The continuous-spontaneous-localization dynamical collapse structure, adapted to the relativistically invariant model where the collapse-generating operator is a one-dimensional scalar field $\widehat{\varphi }(x,t)$ (mass $m$) is discussed. A complete solution for the density matrix is given, for an initial state $|\psi ,0\rangle =\frac{1}{\sqrt{2}}\left[\right|L\rangle +|R\rangle ]$ when the Hamiltonian $\widehat{H}$ is set equal to 0, and when $\widehat{H}$ is the free field Hamiltonian. Here $|L\rangle ,|R\rangle$ are coherent states which represent clumps of particles, with mean particle number density $N{\chi }_i^2\left(x\right)$, where ${\chi }_1\left(x\right),{\chi }_2\left(x\right)$ are Gaussians of width $\sigma \gg m^{-1}$ with mean positions separated by distance $\gg \sigma$. It is shown that, with high probability, the solution for $\widehat{H}=0$ (identical to the short time solution for $\widehat{H}\ne 0$) favors collapse toward eigenstates of the scalar field whose eigenvalues are close to $\sim {\chi }_i\left(x\right)$. Thus, this collapse dynamics results in essentially one clump of particles. However, eventually particle production dominates the density matrix since, as is well known, the collapse generates energy/sec-volume of every particle momentum in equal amounts. Because of the particle production, this is not an experimentally viable physical theory but, as is emphasized by the discussion, it is a sound relativistic collapse model, with sensible collapse behavior.

Topology has rapidly become one of the central topics in modern physics because of its ability to explain various interesting phenomena, especially in condensed matter physics. Topological invariants, serving as indicators for different topological phases, have been widely studied in various quantum systems. Generally, topological invariants are defined in (quasi)equilibrium systems through their ground-state manifold and are used to classify different topological phases. Recently, topological invariants in quantum systems far from equilibrium have been taken into account theoretically in quite different ways. Here, the dynamical Chern number, originally introduced in quenches of static systems, is extended to the quenches of periodically driven systems. Moreover, experimental measurements of dynamical topological invariants appearing in different quantum quenches are reported. The results show that the dynamical Chern number offers an intrinsic way to classify quenched quantum walks, and they demonstrate further its relation to quasiequilibrium topological bulk invariants associated with quenched quantum walks between different topological phases. The classifications by the dynamical Chern number are also compared with the classifications by the behavior of the dynamical topological order parameter. The platform used in this study provides an ideal way to investigate the topology in nonequilibrium quantum systems.

The thermodynamic properties of the Shastry-Sutherland model have posed one of the longest-lasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product state to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled-pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials.

In turbulent Rayleigh-Bénard convection, the boundary layers are nonsteady with fluctuations, the time-averaged large-scale circulating velocity vanishes far away from the top and bottom plates, and the motion arises from buoyancy. In this paper, we derive the full set of boundary layer equations for both the temperature and velocity fields from the Boussinesq equations for a quasi-two-dimensional flow above a heated plate, taking into account all the above effects. By solving these boundary layer equations, both the time-averaged temperature and velocity boundary layer profiles are obtained.

The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain range of dynamics on complex graphs, higher-dimensional coins are necessary to unleash the full potential of discrete-time quantum walks. In this work, we present an experimental realization of a discrete-time quantum walk on a line graph that, instead of two-dimensional, exhibits a four-dimensional coin space. Making use of the extra degree of freedom we observe multiple ballistic propagation speeds specific to higher-dimensional coin operators. By implementing a scalable technique, we demonstrate quantum walks on circles of various sizes, as well as on an example of a Husimi cactus graph. The quantum walks are realized via time-multiplexing in a Michelson interferometer loop architecture, employing as the coin degrees of freedom the polarization and the traveling direction of the pulses in the loop. Our theoretical analysis shows that the platform supports implementations of quantum walks with arbitrary $4\times 4$ unitary coin operations, and usual quantum walks on a line with various periodic and twisted boundary conditions.

We demonstrate a trap that confines polarizable particles around the antinode of a standing-wave microwave field. The trap relies only on the polarizability of the particles far from any resonances and so can trap a wide variety of atoms and molecules in a wide range of internal states, including the ground state. The trap has a volume of about $10{\mathrm{cm}}^3$ and a depth approaching $1\mathrm{K}$ for many polar molecules. We measure the trap properties using ${}^7\mathrm{Li}$ atoms, showing that when the input microwave power is $610\mathrm{W}$, the atoms remain trapped with a $1/e$ lifetime of $1.76\left(12\right)\mathrm{s}$, oscillating with an axial frequency of $28.55\left(5\right)\mathrm{Hz}$ and a radial frequency of $8.81\left(8\right)\mathrm{Hz}$. The trap could be loaded with slow molecules from a range of available sources and is particularly well suited to sympathetic cooling and evaporative cooling of molecules.

