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Advances in physics have required the application of more and more sophisticated mathematics. I present arguments supporting the contention that the next advance beyond quantum field theory will require the application of a non-associative algebra. The principle observable effect would be the appearance of a fundamental length. An experimental search for such an effect may be feasible.
The electronic structure and ultrafast (10-15 s-femtosecond timescale) electron dynamics were investigated for clean and atom/molecule covered metal surfaces. The studies were performed by scanning tunneling microscopy (STM) to measure the structure of adsorbed atoms and molecules on metal surfaces, and to investigate their electronic properties. The electronic structure of the observed molecular networks was calculated by electronic structure theory in collaboration with Prof. Jin Zhao, who is a long-time collaborator, a Professor at the University of Science and Technology of China, and holds an Adjunct Professorship at the University of Pittsburgh. We also investigated the electronic properties of C60 molecules when they are templated by corrugated black phosphorous surfaces. We found unexpected charge delocalization that is enabled by the templating. This research was done in collaboration with Professor Min Feng at the Wuhan University, and who also holds an Adjunct Professorship at the University of Pittsburgh. Moreover, the electronic structure and electron dynamics in metal surfaces were investigated by time-resolved photoemission electron spectroscopy. The focus of ultrafast spectroscopy has been on the plasmonic response of silver surfaces. One direction has been to develop multidimensional (energy, momentum, and time) photoelectron spectroscopy of the coherent response of solid surfaces. This method was applied to study the collective electron excitations known generally as plasmons, which screen optical fields from penetration into metals. Although this collective response has been known for more than 60 years and is used extensively to deposit optical energy into metals, how this happens is poorly known. We investigated the plasmonic response of silver at the point where the dielectric response passes through zero and bulk plasmon is excited by light. We discovered that the plasmon excitation decays by exciting electrons from the Fermi level of a metal, which is contrary to what is believed in the plasmonic science community. This research has been performed in collaboration with Dr. Marcel Reutzel, who was a postdoctoral fellow working on this research at the University of Pittsburgh, and now has a faculty position at the University of Göttingen in Germany. Prof. Branko Gumhalter from the Institute of Physics in Zagreb contributed on the theory of plasmonic decay processes. Furthermore, we investigated the Floquet engineering of electronic bands in metals leading to multiphoton photoemission and above threshold photoemission. Finally, we demonstrated that it is possible to change the electronic structure of metals by application of optical fields. Our studies indicated that this happens on subfemtosecond time scale and could potentially be used in ultrafast information processing and quantum computation. Related document information
Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality.
Quantum gravity effects are traditionally tied to short distances and high energies. In this essay, we argue that, perhaps surprisingly, quantum gravity may have important consequences for the phenomenology of the infrared. We center our discussion around a conception of quantum gravity involving a notion of quantum spacetime that arises in metastring theory. This theory allows for an evolution of a cosmological Universe in which string-dual degrees of freedom decouple as the Universe ages. Importantly, such an implementation of quantum gravity allows for the inclusion of a fundamental length scale without introducing the fundamental breaking of Lorentz symmetry. The mechanism seems to have potential for an entirely novel source for dark matter/energy. The simplest observational consequences of this scenario may very well be residual infrared modifications that emerge through the evolution of the Universe.
This paper derives an expression for the rate of collisional slowing of charges in a magnetized plasma for which r{sub c} < λ{sub D}, where r{sub c} is the mean thermal cyclotron radius and λ{sub D} is the Debye length. The rate depends on a new fundamental length scale d that separates collisions into two impact parameter ranges that yield different slowing rates: a Boltzmann rate due to isolated binary collisions for impact parameters ρ < d and a Fokker-Planck rate due to multiple small scatterings for ρ > d. Slowing due to Boltzmann collisions is also shown to depend on the sign of the Coulomb interaction: for repulsive interactions, the slowing is enhanced by “collisional caging,” while for attractive interactions the Boltzmann slowing rate is zero.
Spin glass coherence lengths can be extracted from experiment and from numerical simulations. They encompasses the correlated region, and their growth in time makes them a useful tool for exploration of spin glass dynamics. Because they play the role of a fundamental length scale, they control the transition from the reversible to the chaotic state. This review explores their use for spin glass properties, ranging from scaling laws to rejuvenation and memory.
With the introduction of x-ray free electron laser sources around the world, new scientific approaches for visualizing matter at fundamental length and time-scales have become possible. As it relates to magnetism and ‘magnetic-type’ systems, advanced methods are being developed for studying ultrafast magnetic responses on the time-scales at which they occur. We describe three capabilities which have the potential to seed new directions in this area and present original results from each: pump-probe x-ray scattering with low energy excitation, x-ray photon fluctuation spectroscopy, and ultrafast diffuse x-ray scattering. By combining these experimental techniques with advanced modeling together with machine learning, we describe how the combination of these domains allows for a new understanding in the field of magnetism. Finally, we give an outlook for future areas of investigation and the newly developed instruments which will take us there.
