Code Verification for MCNP Unstructured Mesh Geometry
Abstract not provided.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Results for “quantum geometry”
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Non-relativistic geometry and the equivalence principle
Abstract We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a curved and time-dependent spatial metric. It is this requirement that forces the gravitational mass to be equal to the inertial mass. We identify the symmetry responsible for the equivalence principle as the remnant of time-reparameterization symmetry of the relativistic theory. We also clarify the transformation properties of the Schrödinger wave-function under arbitrary frame changes.
Astronomy & Astrophysics↗
Hidden Killing fields, geometric symmetries and black hole mergers
Highlights: • Construction of geometric models with a variable degree of symmetry. • Formulation of Energy and Momentum Balance Laws. • Description of backreactions on spacetime geometries caused by dissipative effects. • Analytic description of accretion and/or merger processes in GR. • Exact model for the merger of two extremal Reissner–Nordström black holes. In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields – so-called hidden Killing vector fields – are constructed, which solve the Killing equation not globally, but only locally, i.e. in local subregions of spacetime. Taking advantage of the fact that the vector fields coincide locally with Killing fields and therefore allow the consideration of integral laws that convert into exact physical conservation laws on local scales, balance laws in dynamical systems without global Killing symmetries are derived that mimic as closely as possible the conservation laws for energy and angular momentum of highly symmetric models. The utility of said balance laws is demonstrated by a concrete geometric example, namely a toy model for the binary merger of two extremal Reissner–Nordström black holes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Entanglement between two gravitating universes
Abstract We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard ‘island formula’ for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2 n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Z n replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a ‘swap wormhole’, a geometry in which the boundaries of the two universes are glued together by a ‘swaperator’. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes—a realization of the ER = EPR idea. The new wormhole restores unitarity of quantum information.
79 ASTRONOMY AND ASTROPHYSICS↗
Two 6D origins of 4D SCFTs: Class S and 6D (1, 0) on a torus
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Diagnosis of information scrambling from Hamiltonian evolution under decoherence
We apply a quantum teleportation protocol based on the Hayden-Preskill thought experiment to quantify how scrambling a given quantum evolution is. It has an advantage over the direct measurement of out-of time ordered correlators when used to diagnose the information scrambling in the presence of decoherence effects stemming from a noisy quantum device. We demonstrate the protocol by applying it to two physical systems: Ising spin chain and SU(2) lattice Yang-Mills theory. To this end, we numerically simulate the time evolution of the two theories in the Hamiltonian formalism. The lattice Yang-Mills theory is implemented with a suitable truncation of Hilbert space on the basis of the Kogut-Susskind formalism. On a two-leg ladder geometry and with the lowest nontrivial spin representations, it can be mapped to a spin chain, which we call Yang-Mills-Ising model and is also directly applicable to future digital quantum simulations. Here, we find that the Yang-Mills-Ising model shows the signal of information scrambling at late times.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Anisotropic quantum Hall states in the presence of interactions with fourfold rotational symmetry
We study the effects of anisotropic interactions in the quantum Hall effect in the presence of a fourfold discrete rotational (C 4 ) symmetry. Employing the density matrix renormalization group technique on an infinite cylinder geometry (iDMRG), we calculate the anisotropy response of the Laughlin state at ν = 1/3 and the composite-Fermi liquid (CFL) state at ν = 1/2. We find that the anisotropy transferred from the interaction potential to the ν = 1/3 state is stronger when compared with the complementary case of an anisotropic band. Further, the strength of anisotropy reduces as the interaction is made shorter ranged. Quite surprisingly, at ν = 1/2, the deformation in the CF Fermi surface changes sign as the interaction range is reduced. Our results imply that the short-distance and long-distance parts of the interaction potential have opposite effects on the CFL state in the presence of C 4 -symmetric anisotropy.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Importance of Engineered and Learned Molecular Representations in Predicting Organic Reactivity, Selectivity, and Chemical Properties
