Field Theory Research Articles

Evaluation of Point Group Symmetry in Lanthanide(III) Complexes: A New Implementation of a Continuous Symmetry Operation Measure with Autonomous Assignment of the Principal Axis.

The structure of molecular systems dictates the physical properties, and symmetry is the determining factor for all electronic properties. This makes group theory a powerful tool in quantum mechanics to compute molecular properties. For inorganic compounds, the coordination geometry has been estimated as idealized polyhedra with high symmetry, which, through ligand field theory, provides predictive capabilities. However, real samples rarely have ideal symmetry, and although continuous shape measures (CShM) can be used to evaluate deviation from an ideal reference structure σideal, this often fails for lanthanide(III) complexes with high coordination numbers, no obvious choice of principal axes, and no obvious reference structure. In lanthanide complexes, the unique electronic structures and associated properties are intricately tied to the symmetry around the lanthanide center. Therefore, robust methodologies to evaluate and estimate point group symmetry are instrumental for building structure-property relationships. Here, we have demonstrated an algorithmic approach that orients a molecular structure Q in the best possible way to the symmetry axis of any given point group G and computes a deviation from the ideal symmetry σsym(G,Q). This approach does not compute the deviation from an ideal reference system, but the intrinsic deviation in the structure induced by symmetry operations. If the structure contains the symmetry operation, there is no deviation and σsym(G,Q) = 0. The σsym deviation is generated from all of the symmetry operation ÔS in a point group G using the most correct orientation of the sample structure in each group G. The best orientation is found by an algorithm that minimizes the orientation of the structure with respect to G. To demonstrate the methodology, we have investigated the structure and symmetry of 8- and 9-coordinated lanthanide(III) aqua complexes and correlated the luminescence from 3 europium(III) crystals to their actual symmetry. To document the methodology, the approach has been tested on 26 molecules with different symmetries. It was concluded that the method is robust and fully autonomous.

Computational modeling of near-fault earthquake-induced landslides considering stochastic ground motions and spatially varying soil

Landslides represent a large-deformation process influenced by various factors of uncertainty, such as types of ground motion (GM), randomness of GMs, and spatial variability of soils. The behavior of landslides is profoundly affected, making their assessment and measurement challenging. This paper proposes a computational approach for simulating the large-deformation process of landslides based on three-dimensional (3D) non-ordinary state-based peridynamics (NOSBPD). The analysis results of NOSBPD indicate that the mean runout distance triggered by pulse-like ground motions (PLGMs) is 16% greater than that induced by non-pulse ground motions (NPGMs), suggesting that PLGMs exhibit higher destructiveness. Besides, this paper establishes a runout distance assessment framework by considering the stochastic nature of PLGMs. This framework allows for the evaluation of the specific risk probability of landslides caused by stochastic PLGMs that match the target spectrum specified by codes. By introducing the theory of random fields and implementing a coupled procedure in peridynamics, we conducted a detailed analysis of the impact of spatial heterogeneity on the evolution process and consequences of landslides. Additionally, compared to two-dimensional (2D) analysis, the mean runout distance obtained from 3D analysis increased by 27.5%. This suggests that 2D analysis may underestimate the consequences of landslides. The findings of this study can serve as a scientific foundation for predicting the extent and scope of landslides triggered by near-fault earthquakes.

Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at s=13 TeV

A search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at s=13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb−1 collected in 2016–2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta (pTγ>100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass (mγγ>350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters |ζ1|<0.073 TeV−4 and |ζ2|<0.15 TeV−4, using an effective field theory. Additionally, upper limits are placed on the production of axionlike particles with coupling strength to photons f−1 that varies from 0.03 TeV−1 to 1 TeV−1 over the mass range from 500 to 2000 GeV. © 2024 CERN, for the CMS and TOTEMs Collaboration 2024 CERN

Perturbative quantum evolution of the gravitational state and dressing in general backgrounds

This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schrödinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing, and evolution. Starting with a general time slicing, we give a simple derivation of the relation between the constraints, the Hamiltonian, and its well-known boundary term. Among different approaches to quantization with constraints, we focus on a “gauge-invariant canonical quantization,” which is developed perturbatively in the gravitational coupling. The leading-order solution of the constraints (including the Wheeler-DeWitt equation) for perturbations about the background is given in terms of an explicit construction of gravitational dressings built using certain generalized Green’s functions; different such dressings corresponding to adding propagating gravitational waves to a particular solution of the constraints. Dressed operators commute with the constraints, expressing their gauge invariance, and have an algebraic structure differing significantly from the undressed operators of the underlying field theory. These operators can act on the vacuum to create dressed states, and evolution of general such states is then generated by the boundary Hamiltonian, and alternately may be characterized using other relational observables. This provides a concrete approach to studying perturbative time evolution, including the leading gravitational backreaction, of quantum states of black holes with flat or anti–de-Sitter asymptotics, for example on horizon-crossing slices. This description of evolution in turn provides a starting point for investigating possibly important corrections to quantum evolution, that go beyond quantized general relativity. Published by the American Physical Society 2024

Spin states of metal centers in electrocatalysis.

