between these two mechanisms triggers a phase transition from polarization to consensus, determined by a threshold value of social influence. We analytically study the nature of the depolarization transition and its threshold, depending on the number of topics discussed, the possible correlations between initial opinions, the topology of the underlying social networks, and the correlations between the initial opinion distribution and the network's structure. Theoretical predictions are validated by running numerical simulations on both synthetic and real social networks. We rely on several simplifying assumptions to explore different scenarios, such as a mean-field approximation for high dimension or orthogonal initial orientations. We uncover an upper critical dimension ($D_c=5$ topics) for uncorrelated initial opinions, distinguishing between discontinuous and continuous phase transitions. For the simplest $D=2$ case and correlated initial opinions, we found that the depolarization threshold can vanish if the underlying connectivity is heterogeneous, as predicted by perturbation theory. Such an effect is due to the presence of hubs, which promote consensus in the population. We test this hypothesis by designing a rewiring algorithm that increases the structural heterogeneity of the underlying network, showing that the depolarization threshold decreases. Finally, we demonstrate that if hubs share the same initial opinion, the depolarization dynamics is significantly hindered. Our findings contribute to understanding the mechanisms to mitigate polarization in real-world scenarios, suggesting which settings can promote the depolarization process. The presence of very popular individuals on online social networks and the alignment of their opinions, in particular, may play a pivotal role in the multidimensional depolarization dynamics.

Weak measurement enables the extraction of targeted information from a quantum system while minimizing decoherence due to measurement backaction. However, in many-body quantum systems, backaction can have unexpected effects on wave-function collapse. We theoretically study a minimal many-particle model consisting of weakly measured noninteracting fermions in a one-dimensional lattice. Repeated measurement of the on-site occupation number with single-site resolution stochastically drives the system toward a Fock state, regardless of the initial state. This need not be the case for measurements that do not, even in principle, have single-site spatial resolution. We numerically show for systems with up to 16 sites that decreasing the spatial resolution strongly affects both the rate of stochastic evolution for each quantum trajectory and the allowed final states. The full Hilbert space can be partitioned into backaction-free subspaces (BFSs), the elements of which are indistinguishable for these measurements. Repeated measurements will drive any initial state into a single BFS, leading to a steady state that is a fixed point of the measurement process. We exactly calculate the properties of these BFSs for systems up to 32 sites, and we find that even for moderate reductions in measurement resolution, they yield nontrivial steady-state entanglement and coherence.

Despite its ubiquitous practical impact, the physics of sorption in hygroscopic materials is still under debate. One major, but not yet understood, characteristic is the sorption-desorption hysteresis observed with such systems despite the absence of capillary effects. Here, through an experimental and theoretical approach, we show that this hysteresis is intimately linked to sorption-induced deformation, and more precisely to the existence of a compressive stress state opposing the swelling of the material. First, with the help of magnetic resonance imaging, in contrast with most previous studies, we get a detailed picture of the moisture distribution and transport through the thickness of a model cellulosic material under well-controlled humidity boundary conditions, which makes it possible to identify the actual local sorption dynamics and equilibrium. We observe that the sorption can be hampered, whereas the desorption process is instantaneous at our scale of observation. Interestingly, only sufficiently compacted samples exhibit reduced sorption, suggesting that the mechanical stress is central. Then, based on a statistical thermodynamic and poromechanical approach, we propose a model coupling adsorption and pressure that predicts our observation. This model is fully parametrized from independent tests, and it suggests that sorption is significantly affected when sample compaction exceeds a few megapascals. These developments clarify the link between adsorption hysteresis and mechanics with important implications for biopolymers sensitive to moisture (wood, textiles, paper, etc.).

Disorder, traditionally believed to hinder the propagation of waves, has recently been shown to prompt the occurrence of topological phase transitions. For example, when disorder strength continuously increases and surpasses a certain critical value, a transition from topologically trivial to nontrivial insulating phases can occur. However, in the nontrivial phase region, it remains unclear whether a finer phase diagram can be further classified by varying disorder strengths. Here, we present a successive topological phase transition driven by the disorder strength in a higher-order topological insulator with long-range couplings. As the disorder strength gradually increases, the real-space topological invariant of the system undergoes a consecutive change from 0 to 4, accompanied by a stepped increase in the number of boundary-localized corner states. Our work opens a pathway for utilizing disorder to induce phase transitions among different higher-order topological insulators.