Machine-readable chemical structure representations are foundational in all attempts to harness machine learning for the prediction of reactivities, selectivities, and chemical properties directly from molecular structure. The featurization of discrete chemical structures into a continuous vector space is a critical phase undertaken before model selection, and the development of new ways to quantitatively encode molecules is an active area of research. Here, we highlight the application and suitability of different representations, from expert-guided “engineered” descriptors to automatically “learned” features, in different prediction tasks relevant to organic and organometallic chemistry, where differing amounts of training data are available. These tasks include statistical models of stereo- and enantioselectivity, thermochemistry, and kinetics developed using experimental and quantum chemical data. The use of expert-guided molecular descriptors provides an opportunity to incorporate chemical knowledge, domain expertise, and physical constraints into statistical modeling. In applications to stereoselective organic and organometallic catalysis, where data sets may be relatively small and 3D-geometries and conformations play an important role, mechanistically informed features can be used successfully to obtain predictive statistical models that are also chemically interpretable. We provide an overview of several recent applications of this approach to obtain quantitative models for reactivity and selectivity, where topological descriptors, quantum mechanical calculations of electronic and steric properties, along with conformational ensembles, all feature as essential ingredients of the molecular representations used. Alternatively, more flexible, general-purpose molecular representations such as attributed molecular graphs can be used with machine learning approaches to learn the complex relationship between a structure and prediction target. This approach has the potential to out-perform more traditional representation methods such as “hand-crafted” molecular descriptors, particularly as data set sizes grow. One area where this is particularly relevant is in the use of large sets of quantum mechanical data to train quantitative structure–property relationships. A general approach toward curating useful data sets and training highly accurate graph neural network models is discussed in the context of organic bond dissociation enthalpies, where this strategy outperforms regression using precomputed descriptors. Finally, we describe how graph neural network predictions can be incorporated into mechanistically informed statistical models of chemical reactivity and selectivity. Once trained, this approach avoids the expensive computational overhead associated with quantum mechanical calculations, while maintaining chemical interpretability. We illustrate examples for which fast predictions of bond dissociation enthalpy and of the identities of radicals formed through cleavage of a molecule’s weakest bond are used in simple physical models of site-selectivity and reactivity.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Helical Edge States and Quantum Phase Transitions in Tetralayer Graphene
Helical conductors with spin-momentum locking are promising platforms for Majorana fermions. Here we report observation of two topologically distinct phases supporting helical edge states in charge neutral Bernal-stacked tetralayer graphene in Hall bar and Corbino geometries. As the magnetic field B ⊥ and out-of-plane displacement field D are varied, we observe a phase diagram consisting of an insulating phase and two metallic phases, with 0, 1, and 2 helical edge states, respectively. These phases are accounted for by a theoretical model that relates their conductance to spin-polarization plateaus. Transitions between them arise from a competition among interlayer hopping, electrostatic and exchange interaction energies. Finally, our work highlights the complex competing symmetries and the rich quantum phases in few-layer graphene.
36 MATERIALS SCIENCE↗
AdS 3 Einstein gravity and boundary description: pedagogical review
We review the various aspects of the 3D Einstein gravity theory with a negative cosmological constant and its boundary description. We also explore its connections to conformal field theories (CFTs), modular symmetry, and holography. It is worth noting that this particular theory is topological in nature, which means that all the physical degrees of freedom are located on the boundary. Additionally, we can derive the boundary description on a torus, which takes the form of a 2D Schwarzian theory. This observation suggests that the relevant degrees of freedom for the theory can be described using this 2D theory. Because of the renormalizability of the 3D gravity theory, one can probe the quantum regime. This suggests that it is possible to investigate quantum phenomena. Unlike the conventional CFTs, when considering the AdS 3 background, the boundary theory loses modular symmetry. This represents a departure from the usual behavior of CFT and is quite intriguing. The Weyl transformation induces anomaly in CFTs, and we indicate that applying this transformation to the 2D Schwarzian theory leads to similar results. Summing over all geometries with the asymptotic AdS 3 boundary condition is equivalent to summing over a modular group. The partition function is one-loop exact and therefore an analytical expression from the summation. This theory holds potential applications in Quantum Information and is a recurring theme in the study of holography, where gravitational theories are connected with CFTs.