Understanding the electronic structure of active sites is crucial in efficient catalyst design. The spin state, spin configurations of d-electrons, has been frequently discussed recently. However, its systematic depiction in electrocatalysis is lacking. In this tutorial review, a comprehensive interpretation of the spin state of metal centers in electrocatalysts and its role in electrocatalysis is provided. This review starts with the basics of spin states, including molecular field theory, crystal field theory, and ligand field theory. It further introduces the differences in low spin, intermediate spin, and high spin, and intrinsic factors affecting the spin state. Popular characterization techniques and modeling approaches that can reveal the spin state, such as X-ray absorption microscopy, electron spin resonance spectroscopy, Mössbauer spectroscopy, and density functional theory (DFT) calculations, are introduced as well with examples from the literature. The examples include the most recent progress in tuning the spin state of metal centers for various reactions, e.g., the oxygen evolution reaction, oxygen reduction reaction, hydrogen evolution reaction, carbon dioxide reduction reaction, nitrogen reduction reaction, nitrate reduction reaction, and urea oxidation reaction. Challenges and potential implications for future research related to the spin state are discussed at the end.

Exact evaluation of large-charge correlation functions in nonrelativistic conformal field theory

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in nonrelativistic conformal field theory is obtained. This field is used to compute Schrödinger-invariant n-point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schrödinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large-N expansion at large charge. Published by the American Physical Society 2024

The Unruh-DeWitt model and its joint interacting Hilbert space

Abstract In this work we make the connection between the Unruh-DeWitt particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson model. With some modifications, we show that existing results about the existence of a spin-boson ground state can be adapted to the Unruh-DeWitt model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the Unruh-DeWitt model describes a simplified model of light-matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications.

Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the λϕ4 model

The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field ϕ(x) locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional λϕ4 terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling λ. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the λϕ4 QFT.

Opportunities and Open Questions in Modern Beta Decay

For well over half a century, precision studies of neutron and nuclear β decays have been at the forefront of searches for exotic electroweak physics. Recent advances in nuclear ab initio theory and the widespread use of effective field theories mean that the modern understanding of β decay is going through a transitional phase. This has been propelled by current tensions in the global dataset leading to renewed scrutiny of the theoretical ingredients. In parallel, novel techniques and methods are being investigated that can sidestep many traditional systematic uncertainties and require a diverse palette of skills and collaboration with material science and condensed matter physics. This review highlights the current opportunities and open questions to facilitate the transition to a more modern understanding of β decay.

A Theoretical Investigation on Equilibrium Magnetic Properties in Nanowire Arrays

Abstract The paper focuses on the study of an Ising nanowire array composed of core/shell-structured single nanowires placed at the edges of a square lattice. The phase transition temperature, at which a transition occurs in the magnetic properties, is obtained using effective field theory for two interacting individual nanowires. To understand how the interaction affects the magnetic, we defined the exchange interaction (JR) between the single nanowires. This interaction is assigned both positive and negative values to reveal the ferromagnetic and antiferromagnetic characteristics of the system. Our results revealed that the exchange interaction between individual nanowires significantly influences the magnetic properties of the system.

Smoothed asymptotics: From number theory to QFT

Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultraviolet regularization scheme for loop integrals in quantum field theory which we call η regularization. This reveals a connection between the elimination of divergences in divergent series of powers and the preservation of gauge invariance in the regularization of loop integrals in quantum field theory. In particular, we note that a method for regularizing the series of natural numbers so that it converges to minus one-twelfth inspires a regularization scheme for non-Abelian gauge theories coupled to Dirac fermions that preserves the Ward identity for the vacuum polarization tensor and other higher point functions. We also comment on a possible connection to Schwinger proper time integrals. Published by the American Physical Society 2024

Inner fission barriers of uranium isotopes in the deformed relativistic Hartree-Bogoliubov theory in continuum

Abstract The inner fission barriers of the even-even uranium isotopes from the proton to the neutron drip line are studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. A periodic evolution for the ground state shapes is shown with the neutron number, i.e., spherical shapes at shell closures N=126, 184, 258, and prolate dominated shapes between them. In analogy to the shape evolution, the inner fission barriers also exhibit a periodic behavior: peaks at the shell closures and valleys in the mid-shells. The triaxial effect to the inner fission barrier is evaluated using the triaxial relativistic mean field calculations plus a simple BCS method for pairing. With the triaxial correction included, good consistency in the inner barrier heights is found with the available empirical data.
Besides, the evolution from the proton to the neutron drip line is in accord with the results by the multi-dimensionally constrained relativistic mean field theory. A flat valley in the fission barrier height is predicted around the neutron-rich nucleus 318U which may play a role of fission recycling in the astrophysical r-process nucleosynthesis.