The concept of the irreducible mass ($M_{\mathrm{irr}}$) has led to the mass-energy ($M$) formula of a Kerr black hole (BH), in turn leading to its surface area $S=16\pi M_{\mathrm{irr}}^2$. This also allowed the coeval identification of the reversible and irreversible transformations, soon followed by the concepts of extracted and extractable energy. This new conceptual framework avoids inconsistencies recently evidenced in a repetitive Penrose process. We consider repetitive decays in the ergosphere of an initially extreme Kerr BH and show the processes are highly irreversible. For each decay, the particle that the BH captures causes an increase of the irreducible mass (so the BH horizon), much larger than the extracted energy. The energy extraction process stops when the BH reaches a positive spin lower limit set by the process boundary conditions. Thus, the reaching of a final nonrotating Schwarzschild BH state through this accretion process is impossible. We have assessed such processes for selected decay radii and incoming particle with rest mass $1\%$ of the BH initial mass $M_0$. For $r=1.2M$ and $1.9M$, the sequence stops after 8 and 34 decays, respectively, at a spin 0.991 and 0.857, the energy extracted has been only $1.16\%$, and $0.42\%$, the extractable energy is reduced by $17\%$ and $56\%$, and the irreducible mass increases by $5\%$ and $22\%$, all values in units of $M_0$. These results show the highly nonlinear change of the BH parameters, dictated by the BH mass-energy formula, and that the BH rotational energy is mainly converted into irreducible mass. Thus, evaluating the irreducible mass increase in any energy extraction processes in the Kerr BH ergosphere is mandatory.

Numerical simulations of turbulent flows are well known to pose extreme computational challenges because of the huge number of dynamical degrees of freedom required to correctly describe the complex multiscale statistical correlations of the velocity. On the other hand, kinetic mesoscale approaches based on the Boltzmann equation, have the potential to describe a broad range of flows, stretching well beyond the special case of gases close to equilibrium, which results in the ordinary Navier-Stokes dynamics. Here, we demonstrate that, by properly tuning, a kinetic approach can statistically reproduce the quantitative dynamics of the larger scales in turbulence, thereby providing an alternative, computationally efficient and physically rooted approach toward subgrid scale (SGS) modeling in turbulence. More specifically, we show that by leveraging data from fully resolved direct numerical simulation (DNS), we can learn a collision operator for the discretized Boltzmann equation solver (the lattice Boltzmann method), which effectively implies a turbulence subgrid closure model. The mesoscopic nature of our formulation makes the learning problem fully local in both space and time, leading to reduced computational costs and enhanced generalization capabilities. We show that the model offers superior performance compared to traditional methods, such as the Smagorinsky model, being less dissipative and, therefore, able to more closely capture the intermittency of higher-order velocity correlations. This foundational study lays the basis for extending the proposed framework to different turbulent flow settings and—most importantly—to develop new classes of hybrid data-driven kinetic-based models capable of faithfully capturing the complex macroscopic dynamics of diverse physical systems such as emulsions, non-Newtonian fluid, and multiphase systems.

Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as distinguishing between phases of matter or quantum processes. Similarly, one can consider a more general problem of regression, when the aim is to predict continuous labels quantifying properties of quantum states, such as purity or entanglement. In this work, we propose a method for predicting such properties. The method is based on the notion of parametrized quantum circuits, and it seeks to find an observable the expectation of which gives the prediction of the property of interest with a low variance. We numerically test our approach in learning to predict (i) the parameter of a parametrized channel given its output state, (ii) entanglement of two-qubit states, and (iii) the parameter of a parametrized Hamiltonian given its ground state. The results show that the proposed method is able to find observables such that they provide highly accurate predictions of the considered properties, and in some cases even saturate the Cramer-Rao bound, which characterizes the prediction error. We also compare our method with the Bayesian approach, and find that the latter prefers to minimize the prediction variance, having therefore a larger bias.