Cultural diversity encoded within languages of the world is at risk, as many languages have become endangered in the last decades in a context of growing globalization. To preserve this diversity, it is first necessary to understand what drives language extinction, and which mechanisms might enable coexistence. Here, we study language shift mechanisms using theoretical and data-driven perspectives. A large-scale empirical analysis of multilingual societies using Twitter and census data yields a wide diversity of spatial patterns of language coexistence. It ranges from a mixing of language speakers to segregation with multilinguals on the boundaries of disjoint linguistic domains. To understand how these different states can emerge and, especially, become stable, we propose a model in which language coexistence is reached when learning the other language is facilitated and when bilinguals favor the use of the endangered language. Simulations carried out in a metapopulation framework highlight the importance of spatial interactions arising from people mobility to explain the stability of a mixed state or the presence of a boundary between two linguistic regions. Further, we find that the history of languages is critical to understand their present state.

We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert–Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert–Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert–Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert–Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert–Schmidt distributed states for various experimental conditions.

In strong field ionization, the pump pulse not only photoionizes the molecule, but also drives efficient population exchanges between its ionic ground and excited states. In this study, we investigate the population dynamics after strong field molecular photoionization, using angular distribution of dissociative fragments. Our results reveal that the first and third order processes of the post-ionization population redistribution mechanism (PPRM) in the ion can be disentangled and classified by its angle-resolved kinetic energy release (KER) spectra. We demonstrate that the imprints of PPRM in the KER spectra can be used to determine the branching ratio of the population exchange pathways of different orders, by exploiting the pump-intensity-dependent variation of the spectra.

Electron-electron (e-e) interaction is known as a source of logarithmic renormalizations for Dirac fermions in quantum field theory. The renormalization of electron-optical phonon coupling (EPC) by e-e interaction, which plays a pivotal role in hot carrier and phonon dynamics, has been discussed since the discovery of graphene. We investigate hot carrier dynamics and EPC strength using time-resolved ultrabroadband terahertz (THz) spectroscopy combined with numerical simulation based on the Boltzmann transport equation and a comprehensive temperature model. The numerical simulation demonstrates that the extrinsic carrier scatterings by the Coulomb potential of the charged impurity and surface polar phonons are significantly suppressed by the carrier screening effect and have negligible contributions to the THz photoconductivity in heavily doped graphene on polyethylene terephthalate (PET) substrate. The large negative photoconductivity and the non-Drude behavior of THz conductivity spectra appear under high pump fluence and can be attributed to the temporal variation of the hot carrier distribution and scattering rate. The transient reflectivity well reflects the EPC strength and temporal evolution of the hot carrier and optical phonon dynamics. We successfully estimate the EPC matrix element of the $A_1^{\prime }$ optical phonon mode near the $\mathbf{K}$ point as ${\langle D_{\mathbf{K}}^2\rangle }_{\mathrm{F}}\approx 450$ ${(\mathrm{eV}/\AA )}^2$ from the fitting of THz conductivity spectra and temporal evolution of transient THz reflectivity. The corresponding dimensionless EPC constant ${\lambda }_{\mathbf{K}}\approx 0.09$ at Fermi energy ${\varepsilon }_{\mathrm{F}}=0.43\mathrm{eV}$ is slightly larger than the prediction of the renormalization group approach including the dielectric screening effect of the PET substrate. This leads to a significant difference in hot carrier and phonon dynamics compared with those without the renormalization effect by the e-e interaction. This approach can provide a quantitative understanding of hot carrier and optical phonon dynamics and support the development of future graphene optoelectronic devices.

Transistors are key elements for enabling computational hardware in both classical and quantum domains. Here we propose a voltage-gated spin transistor using itinerant electrons in the Hubbard model which acts at the level of single electron spins. Going beyond classical spintronics, it enables the controlling of the flow of quantum information between distant spin qubits. The transistor has two modes of operation, open and closed, which are realized by two different charge configurations in the gate of the transistor. In the closed mode, the spin information between source and drain is blocked while in the open mode we have free spin information exchange. The switching between the modes takes place within a fraction of the operation time which allows for several subsequent operations within the coherence time of the transistor. The system shows good resilience against several imperfections and opens up a practical application for quantum dot arrays.

