Fermi-surface fluctuations and lattice instabilities in the two-dimensional metallic kagome superconductor ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ are elucidated via polarization-resolved Raman spectroscopy. The presence of a weak electronic continuum in high-quality samples marks the crossover into the charge-density-wave (CDW) ordered phase, while impurity-rich samples promote strong defect-induced electronic scattering processes that affect the coherence of the CDW phase. CDW-induced phonon anomalies appear below $T_{\mathrm{CDW}}$, with emergent $C2$ symmetry for one of the CDW amplitude modes, alluding to nematicity. In conjunction with symmetry-breaking lattice distortions, a kinklike hardening of the $A_{1g}$ phonon energy at $T_{\mathrm{CDW}}$ signifies a concerted interplay of electronic correlations and electron-phonon coupling in the exotic CDW order.

Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of constraint equations efficiently using a self-learning emulator. A self-learning emulator is an active learning protocol that can be used with any emulator that faithfully reproduces the exact solution at selected training points. The key ingredient is a fast estimate of the emulator error that becomes progressively more accurate as the emulator is improved, and the accuracy of the error estimate can be corrected using machine learning. We illustrate with three examples. The first uses cubic spline interpolation to find the solution of a transcendental equation with variable coefficients. The second example compares a spline emulator and a reduced basis method emulator to find solutions of a parametrized differential equation. The third example uses eigenvector continuation to find the eigenvectors and eigenvalues of a large Hamiltonian matrix that depends on several control parameters.

The key to obtaining a mechanistic and reliable understanding of complex public opinion formation processes is to identify the main mechanism governing interpersonal influence. Researchers have long been exploring simple yet predictive mathematical models of opinion dynamics. Although most models are based on the assumption that individuals update their opinions by averaging others' opinions, researchers might need to rethink this universally adopted micro-foundation. The deceivingly simple weighted-averaging mechanism features a non-negligible unrealistic implication, which brings unnecessary difficulties in seeking a proper balance between model complexity and predictive power. In this paper, we fundamentally resolve this problem by proposing the weighted-median mechanism as a new micro-foundation of opinion dynamics. Such an inconspicuous change from averaging to median leads to rich consequences. The weighted-median mechanism, derived from the cognitive dissonance theory in psychology, is well supported by online experiment data. It also broadens the applicability of opinion dynamics models to multiple-choice issues with ordered discrete options, e.g., political elections. Moreover, comparative studies show that the weighted-median mechanism predicts various real-world patterns of opinion evolution while some widely studied averaging-based models fail to, including how group structure affects the likelihood of reaching consensus and how extreme opinions are located in social networks.

Branching with immigration is one of the most common models for the stochastic processes observed in neuronal circuits. However, it is not observed directly and, in order to create branching-like processes, the observed spike time series is processed by attaching time bins to spikes. It has been shown that results such as criticality and size distributions depend on the chosen time bin. A different methodology whose results do not depend on the choice of time bin might therefore be useful and is proposed in this article. This methodology circumvents using time bins altogether by replacing the previously used discrete-time models by continuous-time models. First, the article introduces and characterizes a continuous-time version of the branching process with immigration, which will be called the pumped branching process, and second, it presents an analytical derivation of the corresponding spike statistics, which can be directly compared to observed spike time series. The presented approach allows determining the degree of criticality, the average number of overlapping avalanches, and other observables without using a time bin. Furthermore, the effects caused by using time bins are analyzed and the influence of temporal and spatial subsampling discussed, all of which is compared to experimental data and supported by Monte Carlo simulations.

Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On another front, in condensed matter physics, topology is utilized to realize robust properties like topological edge modes, as demonstrated by celebrated topological insulators. Here, we integrate these two research avenues and propose a nonlinear topological phenomenon, namely, topological synchronization, where only the edge oscillators synchronize while the bulk ones exhibit chaotic dynamics. We analyze concrete prototypical models to demonstrate the presence of positive Lyapunov exponents and Lyapunov vectors localized along the edge. As a unique characteristic of topology in nonlinear systems, we find that unconventional extra topological boundary modes appear at emerging effective boundaries. Furthermore, our proposal shows promise for spatially controlling synchronization, such as on-demand pattern designing and defect detection. The topological synchronization can ubiquitously appear in topological nonlinear oscillators and thus can provide a guiding principle to realize synchronization in a robust, geometrical, and flexible way.