It is commonly assumed that low-mass primordial black holes cannot constitute a significant fraction of the dark matter in our universe due to their predicted short lifetimes from the conventional Hawking radiation and evaporation process. Assuming physical black holes are nonsingular—likely due to quantum gravity or other high-energy physics—we demonstrate that a large class of nonsingular black holes have finite evaporation temperatures. This can lead to slowly evaporating low-mass black holes or to remnant mass states that circumvent traditional evaporation constraints. As a proof of concept, we explore the limiting curvature hypothesis and the evaporation process of a nonsingular black hole solution in two-dimensional dilaton gravity. We identify generic features of the radiation profile and compare them with known regular black holes, such as the Bardeen solution in four dimensions. Remnant masses are proportional to the fundamental length scale, and we argue that slowly evaporating low-mass nonsingular black holes, or remnants, are viable dark matter candidates. Published by the American Physical Society 2025
The manner in which transport properties vary over the entire parameter-space of coupling and magnetization strength is explored in this paper. Four regimes are identified based on the relative size of the gyroradius compared to other fundamental length scales: the collision mean free path, Debye length, distance of closest approach, and interparticle spacing. Molecular dynamics simulations of self-diffusion and temperature anisotropy relaxation spanning the parameter space are found to agree well with the predicted boundaries. Finally, comparison with existing theories reveals regimes where they succeed, where they fail, and where no theory has yet been developed.
Clouds remain the largest source of uncertainty in our understanding of global climate change. Different aspects of the planetary cloud field can provide positive and negative feedback to the Earth’s energy balance, and clouds of course are directly implicated in changes to the planetary distribution of precipitation. A fundamental problem in our current understanding of the role of clouds in the dynamics of climate are that current resolutions do not resolve the fundamental length scales associated with clouds. We expect our understanding of the role of clouds in climate to undergo a qualitative change as the resolutions of global models begin to encompass clouds. At these resolutions (which roughly scale with the tropopause height of 10km) non-hydrostatic dynamics become significant and deep convective processes are resolved. We are poised at the threshold of being able to run global scale simulations that include direct, nonparameterized, simulations of deep convective clouds. The goal of this research is to use the Argonne Leadership Computing Facility to explore the frontier of weather prediction and climate modeling with the newly developed Geophysical Fluid Dynamics (GFDL) global cloud-resolving model. A single unified atmospheric modeling system with a cubed-sphere dynamical core and bulk cloud micro-physics running at 3.5km resolutions was run with the goal of capturing the climatology of clouds and severe storms in a warming world. The ability to reproduce historical tropical storm statistics will be used as a test of this ground-breaking model.
We revisit three variants of the well-known Stommel diagrams that have been used to summarize knowledge of characteristic scales in time and space of some important hydrologic phenomena and modified these diagrams focusing on spatiotemporal scaling analyses of the underlying hydrologic processes. In the present paper we focus on soil formation, vegetation growth, and drainage network organization. We use existing scaling relationships for vegetation growth and soil formation, both of which refer to the same fundamental length and timescales defining flow rates at the pore scale but different powers of the power law relating time and space. The principle of a hierarchical organization of optimal subsurface flow paths could underlie both root lateral spread (RLS) of vegetation and drainage basin organization. To assess the applicability of scaling, and to extend the Stommel diagrams, data for soil depth, vegetation root lateral spread, and drainage basin length have been accessed. The new data considered here include timescales out to 150 Myr that correspond to depths of up to 240 m and horizontal length scales up to 6400 km and probe the limits of drainage basin development in time, depth, and horizontal extent.
Based on the analysis of electron phase trajectories in sinusoidal electric fields, a new point of view on discharge stratification is proposed. It is shown that the positive column can be considered as a spatial resonator in which electric fields with a fundamental period length L{sub S} or higher mode length q/p L{sub S} establish, where p and q are integers and p > q. The fundamental mode length L{sub S} is equivalent to the distance on which electrons gain energy equal to the lowest excitation threshold. This distance determines a length of the S-striation. Unlike kinetic theory, in the presented model resonance properties of the discharge column are not connected with elastic collision energy losses. A point map is used to obtain the resonance trajectories of electrons in the phase plane. Stable points for the positions of inelastic collisions in the resonance trajectories have been found at the positions of field maxima in the case of integer ratios p/q . For non-integer ratios p/q , multiple resonance trajectories arise according to a more complex stability criterion. From this point of view, S-, P-, and R-striations in noble gas discharges can be explained. Due to energy losses in elastic collisions, initial electron energy distribution functions converge to the resonance trajectories (the so-called “bunch effect”). The findings of the discrete model agree with results of kinetic theory and experiment. The new approach avoids difficulties of the kinetic theory in the case of exceptionally large relaxation lengths which can even exceed the positive column length.
The inelastic scattering length (L s ) is a length scale of fundamental importance in condensed matters due to the relationship between inelastic scattering and quantum dephasing. In quantum anomalous Hall (QAH) materials, the mesoscopic length scale L s plays an instrumental role in determining transport properties. Here we examine L s in three regimes of the QAH system with distinct transport behaviors: the QAH, quantum critical, and insulating regimes. Although the resistance changes by five orders of magnitude when tuning between these distinct electronic phases, scaling analyses indicate a universal L s among all regimes. Finally, mesoscopic scaled devices with sizes on the order of L s were fabricated, enabling the direct detection of the value of L s in QAH samples. Our results unveil the fundamental length scale that governs the transport behavior of QAH materials.
