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At least 307 records · Page 17

Emergent Above-Gap Photoluminescence in Molecularly Engineered Hybrid Bilayer Crystals

Bilayer crystals, built by stacking two-dimensional (2D) covalent monolayers, give rise to coupled excitonic states whose properties are constrained by fixed lattice symmetry and orientation. Replacing one covalent monolayer with a 2D molecular crystal––held together by non-covalent forces––overcomes this limitation, as molecular functional groups afford tunable in-plane lattice geometry, intermolecular spacing, and interlayer coupling, providing a powerful knob for exciton engineering. Here, in this study, we report four-atom-thick hybrid bilayer crystals (HBCs) synthesized by directly growing single-crystalline PDI molecular crystal atop WS 2 monolayers, which exhibit a robust photoluminescence (PL) peak 120 meV above the WS 2 optical band gap alongside a belowgap emission. Both peaks display strong polarization anisotropy—nearing unity for the above-gap emission—and maintain a perfectly linear power-law dependence up to an excitation density of ~10 7 mW/cm 2 , indicative of coexisting localized and delocalized excitonic states. Substituting PDI with a PTCDA monolayer on WS 2 fully quenches PL, demonstrating molecular control over excitonic emission. Lattice scale ab initio GW and GW-BSE calculations reveal a significantly hybridized bilayer band structure in PDI/WS 2 that supports interlayer excitonic species both above and below the WS 2 gap with strong polarization anisotropy, in excellent agreement with experiment. Our work introduces a molecule-based bilayer platform for the bottom-up design and control of excitonic phenomena in atomically thin optoelectronic and quantum materials.

2D materials↗

Extreme Transverse Magnetoresistance in TiZn 16

Extreme magnetoresistance (XMR) is a phenomenon characterized by an increase in resistance by factors of 10 4 –10 7 % when a magnetic field is applied. This phenomenon is found in a number of semimetals such as WTe 2 , PtSn 4 , Cd 3 As 2 , and LaSb. The origin of XMR is still hotly debated, possibly with different materials having different (or multiple) explanations. Extreme transverse magnetoresistance of up to 8000% at 14 T and 1.8 K is measured in TiZn 16 , a semimetal with a multitude of bands crossing the Fermi energy, akin to PtSn 4 . The magnetoresistance is suppressed when the magnetic field is rotated to be parallel to the applied current, similar to PtSn 4 and PdSn 4 . The resistance of TiZn 16 follows Kohler's rule, but displays different behavior under an applied transverse field and under a longitudinal magnetic field, suggesting distinct electrical phases. Also present are Shubnikov-de Haas and de Haas-van Alphen oscillations with a transverse magnetic field up to 43 T, showing that despite an insulator-like temperature-resistance curve, charge carriers are still present. This positions TiZn 16 as an interesting addition to the investigation of XMR materials as a multi-band metal with complex Fermi surface geometries.

extreme magnetoresistance↗

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Penrose limit of the Weyl double copy

We embed the Penrose limit into the Weyl classical double copy. Thereby, we provide a lift of the double copy properties of plane wave spacetimes into black hole geometries and we open a novel avenue towards taking the classical double copy beyond statements about algebraically special backgrounds. In particular, the Penrose limit, viewed as the leading order Fermi coordinate expansion around a null geodesic, complements approaches leveraging asymptotic flatness such as the asymptotic Weyl double copy. Along the way, we show how our embedding of the Penrose limit within the Weyl double copy naturally fixes the functional ambiguity in the double copy for Petrov type N spacetimes. Here, we also highlight the utility of a spinorial approach to the Penrose limit. In particular, we use this spinorial approach to derive a simple analytical expression for arbitrary Penrose limits of four-dimensional, vacuum type D spacetimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fundamental bandwidth limits and shaping of frequency-modulated combs

