We exploit a relation between the mean number ${\mathcal{N}}_m$ of minima of random Gaussian surfaces and extreme eigenvalues of random matrices to understand the critical behavior of ${\mathcal{N}}_m$ in the simplest glasslike transition occuring in a toy model of a single particle in an $N$-dimensional random environment, with $N\gg 1$. Varying the control parameter $\mu$ through the critical value ${\mu }_c$ we analyze in detail how ${\mathcal{N}}_m(\mu )$ drops from being exponentially large in the glassy phase to ${\mathcal{N}}_m(\mu )\sim 1$ on the other side of the transition. We also extract a subleading behavior of ${\mathcal{N}}_m(\mu )$ in both glassy and simple phases. The width $\delta \mu /{\mu }_c$ of the critical region is found to scale as $N^{-1/3}$ and inside that region ${\mathcal{N}}_m(\mu )$ converges to a limiting shape expressed in terms of the Tracy-Widom distribution.

Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that phenomenon is displayed. The possibility and significance of breaking of imaginary time-translation symmetry is discussed.

We consider the possibility that classical dynamical systems display motion in their lowest-energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling density waves.

Two years after the discovery of element 117, we undertook a second campaign using the ${}^{249}\mathrm{Bk}+{}^{48}\mathrm{Ca}$ reaction for further investigations of the production and decay properties of the isotopes of element 117 on a larger number of events. The experiments were started in the end of April 2012 and are still under way. This Letter presents the results obtained in 1200 hours of an experimental run with the beam dose of ${}^{48}\mathrm{Ca}$ of about $1.5\times {10}^{19}$ particles. The ${}^{249}\mathrm{Bk}$ target was irradiated at two energies of ${}^{48}\mathrm{Ca}$ that correspond to the maximum probability of the reaction channels with evaporation of three and four neutrons from the excited ${}^{297}117$. In this experiment, two decay chains of ${}^{294}117$ ($3n$) and five decay chains of ${}^{293}117$ ($4n$) were detected. In the course of the long-term work, ${}^{249}\mathrm{Cf}$—the product of decay of ${}^{249}\mathrm{Bk}$ (330 d)—is being accumulated in the target. Consequently, in the present experiment, we also detected a single decay of the known isotope ${}^{294}118$ that was produced during 2002–2005 in the reaction ${}^{249}\mathrm{Cf}({}^{48}\mathrm{Ca},3n){}^{294}118$. The obtained results are compared with the data from previous experiments. The experiments are carried out in the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, using the heavy-ion cyclotron U400.

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.

Aberration-corrected microscopes with subatomic resolution will impact broad areas of science and technology. However, the experimentally observed lifetime of the corrected state is just a few minutes. Here we show that the corrected state is intrinsically unstable; the higher its quality, the more unstable it is. Analyzing the contrast transfer function near optimum correction, we define an “instability budget” which allows a rational trade-off between resolution and stability. Unless control systems are developed to overcome these challenges, intrinsic instability poses a fundamental limit to the resolution practically achievable in the electron microscope.

The morphology and stability of thin volatile wetting films on model chemically patterned surfaces composed of periodic arrays of alternating completely and partially wettable nanostripes are investigated. The equilibrium film morphology is recorded as a function of undersaturation using noncontact atomic force microscopy. Films spanning the entire pattern are found to be stable only for thicknesses in excess of a critical value, $h_c$, whereas thinner films spontaneously dewet the partially wettable regions of the substrate. The critical thickness $h_c$ increases linearly with the width of the partially wettable stripes in good agreement with an interface displacement model derived from microscopic density functional theory. These results provide detailed insights into the dewetting of thin films driven by competing intermolecular forces.

We employ inelastic light scattering with magnetic fields to study intersubband spin plasmons in a quantum well. We demonstrate the existence of a giant collective spin-orbit (SO) field that splits the spin-plasmon spectrum into a triplet. The effect is remarkable as each individual electron would be expected to precess in its own momentum-dependent SO field, leading to D’yakonov-Perel’ dephasing. Instead, many-body effects lead to a striking organization of the SO fields at the collective level. The macroscopic spin moment is quantized by a uniform collective SO field, five times higher than the individual SO field. We provide a momentum-space cartography of this field.

