We present an exact solution for the probability density function $P(\tau =t_{\min }-t_{\max }|T)$ of the time difference between the minimum and the maximum of a one-dimensional Brownian motion of duration $T$. We then generalize our results to a Brownian bridge, i.e., a periodic Brownian motion of period $T$. We demonstrate that these results can be directly applied to study the position difference between the minimal and the maximal heights of a fluctuating ($1+1$)-dimensional Kardar-Parisi-Zhang interface on a substrate of size $L$, in its stationary state. We show that the Brownian motion result is universal and, asymptotically, holds for any discrete-time random walk with a finite jump variance. We also compute this distribution numerically for Lévy flights and find that it differs from the Brownian motion result.

Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multiparameter quantum estimation is the Holevo Cramér-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We show that it also satisfies strong duality. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multiqubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a nontrivial interplay between the HCRB and incompatibility and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless 2-qubit case.

Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly nongeodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble scales, and to their exponential amplification. Supported by first-principles numerical computations, and by the analytical insight provided by the effective field theory of inflation, we show that the bispectrum is enhanced in flattened configurations, and we argue that an analogous result holds for all higher-order correlation functions. These “hyper-non-Gaussianities” thus provide powerful model-independent constraints on nonstandard inflationary attractors motivated by the search for ultraviolet completions of inflation.

The nuclear response theory for charge-exchange modes in the relativistic particle-vibration coupling approach is extended to include for the first time particle-vibration coupling effects in the ground state of the parent nucleus. In a framework based on the effective meson-nucleon Lagrangian, we investigate the role of such complex ground-state correlations in the description of Gamow-Teller transitions in ${}^{90}\mathrm{Zr}$ in both ($p$, $n$) and ($n$, $p$) channels. The particle-vibration coupling effects are calculated without introducing new parameters. We find that this new correlation mechanism is fully responsible for the appearance of the strength in the ($n$, $p$) branch. Comparison of our results to the available experimental data shows a very good agreement up to excitation energies beyond the giant resonance region when taking into account a phenomenological admixture of the isovector spin monopole transitions. The parent-daughter binding-energy differences are also greatly improved by the inclusion of the new correlations.

We provide a fully analytical treatment for the partial refrigeration of the thermal motion of a quantum mechanical resonator under the action of feedback. As opposed to standard cavity optomechanics where the aim is to isolate and cool a single mechanical mode, the aim here is to extract the thermal energy from many vibrational modes within a large frequency bandwidth. We consider a standard cold-damping technique, where homodyne readout of the cavity output field is fed into a feedback loop that provides a cooling action directly applied on the mechanical resonator. Analytical and numerical results predict that low final occupancies are achievable independent of the number of modes addressed by the feedback, as long as the cooling rate is smaller than the intermode frequency separation. For resonators exhibiting a few nearly degenerate pairs of modes, cooling is less efficient and a weak dependence on the number of modes is obtained. These scalings hint toward the design of frequency-resolved mechanical resonators, where efficient refrigeration is possible via simultaneous cold-damping feedback.

Magnetized laser-produced plasmas are central to many novel laboratory astrophysics and inertial confinement fusion studies, as well as in industrial applications. Here we provide the first complete description of the three-dimensional dynamics of a laser-driven plasma plume expanding in a 20 T transverse magnetic field. The plasma is collimated by the magnetic field into a slender, rapidly elongating slab, whose plasma-vacuum interface is unstable to the growth of the “classical,” fluidlike magnetized Rayleigh-Taylor instability.

The bulk viscosity determines dissipation during hydrodynamic expansion. It vanishes in scale invariant fluids, while a nonzero value quantifies the deviation from scale invariance. For the dilute Fermi gas the bulk viscosity is given exactly by the correlation function of the contact density of local pairs. As a consequence, scale invariance is broken purely by pair fluctuations. These fluctuations give rise also to logarithmic terms in the bulk viscosity of the high-temperature nondegenerate gas. For the quantum degenerate regime I report numerical Luttinger-Ward results for the contact correlator and the dynamical bulk viscosity throughout the BEC-BCS crossover. The ratio of bulk to shear viscosity $\zeta /\eta$ is found to exceed the kinetic theory prediction in the quantum degenerate regime. Near the superfluid phase transition the bulk viscosity is enhanced by critical fluctuations and has observable effects on dissipative heating, expansion dynamics, and sound attenuation.

