Field Theoretical Approach Research Articles

A Variational Field-Theoretical Approach to Control the Center-Of-Mass of Macromolecules

A Variational Field-Theoretical Approach to Control the Center-Of-Mass of Macromolecules

Hall-like behaviour of higher rank Chern-Simons theory of fractons

Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasi-particles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless “electric” field and a “magnetic” vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial “flux-attachment” relation for dipoles. This gives a possible starting point for a fracton-vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model.

Casimir energy with perfect electromagnetic boundary conditions and duality: A field-theoretic approach

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral and once as the vacuum expectation value of the 00 component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation. Published by the American Physical Society 2024

Field theory of active Brownian particles with dry friction

Abstract We present a field theoretic approach to capture the motion of a particle with dry friction for one- and two-dimensional (2D) diffusive particles, and further expand the framework for 2D active Brownian particles. Starting with the Fokker–Planck equation and introducing the Hermite polynomials as the corresponding eigen-functions, we obtain the actions and propagators. Using a perturbation expansion, we calculate the effective diffusion coefficient in the presence of both wet and dry frictions in a perturbative way via the Green–Kubo relation. We further compare the analytical result with the numerical simulation. Our result can be used to estimate the values of dry friction coefficient in experiments.

Critical surface adsorption of confined binary liquids with locally conserved mass and composition

Close to a solid surface, the properties of a fluid deviate significantly from their bulk values. In this context, we study the surface adsorption profiles of a symmetric binary liquid confined to a slit pore by means of molecular dynamics simulations; the latter naturally entails that mass and concentration are locally conserved. Near a bulk consolute point, where the liquid exhibits a demixing transition with the local concentration as the order parameter, we determine the order parameter profiles and characterise the relevant critical scaling behaviour, in the regime of strong surface attraction, for a range of pore widths and temperatures. The obtained order parameter profiles decay monotonically near the surfaces, also in the presence of a pronounced layering in the number density. Overall, our results agree qualitatively with recent theoretical predictions from a mesoscopic field-theoretical approach for the canonical ensemble.

The Casimir-like effect induced by active nematics

We consider an active nematic phase and use hydrodynamical equations of it to model the activity as an internal field. The interaction of this field with the nematic director in a confined geometry is included in the Hamiltonian of the system. Based on this model Hamiltonian and the standard field theoretical approach, the Casimir-like force induced between the boundaries of such a confined film is discussed. The force depends on the geometrical shape and the dynamical character of the constituents of our active phase, as well as the anchoring conditions. For homeotropically aligned rod-like particles which in principle tend to align along a planar flow field, extensile activity enhances the attraction present in a thin nematic film. As the film thickness increases the force reduces. Beyond a critical thickness, a planar flow field instantaneous to a bend distortion sets in. Near but below the threshold of this activity-induced instability, the force crosses zero and repulsively diverges right at the critical threshold of this so-called flow instability. For contractile rods, in the same geometry as above, the structure is stable and the Casimir-like force diminishes by an exponential factor as a function of the film thickness. On the other side for a planar director alignment, rod-like contractile particles can induce opposite shear flows at the boundaries creating a splay distortion for the director between the plates. In this configuration, we obtain the same universal pretransitional behavior for the force as above. Vice versa, for extensile rod-like particles in this geometry, the director fluctuations become massive and the Casimir-like force diminishes again by an exponential factor as the film thickness increases. The effect of the active field on thermal fluctuations of the director and the fluctuation-induced Casimir force per area is derived through a "semi"-dynamical approach as well. However, the results of the calculation due to a mathematical sum over the fluctuating modes do not lead to an approved closed form.

Expectations of Linear and Nonlinear Hawkes Processes Using a Field-Theoretical Approach

Expectations of Linear and Nonlinear Hawkes Processes Using a Field-Theoretical Approach

Planar anisotropic CPT-odd systems: A field theoretical approach

The primary objective of this study is to introduce field-theoretical tools into the realm of physical properties within planar systems exhibiting possible anisotropic features. This goal is achieved by fitting a specific field-theoretical model to simulate the presence of such a system. The proposed approach enables the investigation of in-plane physical phenomena using analytic methods. Specifically, our focus is on phenomena related to stationary point-like field sources that can mimic defects in material layers. We employ a dimensional reduction procedure on the well-known Carroll–Field–Jackiw model to derive a planar theory. This theory includes an electromagnetic sector governed by Maxwell-Chern–Simons electrodynamics, a scalar sector described by a massless Klein–Gordon field, and a mixed sector where the background vector controls the interactions between the scalar and gauge fields. Across all sectors of this planar theory, we explore physical phenomena arising from interactions with external sources. Specifically, we analyze perturbative effects up to second order in the background vector, examining contributions from both electric and scalar planar charges as well as Dirac points.

