Multidimensional stochastic integrate-and-fire (IF) models are a standard spike-generator model in studies of firing variability, neural information transmission, and neural network dynamics. Most popular is a version with Gaussian noise and adaptation currents that can be described via Markovian embedding by a set of $d+1$ stochastic differential equations corresponding to a Fokker-Planck equation (FPE) for one voltage and $d$ auxiliary variables. For the specific case $d=1$, we find a set of partial differential equations that govern the stationary probability density, the stationary firing rate, and, central to our study, the spike-train power spectrum. We numerically solve the corresponding equations for various examples by a finite-difference method and compare the resulting spike-train power spectra to those obtained by numerical simulations of the IF models. Examples include leaky IF models driven by either high-pass-filtered (green) or low-pass-filtered (red) noise (surprisingly, already in this case, the Markovian embedding is not unique), white-noise-driven IF models with spike-frequency adaptation (deterministic or stochastic) and models with a bursting mechanism. We extend the framework to general $d$ and study as an example an IF neuron driven by a narrow-band noise (leading to a three-dimensional FPE). The many examples illustrate the validity of our theory but also clearly demonstrate that different forms of colored noise or adaptation entail a rich repertoire of spectral shapes. The framework developed so far provides the theory of the spike statistics of neurons with known sources of noise and adaptation. In the final part, we use our results to develop a theory of spike-train correlations when noise sources are not known but emerge from the nonlinear interactions among neurons in sparse recurrent networks such as found in cortex. In this theory, network input to a single cell is described by a multidimensional Ornstein-Uhlenbeck process with coefficients that are related to the output spike-train power spectrum. This leads to a system of equations which determine the self-consistent spike-train and noise statistics. For a simple example, we find a low-dimensional numerical solution of these equations and verify our framework by simulation results of a large sparse recurrent network of integrate-and-fire neurons.

We investigate the quantum transition to a correlated state of coupled oscillators in the regime where they display period tripling in response to a drive at triple the eigenfrequency. Correlations are formed between the discrete oscillation phases of individual oscillators. The evolution toward the ordered state is accompanied by the transient breaking of the symmetry between seemingly equivalent configurations. We attribute this to the nontrivial geometric phase that characterizes period tripling. We also show that the Wigner distribution of a single damped quantum oscillator can display a minimum at the classically stable zero-amplitude state.

In this paper, we take a fresh look at the long-standing issue of the nature of macroscopic density fluctuations in the grand canonical treatment of the Bose-Einstein condensation (BEC). Exploiting the close analogy between the spherical and mean-spherical models of magnetism with the canonical and grand canonical treatments of the ideal Bose gas, we show that BEC stands for different phenomena in the two ensembles: an ordering transition of the type familiar from ferromagnetism in the canonical ensemble and condensation of fluctuations, i.e., growth of macroscopic fluctuations in a single degree of freedom, without ordering, in the grand canonical case. We further clarify that this is a manifestation of nonequivalence of the ensembles, due to the existence of long-range correlations in the grand canonical one. Our results shed new light on the recent experimental realization of BEC in a photon gas, suggesting that the observed BEC when prepared under grand canonical conditions is an instance of condensation of fluctuations.

We propose a scheme to entangle two magnon modes via the Kerr nonlinear effect when driving the systems far from equilibrium. We consider two macroscopic yttrium iron garnets interacting with a single-mode microcavity through the magnetic dipole coupling. The Kittel mode describing the collective excitations of a large number of spins is excited through the driving cavity with a strong microwave field. We demonstrate how Kerr nonlinearity creates the entangled quantum states between the two macroscopic ferromagnetic samples, when the microcavity is strongly driven by a blue-detuned microwave field. Such quantum entanglement survives at the steady state. Our work offers insights and guidance in designing experiments for observing entanglement in massive ferromagnetic materials. It can also find broad applications in macroscopic quantum effects and magnetic spintronics.

Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics schemes, especially the continuous-time quantum walk. Difficulty exists, however, in producing closed-form solutions with controllable accuracy against the complexity of memory kernels. Here, we introduce a new multiple-scale perturbation method that works on integro-differential equations for general study of memory effects in dynamical systems. We propose an open-system model in which a continuous-time quantum walk is enclosed in a non-Markovian reservoir, that naturally corresponds to an error correction algorithm scheme. By applying the multiple-scale method we show how emergence of different timescales is related to transition of system dynamics into the non-Markovian regime. We find that up to two long-term modes and two short-term modes exist in regular networks, limited by their intrinsic symmetries. In addition to the effective approximation by our perturbation method on general forms of reservoirs, the speed-up of quantum walks assisted by non-Markovianity is also confirmed, revealing the advantage of reservoir engineering in designing time-sensitive quantum algorithms.