Frequency-modulated (FM) combs based on active cavities like quantum cascade lasers have recently emerged as promising light sources in many spectral regions. Unlike passive modelocking, which generates amplitude modulation using the field’s amplitude, FM comb formation relies on the generation of phase modulation from the field’s phase. They can therefore be regarded as a phase-domain version of passive modelocking. However, while the ultimate scaling laws of passive modelocking have long been known—Haus showed in 1975 that pulses modelocked by a fast saturable absorber have a bandwidth proportional to effective gain bandwidth—the limits of FM combs have been much less clear. Here, we show that FM combs based on fast gain media are governed by the same fundamental limits, producing combs whose bandwidths are linear in the effective gain bandwidth. Not only do we show theoretically that the diffusive effect of gain curvature limits comb bandwidth, but we also show experimentally how this limit can be increased. By adding carefully designed resonant-loss structures that are evanescently coupled to the cavity of a terahertz laser, we reduce the curvature and increase the effective gain bandwidth of the laser, demonstrating bandwidth enhancement. Our results can better enable the creation of active chip-scale combs and be applied to a wide array of cavity geometries.

47 OTHER INSTRUMENTATION↗

Vibrational Signatures of Unrealized Phosphorus Suboxide Intermediates in White Phosphorus Oxidation Reactions

White phosphorus ignition notoriously produces the phosphoric acid anhydride P 4 O 10 , yet the intermediate oxidation steps remain undetermined. Here, we report the first geometric and vibrational characterization of two P 4 O 2 isomers, P 3 OPO and P 3 PO 2 , and substantiate a previously proposed cyclic P 4 O 2 isomer. We formally assign the infrared bands observed by Andrews and Mielke at 898 and 891 cm −1 to the antisymmetric P− O−P vibrations of P 3 OPO species. Additional bands corresponding to terminal P=O and −PO 2 stretches of P 3 OPO and P 3 PO 2 discussed herein also went unrecognized due to the peculiar bonding of P 4 O 2 species compared to oxo-bridged P 4 O x (x = 3−6) species. Sequential addition of oxygen atoms to the P 4 tetrahedron appears to form P 3 OPO and P 3 PO 2 , while cyclic P 4 O 2 is formed from P 2 O dimerization. CCSD(T) geometries, CCSD(T) + MP2[δVPT2] fundamental frequencies, and enthalpies of formation extrapolated using focal-point analysis are reported. The predicted enthalpies of formation relative to tetrahedral P 4 plus 3 Σ g − O 2 for bent-P 3 OPO, extended-P 3 OPO, P 3 PO 2 , and cyclic-P 4 O 2 are −93, −88, −85, and −63 kcal mol −1 , respectively.

Molecular structure↗

High-Pressure Effects on an Octa-Hydrated Curium Complex: An Experimental and Theoretical Investigation

An octa-hydrated curium compound [Cm(H 2 O) 8 ](Hdtp)(dtp)·H 2 O (Cm1,H 2 dtp = 2,3-di(tetrazol-5-yl)pyrazine) along with its lanthanide analogues [Ln(H 2 O) 8 ](Hdtp)-(dtp)·H 2 O (Ln1, Ln 3+ = La 3+ –Nd 3+ , Sm 3+ –Lu 3+ ) were synthesized and characterized using single crystal X-ray diffraction and spectroscopic methods. Bond length analysis of VIII Cm(III)–OH 2 (where VIII refers to the coordination number) was compared to VIII Ln(III)–OH 2 (Ln 3+ = Nd 3+ and Sm 3+ ), indicating similar VIII M(III)–OH 2 bond lengths owing to the similar eight-coordinate ionic radii of these VIII M(III) cations. Owing to the reduced coordination number, the VIII Cm(III)–OH 2 bond lengths were shorter than previously reported IX Cm(III)–OH 2 bonds in [Cm(H 2 O) 9 ](CF 3 SO 3 ) 3 . The octa-aquo complexes were also characterized by solid-state UV–vis–NIR spectroscopy in addition to variable-temperature and variable-pressure photoluminescence. Variable-pressure absorption spectra of Cm1 were compared with Ln1 and show that the Cm(III) f → f transitions have a stronger dependence on pressure than that observed in Ln1 (Ln 3+ = Nd 3+ and Sm 3+ ). The experimental and computational analyses reveal that the monotonic decrease in the computed energy difference between the ground state and the first excited state corresponds to the observed red shift of the photoluminescence peak. This is accompanied by a gradual reduction in the average Cm(III)–OH 2 bond length and a delocalization of spin densities, alongside an intensified interaction involving the 5f orbitals under increasing pressure. Furthermore, these changes accommodate the new geometry and collectively modify the energy landscape, resulting in peak broadening and quenching.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Twist-engineered phonon polaritons in α − V 2 O 5