We measure the temperature-dependent carrier density and resistivity of the topological surface state of thin exfoliated ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ in the absence of bulk conduction. When the gate-tuned chemical potential is near or below the Dirac point, the carrier density is strongly temperature-dependent, reflecting thermal activation from the nearby bulk valence band, while, above the Dirac point, unipolar $n$-type surface conduction is observed with negligible thermal activation of bulk carriers. In this regime, linear resistivity vs temperature reflects intrinsic electron-acoustic phonon scattering. A quantitative comparison with a theoretical transport calculation including both phonon and disorder effects gives the ratio of deformation potential to Fermi velocity $D/\hslash {\nu }_{\mathrm{F}}=4.7{\AA }^{-1}$. This strong phonon scattering in the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface state gives intrinsic limits for the conductivity and charge carrier mobility at room temperature of $\sim 550\mu \mathrm{S}$ per surface and $\sim 10000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$.

Here we establish the systematic existence of a $U(1)$ degeneracy of all symmetry-allowed Hamiltonians quadratic in the spins on the pyrochlore lattice, at the mean-field level. By extracting the Hamiltonian of ${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ from inelastic neutron scattering measurements, we then show that the $U(1)$-degenerate states of ${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ are its classical ground states, and unambiguously show that quantum fluctuations break the degeneracy in a way which is confirmed by experiment. The degree of symmetry protection of the classical $U(1)$ degeneracy in ${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is unprecedented in other materials. As a consequence, our observation of order by disorder is unusually definitive. We provide further verifiable consequences of this phenomenon, and several additional comparisons between theory and experiment.

We study the magneto-optical (MO) response of the polar semiconductor BiTeI with giant bulk Rashba spin splitting at various carrier densities. Despite being nonmagnetic, the material is found to yield a huge MO activity in the infrared region under moderate magnetic fields (up to $3\mathrm{T}$). Our first-principles calculations show that the enhanced MO response of BiTeI comes mainly from the intraband transitions between the Rashba-split bulk conduction bands. These transitions connecting electronic states with opposite spin directions become active due to the presence of strong spin-orbit interaction and give rise to distinct features in the MO spectra with a systematic doping dependence. We predict an even more pronounced enhancement in the low-energy MO response and dc Hall effect near the crossing (Dirac) point of the conduction bands.

We study, using the Bethe-Salpeter formalism, the singlet excitation energies of the zincbacteriochlorin-bacteriochlorin dyad, a paradigmatic photosynthetic complex. In great contrast with standard time-dependent density functional theory calculations with (semi)local kernels, charge transfer excitations are correctly located above the intramolecular $Q$-band transitions found to be in excellent agreement with experiment. Further, the asymptotic Coulomb behavior towards the true quasiparticle gap for charge transfer excitations at long distance is correctly reproduced, showing that the present scheme allows us to study with the same accuracy intramolecular and charge transfer excitations at various spatial ranges and screening environments without any adjustable parameter.

Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. An analytical expression for the effective potential between a pair of coarse-grained units is derived starting from the first-principles Ornstein-Zernike equation, for a polymer liquid where each chain is represented as a collection of interpenetrating blobs, with a variable number of blobs, $n_b$, of size $N_b$. The potential is characterized by a long tail, slowly decaying with characteristic scaling exponent of $N_b^{1/4}$. This general result applies to any coarse-grained model of polymer melts with units larger than the persistence length, highlighting the importance of the long, repulsive, potential tail for the model to correctly predict both structural and thermodynamic properties of the macromolecular liquid.