Trapped ion systems constitute a well controllable scenario for the study and emulation of nanofriction, and in particular of Frenkel-Kontorova-like models. This is in particular the case when a topological defect is created in a zigzag ion Coulomb crystal, which results in an Aubry transition from free sliding to pinned phase as a function of the trap aspect ratio. We explore the quantum effects of the Aubry transition by means of an effective simplified model, in which the defect is treated like a single quantum particle that experiences an effective Peierls-Nabarro potential and a position-dependent mass. We demonstrate the relevance of quantum tunneling in a finite range of aspect ratios close the critical point, showing that the quantum effects may be observed in the kink dynamics for sufficiently low temperatures. Finally, we discuss the requirements to reveal quantum effects at the Aubry transition in future experiments on trapped ions.

The production of high-energy ions is a momentous goal of ultraintense laser lights. So far a number of experiments and numerical simulations have been conducted to obtain the scaling of the ion energy to find the optimal experimental condition. Due to the complexity of the relativistic laser-plasma interactions, it is not easy to evaluate the ion energy for different experimental configurations. We propose a statistical approach using the Bayesian inference to obtain a multivariate scaling to predict the maximum proton energy via the target normal sheath acceleration. We derive the scaling for the experimental parameters and also for the hot electron temperature and density observed in the corresponding particle-in-cell simulations. We demonstrate the effectiveness of our approach in the prediction of the maximum proton energy and provide the experimental condition to achieve a proton energy over 100 MeV.

Employing time-dependent density-functional theory, we have studied dynamical equilibration and binary head-on collisions of quantum droplets taking as a case of study droplets made of a ${}^{39}\mathrm{K}\text{−}{}^{39}\mathrm{K}$ Bose mixture. The phase space of collision outcomes is extensively explored by performing fully three-dimensional calculations with effective single-component Quantum Monte Carlo-based and two-component LHY-corrected mean-field functionals. We exhaustively explored the important effect—not considered in previous studies—of the initial population ratio deviating from the optimal mean-field value $N_2/N_1=\sqrt{a_{11}/a_{22}}$. Both stationary and dynamical calculations indicate sensitivity to an initial nonoptimal concentration. When three-body losses (3BL) are present our two-component approach allows to theoretically address situations in which they mainly act on one of the components of the mixture. Our approach also allows to simultaneously explore the effect on the simulation of population imbalance and 3BL, which are coupled when they act.

In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e., spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum $j$ and introduce the transformations between them by upgrading the Euler angles occurring in classical $\text{SO}\left(3\right)$ spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large $j$, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is a development of the quantum reference frame formalism for a non-Abelian group.

Metastable states in stochastic systems are often characterized by the presence of small eigenvalues in the generator of the stochastic dynamics. We here show that metastability in many-body systems is not necessarily associated with small eigenvalues. Instead, many-body explosion of eigenmode expansion coefficients characterizes slow relaxation, which is demonstrated for two models, interacting particles in a double-well potential and the Fredrickson-Andersen model, the latter of which is a prototypical example of kinetically constrained models studied in glass and jamming transitions. Our results provide insights into slow relaxation and metastability in many-body stochastic systems.

Interactions between elements, which are usually represented by networks, have to delineate potentially unequal relationships in terms of their relative importance or direction. The intrinsic unequal relationships of such kind, however, are opaque or hidden in numerous real systems. For instance, when a node in a network with limited interaction capacity spends its capacity to its neighboring nodes, the allocation of the total amount of interactions to them can be vastly diverse. Even if such potentially heterogeneous interactions epitomized by weighted networks are observable, as a result of the aforementioned egocentric allocation of interactions, the relative importance or dependency between two interacting nodes can only be implicitly accessible. In this work, we precisely pinpoint such relative dependency by proposing the framework to discover hidden dependent relations extracted from weighted networks. For a given weighted network, we provide a systematic criterion to select the most essential interactions for individual nodes based on the concept of information entropy. The criterion is symbolized by assigning the effective number of neighbors or the effective out-degree to each node, and the resultant directed subnetwork decodes the hidden dependent relations by leaving only the most essential directed interactions. We apply our methodology to two time-stamped empirical network data, namely, the international trade relations between nations in the world trade web (WTW) and the network of people in the historical record of Korea, Annals of the Joseon Dynasty (AJD). Based on the data analysis, we discover that the properties of mutual dependency encoded in the two systems are vastly different. The nations in the WTW show much more asymmetric dependent relations than its random counterpart, which implies the global economic inequality in international trades. In contrast, the relationships of people in the AJD are much more mutual than the nations in the WTW. The difference comes from nontrivial correlations (or lack thereof) in the networks, for which we provide the relevant network properties and representative example nations in the case of the WTW.

