Quantum acoustics unravels Planckian resistivity.

Strange metals exhibit universal linear-in-temperature resistivity described by a Planckian scattering rate, the origin of which remains elusive. By employing an approach inspired by quantum optics, we arrive at the coherent state representation of lattice vibrations: quantum acoustics. Utilizing this nonperturbative framework, we demonstrate that lattice vibrations could serve as active drivers in the Planckian resistivity phenomenon, challenging prevailing theories. By treating charge carriers as quantum wave packets negotiating the dynamic acoustic field, we find that a competition ensues between localization and delocalization giving rise to the previously conjectured universal quantum bound of diffusion, [Formula: see text], independent of temperature or any other material parameters. This leads to the enigmatic T-linear resistivity over hundreds of degrees, except at very low temperatures. Quantum diffusion also explains why strange metals have much higher electrical resistivity than typical metals. Our work elucidates the critical role of phonons in Planckian resistivity from a unique perspective and reconsiders their significance in the transport properties of strange metals.

Quantum-Acoustical Drude Peak Shift.

Quantum acoustics-a recently developed framework parallel to quantum optics-establishes a nonperturbative and coherent treatment of the electron-phonon interaction in real space. The quantum-acoustical representation reveals a displaced Drude peak hiding in plain sight within the venerable Fröhlich model: the optical conductivity exhibits a finite frequency maximum in the far-infrared range and the dc conductivity is suppressed. Our results elucidate the origin of the high-temperature absorption peaks in strange or bad metals, revealing that dynamical lattice disorder steers the system towards a non-Drude behavior.

Propagation of waves in high Brillouin zones: Chaotic branched flow and stable superwires.

We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brillouin zones. Branched flow appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The strongest branches remain stable indefinitely and may create linear dynamical channels, wherein waves are not confined directly by potential walls as electrons in ordinary wires but rather, indirectly and more subtly by dynamical stability. We term these superwires since they are associated with a superlattice.

Rise and Fall of Anderson Localization by Lattice Vibrations: A Time-Dependent Machine Learning Approach.

The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fröhlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron-lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fröhlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron-lattice properties.

Chaos-Assisted Dynamical Tunneling in Flat Band Superwires.

Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static or energetic confinement observed in traditional wave guides or one-dimensional electron wires. The quantum properties of superwires give rise to elastic dynamical tunneling, linking disjoint regions of the corresponding classical phase space, and enabling the emergence of several parallel channels. This paper provides the underlying theory and mechanisms that facilitate dynamical tunneling assisted by chaos in periodic lattices. Moreover, we show that the mechanism of dynamical tunneling can be effectively conceptualized through the lens of a paraxial approximation. Our results further reveal that superwires predominantly exist within flat bands, emerging from eigenstates that represent linear combinations of conventional degenerate Bloch states. Finally, we quantify tunneling rates across various lattice configurations and demonstrate that tunneling can be suppressed in a controlled fashion, illustrating potential implications in future nanodevices.

Density of Avoided Crossings and Diabatic Representation.

Electronic structure theory describes the properties of solids using Bloch states that correspond to highly symmetrical nuclear configurations. However, nuclear thermal motion destroys translation symmetry. Here, we describe two approaches relevant to the time evolution of electronic states in the presence of thermal fluctuations. On the one hand, the direct solution of the time-dependent Schrodinger equation for a tight-binding model reveals the diabatic nature of time evolution. On the other hand, because of random nuclear configurations, the electronic Hamiltonian falls into the class of random matrices, which have universal features in their energy spectra. In the end, we discuss combining two approaches to obtain new insights into the influence of thermal fluctuations on electronic states.

Bragg Scattering from a Random Potential.

A potential for propagation of a wave in two dimensions is constructed from a random superposition of plane waves around all propagation angles. Surprisingly, despite the lack of periodic structure, sharp Bragg diffraction of the wave is observed, analogous to a powder diffraction pattern. The scattering is partially resonant, so Fermi's golden rule does not apply. This phenomenon would be experimentally observable by sending an atomic beam into a chaotic cavity populated by a single mode laser.

Lazy electrons in graphene.

Within a tight-binding approximation, we numerically determine the time evolution of graphene electronic states in the presence of classically vibrating nuclei. There is no reliance on the Born-Oppenheimer approximation within the p-orbital tight-binding basis, although our approximation is "atomically adiabatic": the basis p-orbitals are taken to follow nuclear positions. Our calculations show that the strict adiabatic Born-Oppenheimer approximation fails badly. We find that a diabatic (lazy electrons responding weakly to nuclear distortions) Born-Oppenheimer model provides a much more accurate picture and suggests a generalized many-body Bloch orbital-nuclear basis set for describing electron-phonon interactions in graphene.

The momentum of models.