The advent of layered materials has unveiled new opportunities for tailoring electromagnetic waves at the subwavelength scale, particularly through the study of polaritons, a hybrid light–matter excitation. In this context, twist-optics, which investigates the optical properties of twisted stacks of van der Waals (vdW) layered specimens, has emerged as a powerful tool. Here, we explore the tunability of phonon polaritons in α-V 2 O 5 via interlayer twisting using scanning nano-infrared (IR) imaging. We show that the polaritonic response can be finely adjusted by varying their interlayer electromagnetic coupling, allowing for precise control over the propagation direction and phase transition from open unidirectional iso-frequency contours to closed elliptic geometries. Furthermore, our experimental results, in conjugate with theoretical modeling, reveal the mechanisms underpinning this tunability, highlighting the role of twist-induced nano-light modifications for advanced nanophotonic control at the nanoscale.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS 3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (S- o -xyl) 4 ] 2– Complexes

Iron–sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (SMe) 4 ] 2–,3–,4– , we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree–Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (S-o-xyl) 4 ] 2– , via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

How Does Metal Spin State Affect Electronic Communication in Mixed-Valence Dimers? Insights from Ultrafast Near-Infrared and Soft X-ray Transient Absorption Spectroscopy

Recent advancements in photocatalysis, photovoltaics, and quantum information science take advantage of electron spin, and determining how spin multiplicity affects electron transfer is key to understanding these phenomena. Here, in this study, we examine how metal spin state affects electronic communication in an organometallic mixed-valence dimer, ferrocenyl cobaltocenium ([Fe II Cp 2 Co III Cp 2 ] + ). This complex can be photoexcited from its low-spin singlet Fe II ground state to form intermediate-spin triplet Fe II and high-spin quintet Fe II excited states. Using femtosecond optical transient absorption (OTA) spectroscopy with visible (vis), near-infrared (NIR), and short-wave IR (SWIR) probes, supported by time-dependent density functional theory (TD-DFT) calculations, we measure Fe II Co III →Fe III Co II intervalence charge transfer (IVCT) bands in each of the Fe II spin states. Mulliken–Hush analysis of the excited-state IVCT bands was used to compute the electronic coupling between the metal centers in all three spin states, which increased as quintet < triplet < singlet. Meanwhile, the peak energy of the bands, and thus the ΔG of the IVCT transition, increased as triplet < quintet < singlet. Then, to directly probe the electronic structure at each metal center, we employed picosecond soft X-ray transient absorption (XTA) spectroscopy at the Fe and Co L 3 edges. Our results show that the low-spin and high-spin states of [Fe II Cp 2 Co III Cp 2 ] + are valence-localized, while the intermediate-spin state is partially delocalized. The differences in charge delocalization are attributed to differences in orbital occupation and geometry that affect the free energy and superexchange coupling.

Burke, John H. [Univ. of Illinois at Urbana-Champa↗

The high explosives & affected targets (HEAT) dataset

Artificial Intelligence (AI) surrogate models offer a computationally efficient alternative to full-physics simulations, yet no existing datasets are publicly available for training, testing, and validation of machine learning models of the dynamics of high-explosive driven shocks through multiple materials. Shock propagation through materials is a computationally challenging problem because simulations must include material-specific equations of state (EOS) along with descriptions of other physical processes such as plastic deformation, phase change, damage processes, fluid instabilities, and multi-material interactions. Shocks are typically initiated by high-velocity impacts or explosive loading. The latter case necessitates the addition of models of reactive materials to represent high-explosive (HE) detonation. Here, to address the lack of an expansive dataset for multi-material shock propagation in the AI/ML community, we present the High-Explosives and Affected Targets (HEAT) Dataset. HEAT is a physics-rich collection of two-dimensional, cylindrically symmetric, simulations generated using an Eulerian, multi-material, shock-propagation code developed at Los Alamos National Laboratory. The dataset includes two partitions: (1) the expanding shock-cylinder (CYL) simulations, Figs. 1, and (2) the Perturbed Layered Interface (PLI) simulations, Fig. 2. Entries in both partitions consist of time series of arrays of thermodynamic fields (pressure, density, and temperature), kinematic fields (position and velocity), and additional fields that depend on thermodynamic and/or kinematic fields (e.g., material stress). Materials in the CYL partition include solids (aluminium, copper, depleted uranium, stainless steel, tantalum, and a generic polymer), a liquid (water), gases (air, nitrogen), and a generic detonating material (high explosive, HE). The PLI partition spans a highly varying geometry but consists of fixed materials across entries: Copper, aluminium, stainless steel, generic polymer, and generic HE. HEAT captures critical phenomena such as momentum transfer, shock propagation, plastic deformation, and thermal effects, making HEAT a valuable benchmark for development of AI/ML emulation of multi-material shock propagation.