Intracellular bidirectional transport of cargo on microtubule filaments is achieved by the collective action of oppositely directed dynein and kinesin motors. Experiments have found that in certain cases, inhibiting the activity of one type of motor results in an overall decline in the motility of the cellular cargo in both directions. This counterintuitive observation, referred to as the paradox of codependence, is inconsistent with the existing paradigm of a mechanistic tug of war between oppositely directed motors. Unlike kinesin motors, dynein motors exhibit catch bonding, wherein the unbinding rates of these motors decrease with increasing force on them. Incorporating this catch-bonding behavior of dyneins in a theoretical model, we show that the functional divergence of the two motor species manifests itself as an internal regulatory mechanism, and leads to codependent-transport behavior in biologically relevant regimes. Using analytical methods and stochastic simulations, we analyze the processivity characteristics and probability distribution of run times and pause times of transported cellular cargoes. We show that catch bonding can drastically alter the transport characteristics and also provide a plausible resolution of the paradox of codependence.

We investigate how the ionization rate of molecules consisting of a pair of phenyl rings depends on the torsional dihedral angle between these two rings. We consider different orientations of the molecules with respect to the external field direction and find differences in the rates in biphenyl and substituted biphenyl. The evaluation of the rates is made possible by application of the integral representation of the weak-field asymptotic theory for tunneling ionization. We report a strong variation of the ionization rates with dihedral angle with contributions from several orbitals and a large difference between biphenyl and substituted biphenyl related to the permanent dipole of the latter system.

We study the time-evolving currents flowing in an interacting ring-shaped nanostructure after a bias voltage has been switched on. The source-to-drain current exhibits the expected relaxation towards its quasistatic equilibrium value at a rate ${\mathrm{\Gamma }}_0$ reflecting the lead-induced broadening of the ring states. In contrast, the current circulating within the ring decays with a different rate $\mathrm{\Gamma }$, which is a rapidly decaying function of the interaction strength and thus can take values orders of magnitude below ${\mathrm{\Gamma }}_0$. This implies the existence of a regime in which the nanostructure is far from equilibrium even though the transmitted current is already stationary. We discuss experimental setups to observe the long-lived ring transients.

Cooled oil emulsion droplets in aqueous surfactant solution have been observed to flatten into a remarkable host of polygonal shapes with straight edges and sharp corners, but different driving mechanisms—(i) a partial phase transition of the liquid bulk oil into a plastic rotator phase near the droplet interface and (ii) buckling of the interfacially frozen surfactant monolayer enabled by a drastic lowering of surface tension—have been proposed. Here, combining experiment and theory, we analyze the initial stages of the evolution of these “shape-shifting” droplets, during which a polyhedral droplet flattens into a polygonal platelet under cooling and gravity. Using reflected-light microscopy, we reveal how icosahedral droplets evolve through an intermediate octahedral stage to flatten into hexagonal platelets. This behavior is reproduced by a theoretical model of the phase transition mechanism, but the buckling mechanism can only reproduce the flattening if the deformations are driven by buoyancy. This requires surface tension to decrease by several orders of magnitude during cooling and yields bending modulus estimates orders of magnitude below experimental values. The analysis thus shows that the phase transition mechanism underlies the observed “shape-shifting” phenomena.

From a semiclassical perspective, the Bohr-Sommerfeld quantization of the closed cyclotron orbits for charged particles such as electrons in an external magnetic field gives rise to discrete Landau levels and a series of fascinating quantum Hall phenomena. Here, we consider topologically nontrivial physics from a distinct origin, where the cyclotron orbits take nontrivial knotting structures such as a trefoil knot. We present a scenario of a Weyl semimetal with a slab geometry, where the Fermi arcs on the opposing surfaces can cross without interfering with each other and form a knot together with the bulk Weyl nodes, and in an external magnetic field, the resulting chiral Landau levels. We provide a microscopic lattice model to realize a cyclotron orbit with an unconventional geometry of a trefoil knot and study the corresponding quantum oscillations. Interestingly, unlike the conventional ring-shaped cyclotron orbit, a trefoil knot is self-threading, allowing the magnetic field line along the cyclotron orbit to contribute to the overall Berry phase and therefore altering the external magnetic field for each quantization level. The cyclotron orbit knot offers an arena of the nontrivial knot theory in three spatial dimensions and its subsequent physical consequences.