There are opportunities for the application of chemical physics style thinking to models central to solid state physics. Solid state physics has largely been left to its own devices by the chemical physics theory community, which is a shame. I will show here that cross fertilization of ideas is real and beneficial to science. This essay is written with the hope of encouraging young theorists with a chemical physics background to enter this rich and promising area. There are many low hanging fruit available essentially because condensed matter physics traditions, models, and standards for progress are so much different than in chemical physics. By way of a warning label, right now neither community is supporting this endeavor. I am hoping this article will help, a little. I make the apology for using mainly (but not exclusively) my own narrow experience and contributions to illustrate this essay. I understand it is only a small piece of the pie, but I do believe the message here is larger: a chemical physics mindset is complementary to the condensed matter physics mindset, and they would work best together.

Schrödinger Correspondence Applied to Crystals.

In 1926, E. Schrödinger showed that the mean position and mean momentum of the displaced ground state in a harmonic oscillator obey the equations of motion of the classical oscillator. This Schrödinger Correspondence Principle, extended to an N-dimensional harmonic oscillator, is an intuitive and powerful way to approach many aspects of harmonic solids by converting the quantum-mechanical problems to the classical ones. For the application of the correspondence principle, the concepts of the phonon and its pseudomomentum are clarified, and the importance of taking into account the center-of-mass momentum is explained. Also, the concept of the antiphonon is introduced through the examples of physical processes in a line and a ring of atoms. With the correspondence principle, the quantum behavior of harmonic solids under a Mössbauer-like kick is analyzed classically, and the simulation verified the formation of an antiphonon.

Reassessing Graphene Absorption and Emission Spectroscopy.

We present a new paradigm for understanding optical absorption and hot electron dynamics experiments in graphene. Our analysis pivots on assigning proper importance to phonon-assisted indirect processes and bleaching of direct processes. We show indirect processes figure in the excess absorption in the UV region. Experiments which were thought to indicate ultrafast relaxation of electrons and holes, reaching a thermal distribution from an extremely nonthermal one in under 5-10 fs, instead are explained by the nascent electron and hole distributions produced by indirect transitions. These need no relaxation or ad-hoc energy removal to agree with the observed emission spectra and fast pulsed absorption spectra. The fast emission following pulsed absorption is dominated by phonon-assisted processes, which vastly outnumber direct ones and are always available, connecting any electron with any hole any time. Calculations are given, including explicitly calculating the magnitude of indirect processes, supporting these views.

Characterizing Time Irreversibility in Disordered Fermionic Systems by the Effect of Local Perturbations.

We study the effects of local perturbations on the dynamics of disordered fermionic systems in order to characterize time irreversibility. We focus on three different systems: the noninteracting Anderson and Aubry-André-Harper (AAH) models and the interacting spinless disordered t-V chain. First, we consider the effect on the full many-body wave functions by measuring the Loschmidt echo (LE). We show that in the extended or ergodic phase the LE decays exponentially fast with time, while in the localized phase the decay is algebraic. We demonstrate that the exponent of the decay of the LE in the localized phase diverges proportionally to the single-particle localization length as we approach the metal-insulator transition in the AAH model. Second, we probe different phases of disordered systems by studying the time expectation value of local observables evolved with two Hamiltonians that differ by a spatially local perturbation. Remarkably, we find that many-body localized systems could lose memory of the initial state in the long-time limit, in contrast to the noninteracting localized phase where some memory is always preserved.

Directed HK propagator.

We offer a more formal justification for the successes of our recently communicated "directed Heller-Herman-Kluk-Kay" (DHK) time propagator by examining its performance in one-dimensional bound systems which exhibit at least quasi-periodic motion. DHK is distinguished by its single one-dimensional integral--a vast simplification over the usual 2N-dimensional integral in full Heller-Herman-Kluk-Kay (for an N-dimensional system). We find that DHK accurately captures particular coherent state autocorrelations when its single integral is chosen to lie along these states' fastest growing manifold, as long as it is not perpendicular to their action gradient. Moreover, the larger the action gradient, the better DHK will perform. We numerically examine DHK's accuracy in a one-dimensional quartic oscillator and illustrate that these conditions are frequently satisfied such that the method performs well. This lends some explanation for why DHK frequently seems to work so well and suggests that it may be applicable to systems exhibiting quite strong anharmonicity.

Communication: HK propagator uniformized along a one-dimensional manifold in weakly anharmonic systems.

A simplification of the Heller-Herman-Kluk-Kay (HK) propagator is presented that does not suffer from the need for an increasing number of trajectories with dimensions of the system under study. This is accomplished by replacing HK's uniformizing integral over all of phase space by a one-dimensional curve that is appropriately selected to lie along the fastest growing manifold of a defining trajectory. It is shown that this modification leads to eigenspectra of quantum states in weakly anharmonic systems that can outperform the comparatively computationally cheap thawed Gaussian approximation method and frequently approach the accuracy of spectra obtained with the full HK propagator.

Collision dynamics of polyatomic molecules containing carbon rings at low temperatures.