36 MATERIALS SCIENCE↗

The Remarkable I 2 O 3 Molecule: A New View from Theory

Atmospheric iodine chemistry has garnered increasing attention as a result of increased iodine emissions. A key subset of this chemistry involves iodine oxides (I 2 O 2–5 ), which serve as precursors to particle formation. Among these, I 2 O 3 is the simplest iodine oxide involved in particle formation, but it has remained undetected in the atmosphere. Previous theoretical studies have characterized this peculiar molecule, primarily using energies to refine geometries obtained at low levels of theory. Due to the reemerging interest in I 2 O 3 , this study presents geometries optimized at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory─marking the first instance, to the best of our knowledge, where this system has been studied exclusively with CCSD(T). Harmonic vibrational frequencies were computed at the same level of theory. Final energetics were obtained using the very high level CCSDT(Q) method with basis sets up to quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) and extrapolated to the CBS limit to yield CCSDT(Q)/CBS//CCSD(T)/aug-cc-pwCVTZ-PP energies. These energies include harmonic zero-point vibrational energy corrections and scalar relativistic energy corrections. Additionally, this study discovers new isomers along the I 2 O 3 potential energy surface, a novel contribution to the field. The performance of different computational methods and DFT functionals commonly used in atmospheric chemistry is also assessed relative to high-level theoretical methods.

basis sets↗

Circularly Polarized Attosecond Pulses Enabled by an Azimuthal Phase and Polarization Grating

High-harmonic generation (HHG) is an extreme nonlinear optical process that can map the properties of an infrared driving laser beam onto short wavelength attosecond pulse trains. However, current techniques for generating circularly polarized high harmonics for probing magnetic materials and chiral systems have limitations: two-color collinear counter-rotating driving lasers result in a low cutoff photon energy, while single-color non-collinear counter-rotating schemes suffer from low conversion efficiency. In this work, we generate circularly polarized attosecond pulse trains by using a structured laser driver which has a rotating polarization and phase grating along the azimuthal coordinate. Furthermore, our experimental and numerical results demonstrate the production of left and right circularly polarized harmonics, which naturally separate upon propagation. Our approach uses a single laser color in a collinear geometry, that can be scaled for high efficiency. Simulations show this scheme can extend into the soft x-ray region when driven by mid-infrared driving lasers, while preserving the same high phase-matching cutoff photon energy as for linearly-polarized high harmonics.

attosecond science↗

Spontaneous generation of athermal phonon bursts within bulk silicon causing excess noise, low energy background events, and quasiparticle poisoning in superconducting sensors

Solid state phonon detectors used in the search for dark matter and coherent neutrino nucleus interactions (CE $v$ NS) require excellent energy resolution (eV-scale or below) and low backgrounds. An unknown source of phonon bursts, the low energy excess (LEE), dominates other above-threshold backgrounds and generates excess shot noise from subthreshold bursts. Here, in this paper, we measure these phonon bursts for 12 days after cooldown in two nearly identical 1 cm 2 silicon detectors that differ only in the thickness of their substrate (1 vs 4 mm thick). We find that both the channel-correlated shot noise and near-threshold shared LEE relax with time since cooldown. Additionally, both the correlated shot noise and LEE rates scale linearly with substrate thickness. When combined with previous measurements of other silicon phonon detectors with different substrate geometries and mechanical support strategies, these measurements strongly suggest that the dominant source of both above and below threshold LEE is the bulk substrate. By monitoring the relation between bias power and excess phonon shot noise, we estimate that the energy scale for subthreshold noise events is 0.68 ± 0.38 meV. In our final dataset, we report a world-leading energy resolution of 258.5 ± 0.4 meV in the 1 mm thick detector. Simple calculations suggest that these silicon substrate phonon bursts are likely a significant source of quasiparticle poisoning in superconducting qubits operated in well shielded and vibration free environments.