2D Schwarzian theory↗
Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons
We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor \nu=2/3 ν = 2 / 3 . The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body M M -clustering property within any given number of Landau levels, that is, wave functions with M M th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the M=3 M = 3 case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Rindler fluids from gravitational shockwaves
We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory
Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in dP 3 , for which we compute the cohomologies. A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model. We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill-Noether theory, are required. Using these ingredients, we introduce a diagrammatic way to express cohomology jumps across the parameter space of each family of matter curves, which reflects a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum. Furthermore, these insights provide an algorithmically efficient way to estimate the possible cohomology dimensions across the entire parameter space.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Microwave impedance microscopy and its application to quantum materials
We report materials in which quantum mechanical effects lead to novel properties on the macroscopic scale are of interest both fundamentally and for applications. For such quantum materials, the ability to measure local conductivity and permittivity with nanoscale spatial resolution, minimal sample preparation, in a contact-free fashion and under a wide range of external conditions (such as temperature and magnetic field) is highly desirable. To this end, microwave impedance microscopy, a scanning probe technique that measures tip–sample admittance (inverse of impedance) in a non-contact geometry at microwave frequencies, has matured over the past decade to become a tool that can do just that. This Technical Review describes its fundamental working principles and practical implementations, discusses its application to a wide range of quantum materials, including correlated, topological and 2D van der Waals materials, and outlines future opportunities in expanding the capabilities of microwave impedance microscopy.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Machine-learning accelerated geometry optimization in molecular simulation
Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of thermodynamic and kinetic properties of molecular and crystal structures. This process is slow at the quantum level of theory because it involves an iterative calculation of forces using quantum chemical codes such as density functional theory (DFT), which are computationally expensive and which limit the speed of the optimization algorithms. It would be highly advantageous to accelerate this process because then one could do either the same amount of work in less time or more work in the same time. Here, we provide a neural network (NN) ensemble based active learning method to accelerate the local geometry optimization for multiple configurations simultaneously. We illustrate the acceleration on several case studies including bare metal surfaces, surfaces with adsorbates, and nudged elastic band for two reactions. In all cases, the accelerated method requires fewer DFT calculations than the standard method. In addition, we provide an Atomic Simulation Environment (ASE)-optimizer Python package to make the usage of the NN ensemble active learning for geometry optimization easier.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Exploring the Structural, Dynamic, and Functional Properties of Metal–Organic Frameworks through Molecular Modeling
This review spotlights the role of atomic-level modeling in research on metal-organic frameworks (MOFs), especially the key methodologies of density functional theory (DFT), Monte Carlo (MC) simulations, and molecular dynamics (MD) simulations. The discussion focuses on how periodic and cluster-based DFT calculations can provide novel insights into MOF properties, with a focus on predicting structural transformations, understanding thermodynamic properties and catalysis, and providing information or properties that are fed into classical simulations such as force field parameters or partial charges. Classical simulation methods, highlighting force field selection, databases of MOFs for high-throughput screening, and the synergistic nature of MC and MD simulations, are described. By predicting equilibrium thermodynamic and dynamic properties, these methods offer a wide perspective on MOF behavior and mechanisms. Additionally, the incorporation of machine learning (ML) techniques into quantum and classical simulations is discussed. These methods can enhance accuracy, expedite simulation setup, reduce computational costs, as well as predict key parameters, optimize geometries, and estimate MOF stability. By charting the growth and promise of computational research in the MOF field, the aim is to provide insights and recommendations to facilitate the incorporation of computational modeling more broadly into MOF research.
36 MATERIALS SCIENCE↗
From shockwaves to the gravitational memory effect
We study the relationship between shockwave geometries and the gravitational memory effect in four-dimensional asymptotically flat spacetime. In particular, we show the ’t Hooft commutation relations of shockwave operators are equivalent to the commutation relation between soft and Goldstone modes parametrizing a sector of the gravitational phase space. We demonstrate this equivalence via a diffeomorphism that takes a shockwave metric to a metric whose transverse traceless component is the gravitational memory. The shockwave momentum in ’t Hooft’s analysis is related to the soft graviton mode, which is responsible for the memory effect, while the shift in the shockwave position is related to the Goldstone mode. This equivalence opens new directions to utilize the gravitational memory effect to explore the observational implications of shockwave geometries in flat space.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