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here we address this challenge by using multifidelity learning, i.e., learning from multifidelity data sets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems.

This paper focuses on topological defects, appearing in mean-field-theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We begin by investigating the ambiguity and addition of topological charges using the mathematical formalism of covering spaces, which clarifies many aspects these phenomena. Subsequently, we classify topological-defect configurations consisting of several monopoles and unknotted ring defects in terms of homotopy groups and fundamental-group actions on them, thus generalizing the previous classifications of a single monopole and a single unknotted ring defect. Finally, we examine the decay of multiply charged topological monopoles under small perturbations of the physical system, and analyze the conditions under which multiply charged monopoles are inclined to split into several singly charged monopoles.

We analyze nonlinear optics schemes for generating pairs of quantum entangled plasmons in the terahertz-infrared range in graphene. We predict that high plasmonic field concentration and strong optical nonlinearity of monolayer graphene enables pair-generation rates much higher than those of conventional photonic sources. The first scheme we study is spontaneous parametric down conversion in a graphene nanoribbon. In this second-order nonlinear process a plasmon excited by an external pump splits into a pair of plasmons, of half the original frequency each, emitted in opposite directions. The conversion is activated by applying a dc electric field that induces a density gradient or a current across the ribbon. Another scheme is degenerate four-wave mixing where the counter-propagating plasmons are emitted at the pump frequency. This third-order nonlinear process does not require a symmetry-breaking dc field. We suggest nano-optical experiments for measuring position-momentum entanglement of the emitted plasmon pairs. We estimate the critical pump fields at which the plasmon generation rates exceed their dissipation, leading to parametric instabilities.

Dicke superradiance in ordered atomic arrays is a phenomenon where atomic synchronization gives rise to a burst in photon emission. This superradiant burst only occurs if there is one—or just a few—dominant decay channels. For a fixed atom number, this happens only below a critical interatomic distance. Here we show that array dimensionality is the determinant factor that drives superradiance. In two-dimensional (2D) and three-dimensional (3D) arrays, superradiance occurs due to constructive interference, which grows stronger with atom number. This leads to a critical distance that scales sublogarithmically with atom number in 2D, and as a power law in 3D. In one-dimensional arrays, superradiance occurs due to destructive interference that effectively switches off certain decay channels, yielding a critical distance that saturates with atom number. Our results provide a guide to explore many-body decay in state-of-the art experimental setups.

When studying a physical system, it is crucial to identify the degrees of freedom that characterize that system. Recently, specific neural networks have been designed to retrieve these underlying degrees of freedom automatically. Indeed, fed with data from a physical system, a variational autoencoder can learn a latent representation of that system that directly corresponds to its underlying degrees of freedom. However, the understanding of these neural networks is limited on two fronts. First, very little is known about the impact of the question vector, a key parameter in designing performant autoencoders. Second, there is the mystery of why the correct degrees of freedom are found in the latent representation, not an arbitrary function of these parameters. Both gaps in our understanding are addressed in this paper. To study the first question on the optimal design of the question vector, we investigate physical systems characterized by analytical expressions with a limited set of degrees of freedom. We empirically show how the type of question influences the learned latent representation. We find that the stochasticity of a random question is fundamental in learning physically meaningful representations. Furthermore, the dimensionality of the question vector should not be too large. To address the second question, we make use of a symmetry argument. We show that the learning of the degrees of freedom in the latent space is related to the symmetry group of the input data. This result holds for linear and nonlinear transformations of the degrees of freedom. In this way, in this paper, we contribute to the research on automated systems for discovery and knowledge creation.