Probing the quantum nature of gravity using a Bose-Einstein condensate

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The general complex scalar field theory with a quadratic self-interaction term has been considered in the presence of a gravitational wave. The gravitational wave perturbation is then considered as a sum of discrete Fourier modes in the momentum space. Varying the action and making use of the principle of least action, one obtains two equations of motion corresponding to the gravitational perturbation and the time-dependent part of the pseudo-Goldstone boson. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonical commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. The entries of the covariance matrix now involves a stochastic contribution which results in an operatorial stochastic structure of the quantum Fisher information. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. It always has a finite value if the gravitons are initially in a squeezed state with high enough squeezing. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in a decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing. Published by the American Physical Society 2024

Research on Electric Field Homogenization in Radial Multi-Nozzle Electrospinning

Electrospinning is an effective method to prepare nanofibers at present. Aiming at problems such as low spinnable viscosity and the low productivity of the traditional multi-needle, a radial nozzle was proposed in this paper. In order to solve the problem of end effects in multi-nozzle electrospinning, COMSOL Multiphysics 6.0 software was used to simulate the electric field in electrospinning with seven radial nozzles. And the influence on the electric field intensity and distribution of the structural parameters of the radial nozzle, including the number, length, tip-shape, and tip-pointing direction of the vanes, were studied. Then, the electric field intensity of any point on the central axis of a radial nozzle was obtained based on the principle of electric field superposition, and then the rotation angle of the vanes corresponding to the minimum Coulomb repulsion force on the target point was deduced. At last, the method of electric field homogenization of a rotating vane arrangement was obtained. In the simulation, the strength and homogenization of the electric field were taken as the research objective, and the optimum structure parameters of the radial nozzle were obtained; the uniform theory of the electric field based on the orientation of the vanes was verified. Then, electrospinning with seven radial nozzles was performed, and it was found that each radial nozzle can produce multiple jets during electrospinning, and the prepared electrospun membranes have even thickness and high porosity. What is more, the fibers are relatively finer and more uniform.

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions.

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions.

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

Quantum deformation of cubic string field theory

In this paper, we will analyze a quantum deformation of cubic string field theory. This will be done by first constructing a quantum deformation of string theory, in a covariant gauge, and then using the quantum deformed stringy theory to construct a quantum deformation of string field theory. This quantum-deformed string field will then be used to contract a quantum-deformed version of cubic string field theory. We will explicitly demonstrate that the axioms of cubic string field theory hold even after quantum deformation. Finally, we will analyze the effect of the quantum deformation of string field theory on the string vertices.

Ising meson spectroscopy on a noisy digital quantum simulator

Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

Gauge reduction in covariant field theory

In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a configuration bundle. In order to reduce the variational principle, we utilize generalized principal connections, a type of Ehresmann connections that are equivariant by the fiberwise action. After obtaining the reduced equations, we give the reconstruction condition and we relate the vertical reduced equation with the Noether theorem. Lastly, we illustrate the theory with several examples, including the classical case (Lagrange–Poincaré reduction), Electromagnetism, symmetry-breaking and non-Abelian gauge theories.

The dressing field method for diffeomorphisms: a relational framework

The dressing field method (DFM) is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M) -invariant objects, which has a natural relational interpretation. Its precise formulation relies on a clear understanding of the bundle geometry of field space. By detailing it, among other things we stress the geometric nature of field-independent and field-dependent diffeomorphisms, and highlight that the heuristic ‘extended bracket’ for field-dependent vector fields often featuring in the covariant phase space literature can be understood as arising from the Frölicher-Nijenhuis bracket. Furthermore, by articulating this bundle geometry with the covariant phase space approach, we give a streamlined account of the elementary objects of the (pre)symplectic structure of a Diff(M) -theory: Noether charges and their bracket, as induced by the standard prescription for the presymplectic potential and 2-form. We give conceptually transparent expressions allowing to read the integrability conditions and the circumstances under which the bracket of charge is Lie, and the resulting Poisson algebras of charges are central extensions of the Lie algebras of field-independent ( diff(M) ) and field-dependent vector fields.We show that, applying the DFM, one obtains a Diff(M) -invariant and manifestly relational formulation of a general relativistic field theory. Relying on results just mentioned, we easily derive the ‘dressed’ (relational) presymplectic structure of the theory. This reproduces or extends results from the gravitational edge modes and gravitational dressings literature. In addition to simplified technical derivations, the conceptual clarity of the framework supplies several insights and allows us to dispel misconceptions.