Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging and valuable open problem in quantum information theory. Here we introduce a systematic approach that, despite the lack of knowledge about the full parametrization of the set of CPTP maps on arbitrary Hilbert-spaced dimension, enables us to construct exactly those extreme channels that are covariant with respect to a finite discrete group or a compact connected Lie group. Innovative labeling of quantum channels by group representations enables us to identify the subset of group-covariant channels whose elements are group-covariant generalized-extreme channels. Furthermore, we exploit essentials of group representation theory to introduce equivalence classes for the labels and also partition the set of group-covariant channels. As a result, we show that it is enough to construct one representative of each partition. We construct Kraus operators for group-covariant generalized-extreme channels by solving systems of linear and quadratic equations for all candidates satisfying the necessary condition for being group-covariant generalized-extreme channels. Deciding whether these constructed instances are extreme or quasiextreme is accomplished by solving a system of linear equations. Proper labeling and partitioning the set of group-covariant channels leads to a novel systematic, algorithmic approach for constructing the entire subset of group-covariant extreme channels. We formalize the problem of constructing and classifying group-covariant generalized extreme channels, thereby yielding an algorithmic approach to solving, which we express as pseudocode. To illustrate the application and value of our method, we solve for explicit examples of group-covariant extreme channels. With unbounded computational resources to execute our algorithm, our method always delivers a description of an extreme channel for any finite-dimensional Hilbert space and furthermore guarantees a description of a group-covariant extreme channel for any dimension and for any finite-discrete or compact connected Lie group if such an extreme channel exists.

We numerically demonstrate and characterize the emergence of distinct dynamical regimes of a finite-temperature bosonic superfluid in an elongated Josephson junction generated by a thin Gaussian barrier over the entire temperature range where a well-formed condensate can be clearly identified. Although the dissipation arising from the coupling of the superfluid to the dynamical thermal cloud increases with increasing temperature as expected, the importance of this mechanism is found to depend on two physical parameters associated (i) with the initial chemical potential difference, compared to some characteristic value, and (ii) the ratio of the thermal energy to the barrier amplitude. The former determines whether the superfluid Josephson dynamics are dominated by gradually damped plasmalike oscillations (for relatively small initial population imbalances), or whether dissipation at early times is instead dominated by vortex- and sound-induced dissipation (for larger initial imbalances). The latter defines the effect of the thermal cloud on the condensate dynamics, with a reversal of roles, i.e., the condensate being driven by the oscillating thermal cloud, being observed when the thermal particles acquire enough energy to overcome the barrier. Our findings are within current experimental reach in ultracold superfluid junctions.

We use a combination of symmetry analysis, phenomenological modeling, and first-principles density functional theory to explore the interplay between the magnetic ground state and the detailed atomic structure in the hexagonal rare-earth manganites. We find that the magnetic ordering is sensitive to a breathing mode distortion of the Mn and O ions in the $ab$ plane, which is described by the ${\mathrm{K}}_1$ mode of the high-symmetry structure. Our density functional calculations of the magnetic interactions indicate that this mode particularly affects the single-ion anisotropy and the interplanar symmetric exchanges. By extracting the parameters of a magnetic model Hamiltonian from our first-principles results, we develop a phase diagram to describe the magnetic structure as a function of the anisotropy and exchange interactions. This in turn allows us to explain the dependence of the magnetic ground state on the identity of the rare-earth ion and on the ${\mathrm{K}}_1$ mode.

Weyl semimetals are phases of matter with gapless electronic excitations that are protected by topology and symmetry. Their properties depend on the dimensions of the systems. It has been theoretically demonstrated that five-dimensional (5D) Weyl semimetals emerge as novel phases during the topological phase transition in analogy to the three-dimensional case. However, experimental observation of such a phenomenon remains a great challenge because the tunable 5D system is extremely hard to construct in real space. Here, we construct 5D electric circuit platforms in fully real space and experimentally observe topological phase transitions in five dimensions. Not only are Yang monopoles and linked Weyl surfaces observed experimentally, but various phase transitions in five dimensions are also proved, such as the phase transitions from a normal insulator to a Hopf link of two Weyl surfaces and then to a 5D topological insulator. The demonstrated topological phase transitions in five dimensions leverage the concept of higher-dimensional Weyl physics to control electrical signals in the engineered circuits.