We examine the atomistic scale dependence of a material’s resistance to failure by numerical simulations and analytical analysis in electrical analogs of brittle crystals. We show that fracture toughness depends on the lattice geometry in a way incompatible with Griffith’s relationship between fracture and free surface energy. Its value finds its origin in the matching between the continuum displacement field at the engineering scale, and the discrete nature of solids at the atomic scale. The generic asymptotic form taken by this field near the crack tip provides a solution for this matching, and subsequently a way to predict toughness from the atomistic parameters with application to graphene.

Time has emerged as a new degree of freedom for metamaterials, promising new pathways in wave control. However, electromagnetism suffers from limitations in the modulation speed of material parameters. Here we argue that these limitations can be circumvented by introducing a traveling-wave modulation, with the same phase velocity of the waves. We show how luminal metamaterials generalize the parametric oscillator concept, realize giant broadband nonreciprocity, achieve efficient one-way amplification, pulse compression, and harmonic generation, and propose a realistic implementation in double-layer graphene.

Finding complex reaction and transformation pathways involving many intermediate states is, in general, not possible on the density-functional theory level with existing simulation methods, due to the very large number of required energy and force evaluations. For complex reactions, it is not possible to determine which atom in the reactant is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. We use a penalty function that is invariant under index permutations to bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker, whose global minimum is the reaction product. By performing a minima-hopping-based global optimization on this biased potential energy surface, we rapidly find intermediate states that lead into the global minimum and allow us to then extract entire reaction pathways. We first demonstrate for a benchmark system, namely, the Lennard-Jones cluster ${\mathrm{LJ}}_{38}$, that our method finds intermediate states relevant to the lowest energy reaction pathway, and hence we need to consider much fewer intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{20}{\mathrm{H}}_{20}$, and show that the reaction pathways found contain valuable information on how these molecules can be synthesized.

Recently discovered Dirac semimetals (DSMs) with two Dirac nodes, such as ${\mathrm{Na}}_3\mathrm{Bi}$ and ${\mathrm{Cd}}_2{\mathrm{As}}_3$, are regarded as carrying the ${\mathbb{Z}}_2$ topological charge in addition to the chiral charge. We study the Floquet phase transition of ${\mathbb{Z}}_2$ topological DSMs subjected to a beam of circularly polarized light. Owing to the resulting interplay of the chiral and ${\mathbb{Z}}_2$ charges, the Weyl nodes are not only chirality dependent but also spin dependent, which constrains the behavior in creation and annihilation of the pair of Weyl nodes. Interestingly, we find a novel phase: One spin band is in the Weyl semimetal phase while the other is in the insulator phase, and we dub it the Weyl half-metal (WHM) phase. We further study the spin-dependent transport in a Dirac-Weyl semimetal junction and find a spin filter effect as a fingerprint of the existence of the WHM phase. The proposed spin filter effect, based on the WHM bulk band, is highly tunable in a broad parameter regime and robust against magnetic disorder, which is expected to overcome the shortcomings of the previously proposed spin filter based on the topological edge or surface states. Our results offer a unique opportunity to explore the potential applications of topological DSMs in spintronics.

Recent progress in condensed matter physics, such as for graphene, topological insulators, and Weyl semimetals, often originate from the specific topological symmetries of their lattice structures. Quantum states with different degrees of freedom, e.g., spin, valley, layer, etc., arise from these symmetries, and the coherent superposition of these states form multiple energy subbands. The pseudospin, a concept analogous to the Dirac spinor matrices, is a successful description of such multisubband systems. When the electron-electron interaction dominates, many-body quantum phases arise. They usually have discrete pseudospin polarizations and exhibit sharp phase transitions at certain universal critical pseudospin energy splittings. In this Letter, we present our discovery of hydrostatic-pressure-induced degeneracy between the two lowest Landau levels. This degeneracy is evidenced by the pseudospin polarization transitions of the fragile correlated quantum liquid phases near the Landau level filling factor $\nu =3/2$. Benefitting from the constant hole concentration and the sensitive nature of these transitions, we study the fine-tuning effect of the hydrostatic pressure at the order of $10\mu \mathrm{eV}$, well beyond the meV-level state-of-the-art resolution of other techniques.