We measure the real part ${\epsilon }^{\prime }$ of the dielectric permittivity of beryl crystals with heavy water molecules ${\mathrm{D}}_2\mathrm{O}$ confined in nanosized cages formed by an ionic crystal lattice. The experiments are performed at a frequency of 1 MHz in the temperature interval from 300 down to 4 K under different hydrostatic pressures up to $P=6.3$ GPa. At high temperatures, a Curie-Weiss-like increase of ${\epsilon }^{\prime }\left(T\right)$ is observed upon cooling. Application of pressure leads to flattening of ${\epsilon }^{\prime }\left(T\right)$ at low temperatures due to quantum effects, i.e., tunneling of deuterium atoms in the hexagonal localizing potential. Analyzing the temperature behavior of ${\epsilon }^{\prime }$ with the Barrett expression allows us to obtain pressure dependencies of the quantum temperature $T_1$, the Curie-Weiss temperature $T_C$, and the Barrett constant $C$. The increase of $T_1$ observed up to 4 GPa is associated with an enhanced azimuthal tunneling of the confined water molecules through the barriers of the potential. For $P>4$ GPa, $T_1\left(P\right)$ levels off since the barriers disappear. Any further pressure increase does not affect the tunneling rate because of the absence of a barrier. The behavior is modeled by solving the Schrödinger equation for the water molecule in the azimuthal potential numerically. Small negative values of $T_C\approx -10$ K obtained for $P<4$ GPa indicate the antiferroelectric ordering tendency of the water dipoles localized in the crystalline nanochannels. For higher pressure, a strong decrease of $T_C$ toward negative values is observed that would correspond to the enhanced interdipole coupling strength, which is however hard to explain in the present case, and thus calls for additional theoretical and experimental studies.

The investigation of optimal processes has a long history in the field of thermodynamics. It is well-known that finite-time processes which minimize dissipation often exhibit discontinuities. We use a combination of numerical and analytical approaches to study the driving cycle that maximizes the output in a simple model of a stochastic pump: a system driven out of equilibrium by a cyclic variation of external parameters. We find that this optimal solution is singular, with an infinite rate of switching between sets of parameters. The appearance of such singular solutions in thermodynamic processes is surprising, but we argue that such solutions are expected to be quite common in models whose dynamics exhibit exponential relaxation, as long as the driving period is not externally fixed and is allowed to be arbitrarily short. Our results have implications to artificial molecular motors that are driven in a cyclic manner.

We investigate the zero-bias behavior of Josephson junctions made of encapsulated graphene boron nitride heterostructures in the long ballistic junction regime. For temperatures down to $2.7$ K, the junctions appear nonhysteretic with respect to the switching and retrapping currents $I_C$ and $I_R$. A small nonzero resistance is observed even around zero-bias current and scales with temperature as dictated by the phase diffusion mechanism. By varying the graphene carrier concentration we are able to confirm that the observed phase diffusion mechanism follows the trend for an overdamped Josephson junction. This is in contrast with the majority of graphene-based junctions which are underdamped and shorted by the environment at high frequencies.

The interplay of a potential and magnetic disorder in superconductors has remained an active field of research for decades. Within the framework of the Usadel equation, we study the local density of states (LDOS) near a solitary classical magnetic impurity in a dirty superconducting film. We find that a potential disorder results in broadening of the $\delta$-function peak in the LDOS at the Yu-Shiba-Rusinov (YSR) energy. This broadening is proportional to the square root of a normal-state spreading resistance of the film. We demonstrate that modification of multiple scattering on the magnetic impurity due to intermediate scattering on surrounding potential disorder crucially affects a profile of the LDOS in the vicinity of the YSR energy. In addition, we find that a scanning-tunneling-microscopy tip can mask a YSR feature in the LDOS. Also, we study the LDOS near a chain of magnetic impurities situated in the normal region of a dirty superconductor/normal-metal junction. We find a resonance in the LDOS near the YSR energy. The energy scale of the resonant peak is controlled by the square root of the film resistance per square in the normal state.