In communication networks, structure and dynamics are tightly coupled. The structure controls the flow of information and is itself shaped by the dynamical process of information exchanged between nodes. In order to reconcile structure and dynamics, a generic model, based on the local interaction between nodes, is considered for the communication in large social networks. In agreement with data from a large human organization, we show that the flow is non-Markovian and controlled by the temporal limitations of individuals. We confirm the versatility of our model by predicting simultaneously the degree-dependent node activity, the balance between information input and output of nodes, and the degree distribution. Finally, we quantify the limitations to network analysis when it is based on data sampled over a finite period of time.

We introduce a new approach to evaluate transition rates for rare events in complex many-particle systems. Building on a path-integral representation of transition probabilities for Markov processes, the rate is first expressed in terms of a free energy in the transition-path ensemble. We then define an auxiliary process where a suitably defined reaction variable is dynamically decoupled from all the others, whose dynamics is left unchanged. For this system the transition rates coincide with those of a unidimensional process whose only coordinate is the reaction variable. The free-energy difference between the auxiliary and the physical transition-path ensembles is finally evaluated using standard techniques. The efficiency of this method is deemed to be optimal because the physical and auxiliary dynamics differ by one degree of freedom only at any system size. Our method is demonstrated numerically on a simple model of Lennard-Jones particles ruled by the overdamped Langevin equation.

Hořava-Lifshitz gravity models contain higher-order operators suppressed by a characteristic scale, which is required to be parametrically smaller than the Planck scale. We show that recomputed synchrotron radiation constraints from the Crab Nebula suffice to exclude the possibility that this scale is of the same order of magnitude as the Lorentz breaking scale in the matter sector. This highlights the need for a mechanism that suppresses the percolation of Lorentz violation in the matter sector and is effective for higher-order operators as well.

We make a detailed experimental study of the threshold for the self-organization of thermal ${}^{87}\mathrm{Rb}$ atoms coupled to a high-finesse cavity over a range of atom numbers and cavity detunings. We investigate the difference between probing with a traveling wave and a retroreflected lattice. These two scenarios lead to qualitatively different behavior in terms of the response of the system as a function of cavity detuning with respect to the probe. In both cases, we confirm a $N^{-1}$ scaling of the threshold with atom number.

Quantum optimal control theory (QOCT) provides the necessary tools to theoretically design driving fields capable of controlling a quantum system towards a given state or along a prescribed path in Hilbert space. This theory must be complemented with a suitable model for describing the dynamics of the quantum system. Here, we are concerned with many electron systems (atoms, molecules, quantum dots, etc.) irradiated with laser pulses. The full solution of the many-electron Schrödinger equation is not feasible in general, and therefore, if we aim for an ab initio description, a suitable choice is the time-dependent density-functional theory (TDDFT). In this Letter, we establish the equations that combine TDDFT with QOCT and demonstrate their numerical feasibility.

Elastic filamentous structures found on swimming and flying organisms are versatile in function, rendering their precise contribution to locomotion difficult to assess. We show in this Letter that a single passive filament hinged on the rear of a bluff body placed in a stream can generate a net lift force without increasing the mean drag force on the body. This is a consequence of spontaneous symmetry breaking in the filament’s flapping dynamics. The phenomenon is related to a resonance between the frequency associated with the von Kármán vortex street developing behind the bluff body and the natural frequency of the free bending vibrations of the filament.

The effect of a large scale flow shear on a linearly unstable turbulent system is considered. A cubic equation describing the effective growth rate is obtained, which is shown to reduce to well-known forms in weak and strong shear limits. A shear suppression rule is derived which corresponds to the point where the effective growth rate becomes negative. The effect of flow shear on nonlinear mode coupling of drift or Rossby waves is also considered, and it is shown that the resonance manifold shrinks and weakens as the vortices are sheared. This leads to a reduction of the efficiency of three-wave interactions. Tilted eddies can then only couple to the large scale sheared flows, because the resonance condition for that interaction is trivially satisfied. It is argued that this leads to absorbtion of the sheared vortices by large scale flow structures. Studying the form of the effective growth rate for weak shear, it was shown that in addition to reducing the overall growth rate, a weak flow shear also reduces the wave number where the fluctuations are most unstable.