We explore the collision dynamics of complex hydrocarbon molecules (benzene, coronene, adamantane, and anthracene) containing carbon rings in a cold buffer gas of (3)He. For benzene, we present a comparative analysis of the fully classical and fully quantum calculations of elastic and inelastic scattering cross sections at collision energies between 1 and 10 cm(-1). The quantum calculations are performed using the time-independent coupled channel approach and the coupled-states approximation. We show that the coupled-states approximation is accurate at collision energies between 1 and 20 cm(-1). For the classical dynamics calculations, we develop an approach exploiting the rigidity of the carbon rings and including low-energy vibrational modes without holonomic constraints. Our results illustrate the effect of the molecular shape and the vibrational degrees of freedom on the formation of long-lived resonance states that lead to low-temperature clustering.

Stability of branched flow from a quantum point contact.

In classically chaotic systems, small differences in initial conditions are exponentially magnified over time. However, it was observed experimentally that the (necessarily quantum) "branched flow" pattern of electron flux from a quantum point contact (QPC) traveling over a random background potential in two-dimensional electron gases remains substantially invariant to large changes in initial conditions. Since such a potential is classically chaotic and unstable to changes in initial conditions, it was conjectured that the origin of the observed stability is purely quantum mechanical, with no classical analog. In this Letter, we show that the observed stability is a result of the physics of the quantum point contact and the nature of the experiment. We show that the same stability can indeed be reproduced classically, or quantum mechanically. In addition, we explore the stability of the branched flow with regards to changes in the eigenmodes of the quantum point contact.

Generalized dephasing relation for fidelity and application as an efficient propagator.

The dephasing relation (DR), a linearization of semiclassical fidelity, is generalized to include the overlap of "off-diagonal" elements. The accuracy of the formulation is tested in integrable and chaotic systems and its scaling with dimensionality is studied in a Caldeira-Leggett model with many degrees of freedom. It is shown that the DR is often in very good agreement with numerically analytic quantum results and frequently outperforms an alternative semiclassical treatment. Most importantly, since there is no computationally expensive prefactor, and Monte Carlo Metropolis sampling is used to facilitate the calculation, the DR is found to scale remarkably well with increasing dimension. We further demonstrate that a propagator based on the DR can include more quantum coherence and outperform other popular linearized semiclassical methods, such as forward-backward semiclassical dynamics (FBSD) and the linearized semiclassical initial value representation (LSC-IVR).

Cold collisions of complex polyatomic molecules.

We introduce a method for classical trajectory calculations to simulate collisions between atoms and large rigid asymmetric-top molecules. We investigate the formation of molecule-helium complexes in buffer-gas cooling experiments at a temperature of 6.5 K for molecules as large as naphthalene. Our calculations show that the mean lifetime of the naphthalene-helium quasi-bound collision complex is not long enough for the formation of stable clusters under the experimental conditions. Our results suggest that it may be possible to improve the efficiency of the production of cold molecules in buffer-gas cooling experiments by increasing the density of helium. In addition, we find that the shape of molecules is important for the collision dynamics when the vibrational motion of molecules is frozen. For some molecules, it is even more crucial than the number of accessible degrees of freedom. This indicates that by selecting molecules with suitable shape for buffer-gas cooling, it may be possible to cool molecules with a very large number of degrees of freedom.

Inflationary dynamics for matrix eigenvalue problems.

Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the acoustic modes of a concert hall, or hundreds of other physical quantities. Often only the few eigenpairs with the lowest or highest frequency (extremal solutions) are needed. Methods that have been developed over the past 60 years to solve such problems include the Lanczos algorithm, Jacobi-Davidson techniques, and the conjugate gradient method. Here, we present a way to solve the extremal eigenvalue/eigenvector problem, turning it into a nonlinear classical mechanical system with a modified Lagrangian constraint. The constraint induces exponential inflationary growth of the desired extremal solutions.

Quantum corral resonance widths: lossy scattering as acoustics.

We present an approach to predicting extrinsic electron resonance widths within quantum corral nanostructures based on analogies with acoustics. Established quantum mechanical methods for calculating resonance widths, such as multiple scattering theory, build up the scattering atom by atom, ignoring the structure formed by the atoms, such as walls or enclosures. Conversely, particle-in-a-box models, assuming continuous walls, have long been successful in predicting quantum corral energy levels, but not resonance widths. In acoustics, partial reflection from walls and various enclosures has long been incorporated for determining reverberation times. Pursuing an exact analogy between the local density of states of a quantum corral and the acoustic impedance of a concert hall, we show electron lifetimes in nanoscopic structures of arbitrary convex shape are well accounted for by the Sabine formula for acoustic reverberation times. This provides a particularly compact and intuitive prescription for extrinsic finite lifetimes in a particle-in-a-box with leaky walls, including quantum corral atomic walls, given single particle scattering properties.