A dynamical system is an information processing apparatus that encodes input streams from the external environment to its state and processes them through state transitions. The information processing capacity (IPC) is an excellent tool that comprehensively evaluates these processed inputs, providing details of unknown information processing in black box systems; however, this measure can be applied only to time-invariant systems. This paper extends the applicable range to time-variant systems and further reveals that the IPC is equivalent to coefficients of polynomial chaos (PC) expansion in more general dynamical systems. To achieve this objective, we tackle three issues. First, we establish a connection between the IPC for time-invariant systems and PC expansion, which is a type of polynomial expansion using orthogonal functions of input history as bases. We prove that the IPC corresponds to the squared norm of the coefficient vector of the basis in the PC expansion. Second, we show that an input following an arbitrary distribution can be used for the IPC, removing previous restrictions to specific input distributions. Third, we extend the conventional orthogonal bases to functions of both time and input history and propose the IPC for time-variant systems. To show the significance of our approach, we demonstrate that our measure can reveal information representations in not only machine learning networks but also a real, cultured neural network. Our generalized measure paves the way for unveiling the information processing capabilities of a wide variety of physical dynamics which have been left behind in nature.

The numerical integration of the Schrödinger equation by discretization of time is explored for the curved manifolds arising from finite representations based on evolving basis states. In particular, the unitarity of the evolution is assessed, in the sense of the conservation of mutual scalar products in a set of evolving states, and with them the conservation of orthonormality and particle number. Although the adequately represented equation is known to give rise to unitary evolution in spite of curvature, discretized integrators easily break that conservation, thereby deteriorating their stability. The Crank-Nicolson algorithm, which offers unitary evolution in Euclidian spaces independent of time-step size $dt$, can be generalized to curved manifolds in different ways. Here we compare a previously proposed algorithm that is unitary by construction, albeit integrating the wrong equation, with a faithful generalization of the algorithm, which is, however, not strictly unitary for finite $dt$.

An iterative algorithm is established which enables one to compute individual Floquet states even for many-body systems with high-dimensional Hilbert spaces that are not accessible to commonly employed conventional methods. A strategy is proposed for following a Floquet state in response to small changes of a given system's Hamiltonian. The scheme is applied to a periodically driven Bose-Hubbard chain, verifying the possibility of a pseudoadiabatic Floquet state following. In particular, it is demonstrated that a driving-induced Mott insulatorlike target Floquet state can be populated with high efficiency if the driving amplitude is turned on smoothly but not too slowly. We conclude that the algorithm constitutes a powerful tool for the future investigation of many-body Floquet systems.

We consider non-Fermi liquids in which the inelastic scattering rate has an intrinsic particle-hole asymmetry and obeys $\omega /T$ scaling. We show that, in contrast to Fermi liquids, this asymmetry influences the low-temperature behavior of the thermopower even when the impurity scattering dominates. Implications for the unconventional sign and temperature dependence of the thermopower in cuprates in the strange metal (Planckian) regime are emphasized.

In this paper we investigate the generation, manipulation and invariance properties of spatially unpolarized light in the context of classical optics. We generate spatially randomly polarized light by exploiting the optical activity of a so-called Cornu depolarizer and demonstrate tailored, spatial polarization distributions on the Poincaré sphere. We begin with the generation of equator states of spatially unpolarized light, i.e., the manifold of the superposition of all linearly polarized light states in the spatial domain. A quarter-wave plate is utilized to transform these equator polarization states into meridian states and finally a second, subsequent quarter-wave plate results in tilted meridian states or generalized great-circle states on the Poincaré sphere. These results of all realized unpolarized states are visually confirmed by tomographic reconstruction of the spatially distributed polarization states on the Poincaré sphere by extracting the data from the spatially resolved Stokes parameter measurements. Furthermore, all these experimental results are in excellent agreement with classical Mueller formalism calculations based on the Mueller matrices for the Cornu depolarizer and the wave plates, yielding the tailored manifold of polarization states on the Poincaré sphere's surface, confirming the naming of the unpolarized light states in accordance with geodesy. Therefore, we have realized a scheme for the tailored generation of spatially depolarized light based on the Cornu depolarizer and quarter-wave plates with interesting application perspectives and giving further insight into polarization.