We study theoretically a junction composed of a $\mathcal{PT}$-symmetric non-Hermitian superconductor (PTS) placed between two conventional superconductors. We show that due to non-Hermitian electron-electron interaction in the PTS region and the combination of symmetries, only discrete values of phases of the conventional superconductors yield solutions for Andreev bound states. Remarkably, in the case of phases 0 and $\pi$, we obtain Andreev bound states that are growing and decaying in time. For $\pi /2$ and $3\pi /2$, there is a Majorana zero mode penetrating through the junction in only one direction forming a quasiparticle supercurrent.

Two-dimensional regular arrays of atoms are a promising platform for quantum networks, with collective subradiant states providing long-lived storage and collimated emission allowing for natural coherent links between arrays in free space. However, a single-layer lattice can only efficiently absorb or emit light symmetrically in the forward and backward directions. Here we show how a bilayer lattice can absorb a single photon either incident from a single direction or an arbitrary superposition of forward and backward propagating components. The excitation can be stored in a subradiant state, transferred coherently between different subradiant states, and released, again in an arbitrary combination of highly collimated forward and backward propagating components. We explain the directionality of single and bilayer arrays by a symmetry analysis based on the scattering parities of different multipole radiation components of collective excitations. The collective modes may exhibit the conventional half-wave loss of fields near the array interface or completely eliminate it. The proposed directional control of absorption and emission paves the way for effective one-dimensional quantum communication between multiple arrays, with single-photons propagating backward and forward between quantum information-processing and storage stages.

We study a Fermi gas with strong, tunable interactions dispersively coupled to a high-finesse cavity. Upon probing the system along the cavity axis, we observe a strong optomechanical Kerr nonlinearity originating from the density response of the gas to the intracavity field and measure it as a function of interaction strength. We find that the zero-frequency density response function of the Fermi gas increases by a factor of two from the Bardeen-Cooper-Schrieffer to the Bose-Einstein condensate regime. The results are in quantitative agreement with a theory based on operator-product expansion, expressing the density response in terms of universal functions of the interactions, the contact, and the internal energy of the gas. This provides an example of a driven-dissipative, strongly correlated system with a strong nonlinear response, opening up perspectives for the sensing of weak perturbations or inducing long-range interactions in Fermi gases.

We analyze the electronic structure of topological surface states in the family of magnetic topological insulators ${\mathrm{MnBi}}_{2n}{\mathrm{Te}}_{3n+1}$. We show that, at natural-cleavage surfaces, the Dirac cone warping changes its symmetry from hexagonal to trigonal at the magnetic ordering temperature. In particular, an energy splitting develops between the surface states of the same band index but opposite surface momenta upon formation of the long-range magnetic order. As a consequence, measurements of such energy splittings constitute a simple protocol to detect the magnetic ordering via the surface electronic structure, alternative to the detection of the surface magnetic gap. Interestingly, while the latter signals a nonzero surface magnetization, the trigonal warping predicted here is, in addition, sensitive to the direction of the surface magnetic flux. Our results may be particularly useful when the Dirac point is buried in the projection of the bulk states, caused by certain terminations of the crystal or in hole-doped systems, since in both situations the surface magnetic gap itself is not accessible in photoemission experiments.