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying distributions that are widely used in statistics and other fields. This definition allows the distribution to deviate from a pure power law arbitrarily but without affecting the power-law tail exponent. We then identify three estimators of these exponents that are proven to be statistically consistent—that is, converging to the true value of the exponent for any regularly varying distribution—and that satisfy some additional niceness requirements. In contrast to estimators that are currently popular in network science, the estimators considered here are based on fundamental results in extreme value theory, and so are the proofs of their consistency. Finally, we apply these estimators to a representative collection of synthetic and real-world data. According to their estimates, real-world scale-free networks are definitely not as rare as one would conclude based on the popular but unrealistic assumption that real-world data come from power laws of pristine purity, void of noise, and deviations.

Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the superfast encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree $d$ to a qubit simulator Hamiltonian composed of Pauli operators of weight $O\left(d\right)$. A system of $m$ Fermi modes gets mapped to $n=O\left(md\right)$ qubits. We propose generalized superfast encodings (GSEs) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree $d\ge 6$. In contrast, we prove that the original superfast encoding lacks the error correction property for $d\le 6$. Second, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O\left(d\right)$ to $O(logd)$. The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.

Molecular dynamics (MD) simulations have been widely recognized as a promising tool for investigating dynamical processes with an atomic resolution. The time span accessible to MD simulations is, however, extremely limited, which makes it difficult to simulate dynamical events on a timescale of milliseconds or longer while maintaining the microscopic-level resolution. Here, we present an approach that allows us to accelerate the dynamical processes (infrequent events) by introducing an additional bias potential and to describe these events on the correct timescale. To this end, we utilize a reparametrization of time (generalized Poincaré time transformation), which leads to the accelerated dynamics and the biased sampling in phase space. The direct link between the timescale and biased sampling demonstrated in this study makes it possible to extend the timescale in MD simulations without invoking the approximation of the transition state theory. A general form of the bias potential is also introduced, which is easily constructed and straightforwardly applied to various systems. The present approach, Poincaré boost dynamics, is applied to the diffusion process of an impurity atom in an amorphous matrix and to conformational changes of a model protein for demonstrating its validity and versatility.

Motivated by recent advances in the fabrication of Josephson junctions in which the weak link is made of a low-dimensional nonsuperconducting material, we present here a systematic theoretical study of the local density of states (LDOS) in a clean two-dimensional normal metal (N) coupled to two $s$-wave superconductors (S). To be precise, we employ the quasiclassical theory of superconductivity in the clean limit, based on Eilenberger's equations, to investigate the phase-dependent LDOS as a function of factors such as the length or the width of the junction, a finite reflectivity, and a weak magnetic field. We show how the spectrum of Andreev bound states that appear inside the gap shape the phase-dependent LDOS in short and long junctions. We discuss the circumstances when a gap appears in the LDOS and when the continuum displays a significant phase dependence. The presence of a magnetic flux leads to a complex interference behavior, which is also reflected in the supercurrent-phase relation. Our results agree qualitatively with recent experiments on graphene SNS junctions. Finally, we show how the LDOS is connected to the supercurrent that can flow in these superconducting heterostructures and present an analytical relation between these two basic quantities.

We describe a technique which minimizes the amount of neurons in the hidden layer of a random recurrent neural network (rRNN) for time series prediction. Merging Takens-based attractor reconstruction methods with machine learning, we identify a mechanism for feature extraction that can be leveraged to lower the network size. We obtain criteria specific to the particular prediction task and derive the scaling law of the prediction error. The consequences of our theory are demonstrated by designing a Takens-inspired hybrid processor, which extends a rRNN with virtual nodes. Virtual nodes are defined as time-delayed versions of real network nodes. Our hybrid architecture is therefore designed including both real and virtual nodes. Via this symbiosis, we show performance of the hybrid processor by stabilizing an arrhythmic neural model. Thanks to our obtained design rules, we can reduce the stabilizing neural network's size by a factor of 15 with respect to a standard system.

We construct an exactly solvable lattice model of a fractional Weyl semimetal. The low-energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function, they provide strong experimental signatures for this exotic gapless state of matter.

A closed-trajectory evolution of a quantum state generally imprints a phase that contains both dynamical and geometrical contributions. While dynamical phases depend on the reference system, geometric phase factors are uniquely defined by the properties of the outlined trajectory. Here we generate and measure geometric phases in a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ using a combination of the dynamical quantum Zeno effect and measurement-free evolution. We show that the dynamical quantum Zeno effect can inhibit the formation of a geometric phase without altering the dynamical phase. This can be used to extract the geometric Aharonov-Anandan phase from any closed-trajectory evolution without requiring knowledge or control of the Hamiltonian.

