We reformulate the full quantum dynamics of spin systems using a phase-space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. This representation is superior in practice to an earlier phase-space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times severalfold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse-field Ising model in one and two dimensions.

In developing the phonon quasiparticle picture, Peierls discovered that, in a perfect crystal, without anharmonic umklapp ($U$) events, a current-carrying distribution can never relax to a zero-current distribution. Callaway introduced a simplified approximate model version of the Peierls-Boltzmann equation, retaining its ability to deal separately with normal ($N$) and $U$ events. This paper clarifies and improves the Callaway model, and shows that Callaway underestimated the suppression of $N$ processes in relaxing thermal current. The new result should improve computations of thermal conductivity from relaxation-time studies.

We show how disorder can be used to guide a broadband ultrasonic wave. The idea is to exploit the transverse localization regime that has been reported for light. Our waveguide consists of a set of parallel cylindrical scatterers randomly distributed in the transverse plane. An ultrasonic beam propagating along the direction of scatterers is found to remain confined in the two other directions on a size smaller than the waveguide diameter and driven by the localization length. Interestingly, the guided wave is also found to propagate with a very limited temporal dispersion.

We present Raman scattering results on phonon polaritons in single crystals of $\alpha$-GaN. A detailed theoretical treatment of their dispersion and Raman scattering efficiency in wurtzite-type crystals is given. Pure symmetry polaritons (ordinary and extraordinary) are accessible in near-forward scattering geometry according to the theory. For this purpose, the experimental setup uses rectangular aperture windows in front of the entrance lens. Thus measurements with well defined wave-vector transfer can be realized. The observed dispersion curves and scattering efficiency results are compared with theoretical ones and are found to be in excellent agreement.

From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics, many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have highlighted the role of its symmetric counterpart, the quantum metric tensor. In this paper, we perform a detailed analysis of the ground state Riemannian geometry induced by the metric tensor, using the quantum $XY$ chain in a transverse field as our primary example. We focus on a particular geometric invariant, the Gaussian curvature, and show how both integrals of the curvature within a given phase and singularities of the curvature near phase transitions are protected by critical scaling theory. For cases where the curvature is integrable, we show that the integrated curvature provides a new geometric invariant, which like the Chern number characterizes individual phases of matter. For cases where the curvature is singular, we classify three types (integrable, conical, and curvature singularities) and detail situations where each type of singularity should arise. Finally, to connect this abstract geometry to experiment, we discuss three different methods for measuring the metric tensor: via integrating a properly weighted noise spectral function or by using leading-order responses of the work distribution to ramps and quenches in quantum many-body systems.

I consider refrigeration and heat engine circuits based on the nonlinear thermoelectric response of point contacts at pinch off, allowing for electrostatic interaction effects. I show that a refrigerator can cool to much lower temperatures than predicted by the thermoelectric figure of merit $ZT$ (which is based on linear-response arguments). The lowest achievable temperature has a discontinuity, called a fold catastrophe in mathematics, at a critical driving current $I=I_{\mathrm{c}}$. For $I>I_{\mathrm{c}}$ one can in principle cool to absolute zero, when for $I<I_{\mathrm{c}}$ the lowest temperature is about half the ambient temperature. Heat backflow due to phonons and photons stops cooling at a temperature above absolute zero, and above a certain threshold turns the discontinuity into a sharp cusp. I also give a heuristic condition for when an arbitrary system's nonlinear response means that its $ZT$ ceases to indicate (even qualitatively) the lowest temperature to which the system can refrigerate.

The dynamic responses of a rhodium catalyst and a graphene sheet are investigated upon random excitation with 80 kV electrons. An extraordinary electron microscope stability and resolution allow studying temporary atom displacements from their equilibrium lattice sites into metastable sites across projected distances as short as 60 pm. In the rhodium catalyst, directed and reversible atom displacements emerge from excitations into metastable interstitial sites and surface states that can be explained by single atom trajectories. Calculated energy barriers of 0.13 eV and 1.05 eV allow capturing single atom trapping events at video rates that are stabilized by the Rh [110] surface corrugation. Molecular dynamics simulations reveal that randomly delivered electrons can also reversibly enhance the $s{p}^3$ and the $s{p}^1$ characters of the $s{p}^2$-bonded carbon atoms in graphene. The underlying collective atom motion can dynamically stabilize characteristic atom displacements that are unpredictable by single atom trajectories. We detect three specific displacements and use two of them to propose a path for the irreversible phase transformation of a graphene nanoribbon into carbene. Collectively stabilized atom displacements greatly exceed the thermal vibration amplitudes described by Debye-Waller factors and their measured dose rate dependence is attributed to tunable phonon contributions to the internal energy of the systems. Our experiments suggest operating electron microscopes with beam currents as small as zepto-amperes/nm${}^2$ in a weak-excitation approach to improve on sample integrity and allow for time-resolved studies of conformational object changes that probe for functional behavior of catalytic surfaces or molecules.

The generation, relaxation, and diffusion dynamics of optically induced lattice distortion in the relaxed excited state of SrTiO${}_3$ are studied by using polarization spectroscopy with the pump-probe technique. The relaxed excited state is generated with a rise time on the order of 100 ps. Three kinds of thermal activation processes of the localized lattice distortion are found, and these processes are considered to be caused by photogenerated carriers in trapped states, which play important roles in photoluminescence or photoconductivity. We observed the lattice distortion induced by a separated pump beam from the probe beam to investigate its itineracy. The lattice-distortion signal appears later as the separation along the [100] axis becomes larger. The temperature dependence of the mobility suggests that the observed diffusive lattice distortion is caused by photogenerated electrons accompanied by lattice distortion, or electron polarons. Thus, the spatial and temporal dynamics of polaron diffusion were observed directly in our experiment.