We propose theoretically and confirm experimentally a general approach to manage multiple nonlinear interactions of coherent solitary wave structures on an unstable background–-breathers. It allows adjusting the initial positions and phases of more than two moving breathers to observe various desired wave states at controllable moments of wave evolution. Our theoretical framework relies on exact multibreather solutions to the one-dimensional focusing nonlinear Schrödinger equation and asymptotic expressions describing shifts of breather positions and phases acquired by them in mutual collisions. As proof-of-principle, we consider a couple of separated pairs of breathers initially synchronized in a small-amplitude patterns; meanwhile, our approach can be generalized to other breather types and wave states. We obtain an explicit expression for the separation interval between the pairs so that the interactions of the breathers from the neighboring patterns lead to the formation of an extreme amplitude wave or recurrence to the initial small-amplitude state. Experiments are carried out on a light wave platform with a nearly conservative optical fiber system, which accurately reproduces the predicted dynamics and proves the viability of our nonlinear wave theory.

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues. We employ a variety of brand-new theoretical techniques allowing for: (i) bring the theoretical framework to quantify the probability of information diffusion among nodes, (ii) identify critical scales and structures of complex networks regardless of their intrinsic properties, and (iii) demonstrate their dynamical relevance in synchronization phenomena. By combining these ideas, we evidence how the information flow on complex networks unravels different resolution scales. Using computational techniques, we focus on entropic transitions, uncovering a generic mesoscale object, the information core, and controlling information processing in complex networks. Altogether, this study sheds much light on allowing new theoretical techniques paving the way to introduce future renormalization group approaches based on diffusion distances.

Strange metals exhibit a variety of anomalous magnetotransport properties, the most striking of which is a resistivity that increases linearly with magnetic field $B$ over a broad temperature and field range. The ubiquity of this behavior across a spectrum of correlated metals—both single- and multiband, with either dominant spin and/or charge fluctuations, of varying levels of disorder or inhomogeneity, and in proximity to a quantum critical point or phase—obligates the search for a fundamental underlying principle that is independent of the specifics of any material. Strongly anisotropic (momentum-dependent) scattering can generate $B$-linear magnetoresistance but only at intermediate field strengths. At high enough fields, the magnetoresistance must eventually saturate. Here, we consider the ultimate limit of such anisotropy, a region or regions on the Fermi surface that impede all orbital (cyclotron) motion through them, but whose imposition can be modelled nonetheless through a modified Boltzmann theoretical treatment. Application of the proposed theorem suggests that the realization of quadratic-to-linear magnetoresistance requires the presence of a bounded sector on the Fermi surface possibly separating two distinct types of carriers. While this bounded sector may have different origins or manifestations, we expect its existence to account for the anomalous magnetotransport found in a wide range of correlated materials.

The hoppings of noninteracting particles in the optical dice lattice result in the gapless dispersions in the band structure formed by the three lowest minibands. In our research, we find that once a periodic driving force is applied to this optical dice lattice, the original spectral characteristics could be changed, forming three gapped quasienergy bands in the quasienergy Brillouin zone. The topological phase diagram containing the Chern number of the lowest quasienergy band shows that when the hopping strengths of the nearest-neighbor hoppings are isotropic, the system persists in the topologically nontrivial phases with Chern number $C=2$ within a wide range of the driving strength. Accompanied by the anisotropic nearest-neighbor hopping strengths, a topological phase transition occurs, making the Chern number change from $C=2$ to $C=1$. This transition is further verified by our analytical method. Our theoretical work implies that it is feasible to realize the nontrivially topological characteristics of optical dice lattices by applying periodic shaking and that topological phase transition can be observed by independently tuning the strength of a type of nearest-neighbor hopping.

We introduce a tensor-network approach to calculate the statistics of work done on one-dimensional quantum lattice systems initially prepared in thermal equilibrium states. In this approach, the dynamics is simulated with time-evolving block decimation (TEBD), and the initial thermal equilibrium state is prepared either directly with TEBD or with minimally entangled typical thermal states, which generates a set of typical states representing the Gibbs canonical ensemble. As an illustrative example, we apply this approach to the Ising chain in mixed transverse and longitudinal fields. Under a prescribed protocol, the moment generating function for work distribution can be calculated, from which the quantum Jarzynski equality and the generalized quantum work relation involving a functional of an arbitrary observable are tested.