Recent progress in nanoscale optics is driven by the physics of electric and magnetic resonances supported by high-index dielectric nanoparticles. Here, we exploit optical bound states in the continuum in a subwavelength particle enhanced by an engineered substrate undergoing an epsilon-near-zero transition from an insulator to a conductor, and uncover how to boost dramatically high-order parametric nonlinear effects. Our strategy makes feasible an observation of a variety of multistep cascaded and multifrequency nonlinear effects in an individual subwavelength resonator. This would expand substantially the range of applications of Mie-resonant dielectric metaphotonics for highly efficient subwavelength optical circuitry, nonlinear metadevices, ultrasensitive hyperspectral sensing, and quantum nanophotonics.

The first indication of a pseudogap in cuprates came from a sudden decrease of the NMR Knight shift at a doping-dependent temperature $T^{*}\left(\delta \right)$. Since then, experiments have found phase transitions at a lower $T_{\text{phase}}^{*}\left(\delta \right)$. Using plaquette cellular dynamical mean field for the square-lattice Hubbard model at high temperature, where the results are reliable, we show that $T^{*}\left(\delta \right)$ shares many features of $T_{\text{phase}}^{*}\left(\delta \right)$. The remarkable agreement with several experiments, including quantum critical behavior of the electronic specific heat, supports the view that the pseudogap is controlled by a finite-doping extension of the Mott transition. We propose further experimental tests.

Interaction of electromagnetic radiation with time-variant objects is a fundamental problem whose study involves foundational principles of classical electrodynamics. Such study is a necessary preliminary step for delineating the novel research field of linear time-varying metamaterials and metasurfaces. A closer look to the literature, however, reveals that this crucial step has not been addressed and important simplifying assumptions have been made. Before proceeding to studies of linear time-varying metamaterials and metasurfaces with their effective parameters, we need to rigorously describe the electric and magnetic responses of a temporally modulated meta-atom. Here, we introduce a theoretical model which describes a time-variant meta-atom and its interaction with incident electromagnetic waves in time domain. The developed general approach is specialized for a dipole emitter/scatterer loaded with a time-varying reactive element. We confirm the validity of the theoretical model with full-wave simulations. Our study is of major significance also in the area of nanophotonics and nano-optics because the optical properties of all-dielectric and plasmonic nanoparticles can be varied in time in order to achieve intriguing scattering phenomena.

In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory and Bloch topological invariants fail to correctly predict energy spectra, topological boundary states, and symmetry-breaking phase transitions in systems with open boundaries. Recently, it has been shown that a correct description requires one to extend Bloch band theory into the complex plane. A still open question is whether the non-Hermitian skin effect and non-Bloch symmetry-breaking phase transitions can be probed by real-space wave dynamics far from edges, which is entirely governed by ordinary Bloch bands. Here it is shown that the Lyapunov exponent in the long-time behavior of bulk wave dynamics can generally reveal non-Bloch symmetry-breaking phase transitions and the existence of the non-Hermitian skin effect.

Broadband spin-photon interfaces for the long-lived storage of photonic quantum states are key elements for quantum information technologies. Yet, the reliable operation of such memories in the quantum regime is challenging due to photonic noise arising from technical and/or fundamental limitations in the storage-and-recall processes controlled by strong electromagnetic fields. Here, we experimentally implement a single-photon-level spin-wave memory in a laser-cooled rubidium gas, based on the recently proposed Autler-Townes splitting (ATS) protocol. We demonstrate the storage of 20-ns-long laser pulses, each containing an average of 0.1 photons, for 200 ns with an efficiency of $12.5\%$ and a signal-to-noise ratio above 30. Notably, the robustness of ATS spin-wave memory against motional dephasing allows for an all-spatial filtering of the control-field noise, yielding an ultralow unconditional noise probability of $3.3\times {10}^{-4}$, without the complexity of spectral filtering. These results highlight that broadband ATS memory in ultracold atoms is a preeminent option for storing quantum light.

Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically, in two dimensions, repeating an isotropic rotation twice maps a given point on the two-dimensional unit sphere (the unit circle) uniformly at random to any point on the unit sphere, reflecting a statistical symmetry as expected. In contrast, in three and higher dimensions, a point is mapped more often closer to the original point than a uniform distribution predicts. Curiously, in the limit of the dimension $d\to \infty$, a symmetric distribution is approached again. We intuitively explain the emergence of this asymmetry and why it disappears in higher dimensions by disentangling isotropic rotations into a sequence of partial actions. The asymmetry emerges in two qualitatively different forms and for a wide range of general random operations relevant in complex systems modeling, including repeated continuous and discrete rotations, roto-reflections and general orthogonal transformations.

The recent discovery of a nonmagnetic nematic quantum critical point (QCP) in the iron chalcogenide family ${\mathrm{FeSe}}_{1\text{−}x}{\mathrm{S}}_x$ has raised the prospect of investigating, in isolation, the role of nematicity on the electronic properties of correlated metals. Here we report a detailed study of the normal state transverse magnetoresistance (MR) in ${\mathrm{FeSe}}_{1\text{−}x}{\mathrm{S}}_x$ for a series of S concentrations spanning the nematic QCP. For all temperatures and $x$ values studied, the MR can be decomposed into two distinct components: one that varies quadratically in magnetic field strength ${\mu }_0\mathit{H}$ and one that follows precisely the quadrature scaling form recently reported in metals at or close to a QCP and characterized by a $H$-linear MR over an extended field range. The two components evolve systematically with both temperature and S substitution in a manner that is determined by their proximity to the nematic QCP. This study thus reveals the coexistence of two independent charge sectors in a quantum critical system. Moreover, the quantum critical component of the MR is found to be less sensitive to disorder than the quadratic (orbital) MR, suggesting that detection of the latter in previous MR studies of metals near a QCP may have been obscured.

Lattices and their underlying symmetries play a central role in determining the physical properties and applications of many natural and engineered materials. This research offers a comprehensive solution to a long-standing challenge regarding the lattice-based materials: how to systematically construct a lattice and transform it among different symmetric configurations in a predictable, scalable, and reversible way. By bridging the lattice geometry and rigid-folding kinematics of a group of origamis consisting of generic degree-4 vertices, we successfully construct all types of two- and three-dimensional Bravais lattices, and demonstrate that they can undergo all diffusionless phase transformations via rigid folding (i.e., dilation, extension, contraction, shear, and shuffle). Such folding-induced lattice transformations can trigger fundamental lattice-symmetry switches, which can either maintain or reconstruct the nearest-neighbor relationships according to a continuous symmetry measure. This study can foster the next generation of transformable lattice structures and materials with on-demand property tuning capabilities.

We present a topological characterization of time-periodically driven two-band models in $2+1$ dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three-dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing the topology of knots in three dimensions. Moreover, after being cast as a Hopf insulator, not only the Chern numbers but also the winding numbers of the Floquet topological insulator become accessible in experiments as linking numbers. We exploit this description to propose a feasible scheme for measuring the complete set of their Floquet topological invariants in optical lattices.

A continuous transition for a system moving in a three-dimensional (3D) space to moving in a lower-dimensional space, 2D or 1D, can be made by means of an external squeezing potential. A squeeze along one direction gives rise to a 3D to 2D transition, whereas a simultaneous squeeze along two directions produces a 3D to 1D transition, without going through an intermediate 2D configuration. In the same way, for a system moving in a 2D space, a squeezing potential along one direction produces a 2D to 1D transition. In this work we investigate the equivalence between this kind of confinement procedure and calculations without an external field, but where the dimension $d$ is taken as a parameter that changes continuously from $d=3$ to $d=1$. The practical case of an external harmonic oscillator squeezing potential acting on a two-body system is investigated in detail. For the three transitions considered, $3\mathrm{D}\to 2\mathrm{D}, 2\mathrm{D}\to 1\mathrm{D}$, and $3\mathrm{D}\to 1\mathrm{D}$, a universal connection between the harmonic oscillator parameter and the dimension $d$ is found. This relation is well established for infinitely large 3D scattering lengths of the two-body potential for $3\mathrm{D}\to 2\mathrm{D}$ and $3\mathrm{D}\to 1\mathrm{D}$ transitions, and for infinitely large 2D scattering length for the $2\mathrm{D}\to 1\mathrm{D}$ case. For finite scattering lengths size corrections must be applied. The traditional wave functions for external squeezing potentials are shown to be uniquely related to the wave functions for specific noninteger dimension parameters, $d$.