Relative stabilities of small Ga{sub n}As{sub m} clusters, as well as their structural electronic and vibrational properties, were computed and analysed using a CCSD(T) reference method since experimental data in this area are sparse or unknown. With the aim of investigating larger clusters, we explored several DFT functionals and basis sets able to mimic the reliable CCSD(T) approach. Among them, the PBE0/SBKJC+sp,d appears as the most efficient to describe the structural and vibrational properties since average differences of about 0.042Å and 5.1cm{sup −1} were obtained for bond lengths and fundamental vibrational frequencies, respectively for the first small clusters [1] of the series found from our GSAM method [2]. As further test, this model is used in order to investigate and revisit an experimental IR spectrum of Ga{sub n}As{sub m} mixture previously published by Li et al. [3]. More complicated is the difficulty which arises in the electronic description due to the presence of numerous low lying electronic states nearly degenerated to correctly describe the electronic structure. The case of Ga{sub 2}As will be discussed and the photoelectron spectra of the Ga{sub 2}As anion reanalyzed on the ground of our calculations [4] comparatively to the experimental spectra obtained by Neumark and co-workers [5].
Here, this article provides a brief overview of advanced magnetic X-ray spectro-microscopies that are widely used in characterizing mesoscopic magnetic materials. Common to those techniques are various X-ray magnetic dichroism effects that are used as magnetic contrast mechanism. A particular interest is to use those techniques to image the underlying microscopic spin structures in magnetic materials with high spatial resolution and to ultimately resolve their full 3D mesoscale characteristics with elemental sensitivity, as well as their ultrafast dynamics upon excitations with field and current pulses. Recent research examples using various magnetic X-ray spectro-microscopies are presented to showcase their specific features with a focus on imaging novel topological spin textures, such as vortices, skyrmions and Hopfions, which are considered as potential building blocks towards low power, high-speed and high-density magnetic devices that could transform information technologies and potentially be used in biomedical applications. Future developments with magnetic X-ray spectro-microscopies harness the full coherence of next generation X-ray sources and could open the path towards single shot imaging with spatial and temporal resolutions down to fundamental magnetic length and time scales.
Cracks, the major vehicle for material failure, undergo a micro-branching instability at ~40% of their sonic limiting velocity in three dimensions. Recent experiments showed that in thin systems cracks accelerate to nearly their limiting velocity without micro-branching, until undergoing an oscillatory instability. Despite their fundamental importance, these dynamic instabilities are not explained by the classical theory of cracks, which is based on linear elasticity and an extraneous local symmetry criterion to predict crack paths. We develop a two-dimensional theory for predicting arbitrary paths of ultrahigh-speed cracks, which incorporates elastic nonlinearity without extraneous criteria. We show that cracks undergo an oscillatory instability controlled by small-scale, near crack-tip, elastic nonlinearity. This instability occurs above an ultrahigh critical velocity and features an intrinsic wavelength proportional to the ratio of the fracture energy to the elastic modulus, in quantitative agreement with experiments. As a result, this ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics.
The most obvious obstacle behind a direct test of quantum gravity (QG) is its energy scale (1019 GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective theories of QG which can be performed in a lower energy scale. This paper is aimed in this direction, and shows a promising path to test the existence of the fundamental minimal length scale of Nature by measuring the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relationship between the position and momentum operators and, in this paper, we show that such a modification of the commutator has a profound effect on the dispersion rate of free wave-packets, and precise measurement on the broadening times of large molecular wave-packets (such as C 60, C 176 and large organic molecules) provide a promising path for an indirect test of quantum gravity, in a laboratory setting.
The scientific and technological exploration of artificially designed three-dimensional magnetic nanostructures opens the path to exciting novel physical phenomena, originating from the increased complexity in spin textures, topology, and frustration in three dimensions. Theory predicts that the equilibrium magnetic ground state of two-dimensional systems which reflects the competition between symmetric (Heisenberg) and antisymmetric (Dzyaloshinskii-Moriya interaction (DMI)) exchange interaction is significantly modified on curved surfaces when the radius of local curvature becomes comparable to fundamental magnetic length scales. In this CRADA we performed collaboratively an experimental study of the spin texture in an 8 nm thin magnetic multilayer with growth-induced in-plane anisotropy and DMI deposited onto the curved surface of a 1.8µm long non-magnetic carbon nanowire with a 67 nm radius. The sample was fabricated in Juelich and with collaborators at BESSY in Berlin. Using magnetic soft x-ray tomography at the ALBA synchrotron in Spain, the three-dimensional spin configuration in this nanotube was retrieved with about 30nm spatial resolution. The transition between two vortex configurations on the two ends of the nanotube with opposite circulation occurs through a domain wall that is aligned at an inclined angle relative to the wire axis. Three-dimensional micromagnetic simulations support the experimental observations and represent a visualization of the curvature-mediated DMI. They also allow a quantitative estimate of the DMI value for the magnetic multilayered nanotube.