At the core of some of the most important problems in plasma physics—from controlled nuclear fusion to the acceleration of cosmic rays—is the challenge to describe nonlinear, multiscale plasma dynamics. The development of reduced plasma models that balance between accuracy and complexity is critical to advancing theoretical comprehension and enabling holistic computational descriptions of these problems. Here we report the data-driven discovery of accurate reduced plasma models, in the form of partial differential equations, directly from first-principles particle-in-cell simulations. We achieve this by using an integral formulation of sparsity-based model-discovery techniques and show that this is crucial to robustly identify the governing equations in the presence of discrete particle noise. We demonstrate the potential of this approach by recovering the fundamental hierarchy of plasma physics models—from the Vlasov equation to magnetohydrodynamics. Our findings show that this data-driven methodology offers a promising route to accelerate the development of reduced theoretical models of complex nonlinear plasma phenomena and to design computationally efficient algorithms for multiscale plasma simulations.

We consider growing open chemical reaction systems (CRSs), in which autocatalytic chemical reactions are encapsulated in a finite volume and its size can change in conjunction with the reactions. The thermodynamics of growing CRSs is indispensable for understanding biological cells and designing protocells by clarifying the physical conditions and costs for their growing states. In this paper, we establish a thermodynamic theory of growing CRSs by extending the Hessian geometric structure of nongrowing CRSs. The theory provides the environmental conditions to determine the fate of the growing CRSs; growth, shrinking, or equilibration. We also identify thermodynamic constraints: one to restrict the possible states of the growing CRSs and the other to further limit the region where a nonequilibrium steady growing state can exist. Moreover, we evaluate the entropy production rate in the steady growing state. The growing nonequilibrium state has its origin in the extensivity of thermodynamics, which is different from the conventional nonequilibrium states with constant volume. These results are derived from general thermodynamic considerations without assuming any specific thermodynamic potentials or reaction kinetics; i.e., they are obtained based solely on the second law of thermodynamics.

The utility of classical neural networks as universal approximators suggests that their quantum analogues could play an important role in quantum generalizations of machine-learning methods. Inspired by the proposal in Torrontegui and García-Ripoll [Europhys. Lett. 125, 30004 (2019)], we demonstrate a superconducting qubit implementation of a controlled gate, which generalizes the action of a classical perceptron as the basic building block of a quantum neural network. In a two-qubit setup we show full control over the steepness of the perceptron activation function, the input weight and the bias by tuning the gate length, the coupling between the qubits, and the frequency of the applied drive, respectively. In its general form, the gate realizes a multiqubit entangling operation in a single step, whose decomposition into single- and two-qubit gates would require a number of gates that is exponential in the number of qubits. Its demonstrated direct implementation as perceptron in quantum hardware may therefore lead to more powerful quantum neural networks when combined with suitable additional standard gates.

Optimally doped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ (YBCO) has a high critical temperature, at 92 K. It is largely believed that Cooper pairs form in YBCO and other cuprates because of spin fluctuations, but the issue and the detailed mechanism are far from settled. In the present work, we employ a state-of-the-art first-principles ability to compute both the low- and high-energy spin fluctuations in optimally doped YBCO. We benchmark our results against recent inelastic neutron scattering and resonant inelastic x-ray scattering measurements. Further, we use strain as an external parameter to modulate the spin fluctuations and superconductivity. We disentangle the roles of barium-apical oxygen hybridization, interlayer coupling, and orbital symmetries by applying an idealized strain, and also a strain with a fully relaxed structure. We show that shortening the distance between Cu layers is conducive to enhanced Fermi surface nesting, which increases spin fluctuations and drives up $T_c$. However, when the structure is fully relaxed, electrons flow to the $d_{z^2}$ orbital as a consequence of a shortened Ba-O bond, which is detrimental for superconductivity.