We have performed systematic studies of the lattice dynamics in $L$FeAsO ($L=\text{La}$, Ce, Pr, Nd, Sm) in the parent and in the $\sim$10% F-doped compounds as a function of pressure and temperature. We have found that the modifications in the partial Fe density of phonon states are mainly governed by the Fe-As bond length. The change of this bond length explains the change of the Fe density of phonon states above 25 meV. We further observe anomalies in the behavior of the phonon mode near 16 meV. In the parent phase, this mode softens anomalously upon cooling through the structural phase transition. Upon F doping, this mode hardens indicating a strong electron-phonon coupling. This suggests that the corresponding phonons play an important role in the competition between superconductivity and magnetism in these materials.

Quasilongitudinal and quasitransverse picosecond strain pulses injected into a ferromagnetic (311) (Ga,Mn)As film induce dynamical shear strain in the film, thereby modulating the magnetic anisotropy and inducing resonant precession of the magnetization at a frequency ∼10 GHz. The modulation of the out-of-plane magnetization component by the quasitransverse strain reaches amplitudes as large as 10$\%$ of the equilibrium magnetization. Our theoretical analysis is in good agreement with the observed results, thus providing a strategy for ultrafast magnetization control in ferromagnetic films by strain pulses.

Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to nonequilibrium behavior. The Kibble-Zurek problem is to determine the dynamical evolution of the system parametrically close to its critical point when the change is parametrically slow. The nonequilibrium behavior in this limit is controlled entirely by the critical point and the details of the trajectory of the system in parameter space (the protocol) close to the critical point. Together, they define a universality class consisting of critical exponents, discussed in the seminal work by Kibble and Zurek, and scaling functions for physical quantities, which have not been discussed hitherto. In this article, we give an extended and pedagogical discussion of the universal content in the Kibble-Zurek problem. We formally define a scaling limit for physical quantities near classical and quantum transitions for different sets of protocols. We report computations of a few scaling functions in model Gaussian and large-$N$ problems and prove their universality with respect to protocol choice. We also introduce a protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.

We investigate layered acoustic metamaterials capable of exhibiting a wide variety of wave propagation phenomena, including backward and forward waves with and without negative refraction. The metamaterials are formed by periodically perforated hard plates, which we describe analytically in the limit of small holes compared to both the period and the separation between plates. In particular, we derive expressions for the index of refraction and the transmission and reflection coefficients of finite slabs. We provide illustrative examples of near fields for all four combinations of backward and forward waves with and without negative refraction, along with dispersion diagrams that explain the observed behavior. A comprehensive study of the range of geometrical parameters in which these distinct phenomena are observed is presented as well. These metamaterials hold great promise for achieving full control of sound using simple structures, with potential application to acoustic technologies relying on subwavelength control and imaging of sound.

We study a lattice model of interacting loops in three dimensions with a $1/r^2$ interaction. Using Monte Carlo methods, we have found that the phase diagram contains a line of second-order phase transitions between a phase where the loops are gapped and a phase where they proliferate. The correlation length exponent and critical conductivity vary continuously along this line. Our model is exactly self-dual at a special point on the critical line, which allows us to calculate the critical conductivity exactly at this point.

An ab initio equation of motion method is introduced to calculate the temperature-dependent mean-square vibrational amplitudes ${\sigma }^2$ which appear in the Debye-Waller factors in x-ray absorption, x-ray scattering, and related spectra. The approach avoids explicit calculations of phonon modes, and is based instead on calculations of the displacement-displacement time correlation function from ab initio density functional theory molecular dynamics simulations. The method also yields the vibrational density of states and thermal quantities such as the lattice free energy. Illustrations of the method are presented for a number of systems and compared with other methods and experiment.

The lattice dynamics of the filled skutterudite YbFe${}_4$Sb${}_{12}$ was studied by resonant ultrasound spectroscopy and an anomalous softening in the temperature dependence of the elastic constants at $\sim$50 K was observed. This anomaly can not be explained by the dynamics of the filler, in contrast to other filled skutterudites. We have further investigated the origin of this anomaly using macroscopic and microscopic measurements. A rearrangement of the spectral weight of the Yb phonon states was observed in the temperature dependence of the density of phonon states, obtained by inelastic neutron scattering. We suggest that the anomaly is due to a change of the Yb valence state and that the anomaly and the phonon spectral weight rearrangement have the same origin.

An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic—or higher order—potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated.

The theory of the spectra of coupled magnetoelastic waves in ferromagnetic shape-memory alloys (FSMA) is developed. The possibility of an abnormally strong coupling of spin waves with the soft elastic mode at approaching the martensitic transformation (MT) temperature is disclosed. In particular the magnetoelastic waves in Ni–Mn–Ga single crystals are considered. A considerable (by an order of magnitude) reduction of the shear elastic modulus and an appropriate lowering of the transversal velocity of sound in the applied magnetic field are predicted. Optimum conditions for the experimental observation of the predicted effects are specified.

A quantum many-body system that is prepared in the ground state of an integrable Hamiltonian does not directly thermalize after a sudden small parameter quench away from integrability. Rather, it will be trapped in a prethermalized state and can thermalize only at a later stage. We discuss several examples for which this prethermalized state shares some properties with the nonthermal steady state that emerges in the corresponding integrable system. These examples support the notion that nonthermal steady states in integrable systems may be viewed as prethermalized states that never decay further. Furthermore, we show that prethermalization plateaus are under certain conditions correctly predicted by generalized Gibbs ensembles, which are the appropriate extension of standard statistical mechanics in the presence of many constants of motion. This establishes that the relaxation behaviors of integrable and nearly integrable systems are continuously connected and described by the same statistical theory.