A chiral $p$-wave superconductor is the primary example of topological systems hosting chiral Majorana edge states. Although candidate materials exist, the conclusive signature of chiral Majorana edge states has not yet been observed in experiments. Here, we propose a smoking-gun experiment to detect the chiral Majorana edge states on the basis of theoretical results for the nonlocal conductance in a device consisting of a chiral $p$-wave superconductor and two ferromagnetic leads. The chiral nature of Majorana edge states causes an anomalously long-range and chirality-sensitive nonlocal transport in these junctions. These two drastic features enable us to identify the moving direction of chiral Majorana edge states in the single experimental setup.

The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system. We first demonstrate the essential idea by considering an anomalous topological superconductor with time-reversal symmetry $T^2=1$ in 2D. The physical reason for this is that the fermion parity might be changed locally by certain symmetry action, but it is conserved if we introduce a bulk. Then we discuss the layer structure and systematical construction of ASPT states in interacting fermion systems in 2D with a total symmetry $G_f=G_b\times {\mathbb{Z}}_2^f$. Finally, potential experimental realizations of ASPT states are also addressed.

Inhomogeneous strain applied to lattice systems can induce artificial gauge fields for particles moving on this lattice. Here we demonstrate how to engineer a novel state of matter, namely an antiferromagnet with a Landau-level excitation spectrum of magnons. We consider a honeycomb-lattice Heisenberg model and show that triaxial strain leads to equally spaced pseudo-Landau levels at the upper end of the magnon spectrum, with degeneracies characteristic of emergent supersymmetry. We also present a particular strain protocol which induces perfectly quantized magnon Landau levels over the whole bandwidth. We discuss experimental realizations and generalizations.

Spin-momentum locked surface states in topological insulators (TIs) provide a promising route for achieving high spin-orbit torque (SOT) efficiency beyond the bulk spin-orbit coupling in heavy metals (HMs). However, in previous works, there is a huge discrepancy among the quantitative SOTs from TIs in various systems determined by different methods. Here, we systematically study the SOT in the $\mathrm{TI}(\mathrm{HM})/\mathrm{Ti}/\mathrm{CoFeB}/\mathrm{MgO}$ systems by the same method, and make a conclusive assessment of SOT efficiency for TIs and HMs. Our results demonstrate that TIs show more than one order of magnitude higher SOT efficiency than HMs even at room temperature, at the same time the switching current density as low as $5.2\times {10}^5\mathrm{A}{\mathrm{cm}}^{-2}$ is achieved with ${({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x)}_2{\mathrm{Te}}_3$. Furthermore, we investigate the relationship between SOT efficiency and the position of Fermi level in ${({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x)}_2{\mathrm{Te}}_3$, where the SOT efficiency is significantly enhanced near the Dirac point, with the most insulating bulk and conducting surface states, indicating the dominating SOT contribution from topological surface states. This work unambiguously demonstrates the ultrahigh SOT efficiency from topological surface states.

The effect of intrinsic point defects on relaxor properties of 0.68 ${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_3\text{−}0.32$ ${\mathrm{PbTiO}}_3$ thin films is studied across nearly 2 orders of magnitude of defect concentration via ex post facto ion bombardment. A weakening of the relaxor character is observed with increasing concentration of bombardment-induced point defects, which is hypothesized to be related to strong interactions between defect dipoles and the polarization. Although more defects and structural disorder are introduced in the system as a result of ion bombardment, the special type of defects that are likely to form in these polar materials (i.e., defect dipoles) can stabilize the direction of polarization against thermal fluctuations, and in turn, weaken relaxor behavior.

To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem with the NP approach is traced back to the use of a bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is nontrivially related to the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of $p\mathrm{H}$ and salt concentration.