Chang, C. L. [Argonne National Laboratory 1 , 9700↗

Kinematic flow from the flow of cuts

The wavefunction coefficients of conformally coupled scalars in power-law FRW cosmologies satisfy differential equations governed by a set of simple combinatorial rules known as the kinematic flow. In this paper we derive the kinematic flow, expressed using a set of differential forms referred to as the cut basis, from a geometric perspective, relying solely on the cosmological hyperplane arrangement and without invoking bulk physics. Each element of the cut basis corresponds to the positive geometry associated to an independent cut of the physical FRW-form and can be labeled by decorating (minors of) the truncated Feynman graph with an acyclic orientation. We provide a straightforward prescription to associate a logarithmic differential form to each element of the cut basis by considering its corresponding decorated graph. Moreover, we show that the residues of the physical FRW-form are canonical forms of certain graphical zonotopes labeled by the same set of decorated graphs. These zonotopes control the cut combinatorics -- flow of cuts -- of the physical FRW-form and the cut basis (by construction). Using the theory of relative twisted cohomology and intersection theory, we derive a closed form formula for the differential equations of the cut basis. We also introduce combinatorial rules that compute the kinematic differential of any basis element without explicit calculation. The combinatorics of our differential equations is a natural consequence of the flow of cuts and is equivalent (up to rescaling) to the kinematic flow for the recently studied time integral basis. In particular, our differential equations decouple into exponentially many sectors, one for each way of cutting a subset of edges of the graph.

General Relativity and Quantum Cosmology↗

Water under hydrophobic confinement: entropy and diffusion

The properties of liquid water are known to change drastically in confined geometries. A most interesting and intriguing phenomenon is that the diffusion of water is found to be strongly enhanced by the proximity of a hydrophobic confining wall relative to the bulk diffusion. We report a molecular dynamics simulation using a classical water model investigating the water diffusion near a non-interacting smooth confining wall, which is assumed to imitate a hydrophobic surface, revealing a pronounced diffusion enhancement within several water layers adjacent to the wall. We present evidence that the observed diffusion enhancement can be accounted for, with a quantitative accuracy, using the universal scaling law for liquid diffusion that relates the diffusion rate to the excess entropy. These results show that the scaling law, which has so far only been used for the description of the diffusion in simple liquids, can successfully describe the diffusion in water. It is shown that the law can be used for the analysis of water dynamics under nanoscale hydrophobic confinement, which is currently a subject of intense research activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lines of Bound States in the Continuum in Monodisperse Microsphere Structures

Incorporating epitaxially grown active semiconductor media into self-assembled microsphere crystals has remained a major challenge as the curved geometry of the spheres is incompatible with conventional planar growth and patterning techniques. As a result, active photonic devices based on such self-assembled structures, which have other desirable properties such as enabling the rapid assembly of large area systems, have been elusive. Here, we numerically demonstrate an alternative route to creating high-Q resonances in microsphere-based nanophotonic assemblies compatible with standard optical gain materials. We show that close-packed layers of monodisperse microspheres can exhibit symmetry bandgaps, regardless of their layer stacking order. Thus, this microsphere environment can be used to create lines of bound states in the continuum (BICs) of an embedded slab made of active material. Using a realistic ZnS@SiO 2 (core-shell) architecture and sphere diameters compatible with scalable colloidal assembly, we predict sharp spectral features in angle-resolved transmission that trace these lines of BICs and persist in the presence of some fabrication disorder. Altogether, in enabling the integration of unpatterned epitaxial gain slabs with large-area colloidal microsphere assemblies, this approach opens a practical path toward active, dynamically reconfigurable photonic devices that leverage BIC physics for narrow-linewidth lasing and enhanced light–matter interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