In systems with broken Lorentz invariance the vacuum state of the field can depend on the choice of the inertial reference frame. This leads to observable effects. For example, the motion of an atom with a constant velocity above a flat metal surface can yield atomic excitation with simultaneous emission of a surface plasmon, while uniform motion of the atom through an optical cavity can yield atomic excitation with emission of a photon into cavity modes. We calculate the probability of these processes and make a connection with the Cherenkov radiation of a neutral atom uniformly moving through a medium and Unruh radiation of the atom accelerated in free space. In all these cases the moving atom becomes excited and the field quantum is emitted through vacuum fluctuations at the expense of the kinetic energy of the atom.

The degree of nonorthogonality of eigenstates of non-Hermitian systems governs nuclear scattering, electronic conductance, and wave propagation in disordered media. Here, we determine the impact of non-Hermiticity upon eigenstates inside an open random cavity from measurements of the modal overlap matrix of transmitted microwave radiation. Increasing eigenfunction correlation with spectral modal overlap brought about by the openness of the system leads to modal transmission greatly exceeding unity accompanied by strong modal anticorrelation guaranteeing that transmission does not exceed unity.

We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curved-spacetime geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can also account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials.

We investigate the electronic structure of a recently discovered, heavily electron-doped iron-based superconductor ${\mathrm{LaFe}}_2{\mathrm{As}}_2$. Although first-principles calculation shows apparent absence of hole Fermi surfaces around the $\mathrm{\Gamma }$ point, we reveal, by hypothetically removing the La $d$ orbital contribution, that a hole Fermi surface around the $\mathrm{\Gamma }$ point is essentially present. In the collapsed phase of ${\mathrm{LaFe}}_2{\mathrm{As}}_2$, which is nonsuperconducting, the hole Fermi surface is found to be absent, and the difference from the uncollapsed superconducting phase can be naturally understood within the spin-fluctuation-mediated pairing scenario.

We present a comparison between stochastic simulations and mean-field theories for the epidemic threshold of the susceptible-infected-susceptible model on correlated networks (both assortative and disassortative) with a power-law degree distribution $P\left(k\right)\sim k^{-\gamma }$. We confirm the vanishing of the threshold regardless of the correlation pattern and the degree exponent $\gamma$. Thresholds determined numerically are compared with quenched mean-field (QMF) and pair quenched mean-field (PQMF) theories. Correlations do not change the overall picture: The QMF and PQMF theories provide estimates that are asymptotically correct for large sizes for $\gamma <5/2$, while they only capture the vanishing of the threshold for $\gamma >5/2$, failing to reproduce quantitatively how this occurs. For a given size, PQMF theory is more accurate. We relate the variations in the accuracy of QMF and PQMF predictions with changes in the spectral properties (spectral gap and localization) of standard and modified adjacency matrices, which rule the epidemic prevalence near the transition point, depending on the theoretical framework. We also show that, for $\gamma <5/2$, while QMF theory provides an estimate of the epidemic threshold that is asymptotically exact, it fails to reproduce the singularity of the prevalence around the transition.

We study the behavior of the Eisenbud-Wigner collisional time delay around Feshbach resonances in cold and ultracold atomic and molecular collisions. We carry out coupled-channel scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length and so exhibits a pole as a function of applied field. At high energy, it exhibits a Lorentzian peak as a function of either energy or field. For narrow resonances, the crossover between these two regimes occurs at an energy proportional to the square of the resonance strength parameter $s_{\text{res}}$. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.

Right-handed neutrinos in supersymmetric models can act as the source of lepton flavor violation (LFV). We present experimental implications of lepton flavor-violating processes within a supersymmetric type-I seesaw framework in the three-extra-parameter nonuniversal Higgs model (NUHM3) for large [Pontecorvo-Maki-Nakawaga-Sakata- (PMNS-) like] and small [Cabibbo-–Kobayashi-–Maskawa- (CKM-) like] Yukawa mixing scenarios. We highlight LFV predictions for the natural (low ${\mathrm{\Delta }}_{\mathrm{EW}}$) portion of parameter space. Our numerical analysis includes full two-loop renormalization group running effects for the three neutrino masses and mass matrices. We show the projected discovery reach of various LFV experiments (i.e., Mu2e, Mu3e, MEG-II, Belle-II), and specify regions that have already been excluded by the LHC searches. Our results depend strongly on whether one has a normal sneutrino ordering (NSO) or an inverted sneutrino ordering (ISO). Natural supersymmetry (SUSY) with a NSO is already excluded by MEG-2013 results while large portions of ISO have been or will soon be tested. However, LFV processes from natural SUSY with small Yukawa mixing and an ISO seem below any projected sensitivities. A substantial amount of the remaining parameter space of models with large PMNS-like neutrino mixing will be probed by Mu2e and MEG-II experiments whereas small, CKM-like Yukawa mixing predicts LFV decays which can hide from LFV experiments.