Reply to “Comment on ‘Towards exact solutions for the superconducting Tc induced by electron-phonon interaction' ”

In a series of papers, we have proposed a nonperturbative field-theoretic approach to deal with strong electron-phonon and strong Coulomb interactions. The key ingredient of such an approach is to determine the full fermion-boson vertex corrections by solving a number of self-consistent Ward-Takahashi identities. Palle argued that our Ward-Takahashi identities failed to include some important additional terms and thus are incorrect. We agree that our Ward-Takahashi identities have ignored some potentially important contributions and here give some remarks on the role played by the additional terms. Published by the American Physical Society 2024

Multiaxial ratcheting-fatigue evaluation of pressurized elbow pipe under strong cyclic loading using damage-coupled cyclic plasticity model

Continuous damage mechanics (CDM) is based on the theories of continuous medium mechanics and continuous medium thermodynamics, which considers damage is an irreversible dissipative process within the materials, and employs the field-theoretic approach of image-only science to study the internal macroscopic damage evolution law of the materials and its influence on the deterioration of the macroscopic mechanical properties of the materials. Hence, within the framework of CDM, a damage-coupled cyclic plasticity constitutive model is proposed based on combined isotropic and Chen-Jiao-Kim (CJK) kinematic hardening rule for evaluating the ratcheting-fatigue behavior of 90° elbow pipes under strong cyclic loading in this paper. Stress return mapping and numerical solution procedures of the proposed model are formulated based on the backward finite difference method. Formulation of the consistent tangent operator is presented for the Finite Element implementation of the plasticity model in ABAQUS UMAT. The FE analysis of non-pressurized and pressurized elbow pipes under cyclic displacement-controlled loading is respectively performed using the implemented constitutive model. The results reveal that the predicted results of the damage-coupled cyclic plasticity constitutive model are better than combined isotropic-kinematic hardening model, and well consistent with the experimental data.

Bethe M-layer construction on the Ising model

In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in disordered models, some important finite dimensional second-order phase transitions are qualitatively different or absent in the corresponding fully connected model: in such cases the standard expansion fails. Recently, a new method, the M-layer one, has been introduced that performs an expansion around a different soluble mean field model: the Bethe lattice one. This new method has been already used to compute the upper critical dimension DU of different disordered systems such as the Random Field Ising model or the Spin glass model with field. If then one wants to go beyond and construct an expansion around DU to understand how critical quantities get renormalized, the actual computation of all the numerical factors is needed. This next step has still not been performed, being technically more involved. In this paper we perform this computation for the ferromagnetic Ising model without quenched disorder, in finite dimensions: we show that, at one-loop order inside the M-layer approach, we recover the continuum quartic field theory and we are able to identify the coupling constant g and the other parameters of the theory, as a function of macroscopic and microscopic details of the model such as the lattice spacing, the physical lattice dimension and the temperature. This is a fundamental step that will help in applying in the future the same techniques to more complicated systems, for which the standard field theoretical approach is impracticable.

Schwarzschild Black Hole from Perturbation Theory to All Orders.

Applying the quantum field theoretic perturbiner approach to Einstein gravity, we compute the metric of a Schwarzschild black hole order by order in perturbation theory. Using recursion, this calculation can be carried out in de Donder gauge to all orders in Newton's constant. The result is a geometric series which is convergent outside a disk of finite radius, and it agrees within its region of convergence with the known de Donder gauge metric of a Schwarzschild black hole. It thus provides a first all-order perturbative computation in Einstein gravity with a matter source, and this series converges to the known nonperturbative expression in the expected range of convergence.

A generalized vector-field framework for mobility

Given the identification with travel demand and its relevance for transportation and urban planning, the estimation of trip flows between areas is a fundamental metric for human mobility. Previous models focus on flow intensity, disregarding the information provided by the local mobility orientation. A field-theoretic approach can overcome this issue and handle both intensity and direction at once. Here we propose a general vector-field representation starting from individuals’ trajectories valid for any type of mobility. We also show with simplified models how individuals’ choices determine the mesoscopic properties of the mobility field. Distance optimization in long displacements and random-like local exploration are necessary to reproduce empirical field features observed in Chinese logistic data and in New York City Foursquare check-ins. Our framework is able to capture hidden symmetries in mesoscopic urban mobility and opens the doors to the use of field theory in a wide spectrum of applications.

General bubble expansion at strong coupling

The strongly coupled system like the quark-hadron transition (if it is of first order) is becoming an active play yard for the physics of cosmological first-order phase transitions. However, the traditional field theoretic approach to strongly coupled first-order phase transitions is of great challenge, driving recent efforts from holographic dual theories with explicit numerical simulations. These holographic numerical simulations have revealed an intriguing linear correlation between the phase pressure difference (pressure difference away from the wall) to the nonrelativistic terminal velocity of an expanding planar wall, which has been reproduced analytically alongside both cylindrical and spherical walls from perfect-fluid hydrodynamics in our previous study but only for a bag equation of state. We also found, in our previous study, a universal quadratic correlation between the wall pressure difference (pressure difference near the bubble wall) to the nonrelativistic terminal wall velocity regardless of wall geometries. In this paper, we will generalize these analytic relations between the phase/wall pressure difference and terminal wall velocity into a more realistic equation of state beyond the simple bag model, providing the most general predictions so far for future tests from holographic numerical simulations of strongly coupled first-order phase transitions. Published by the American Physical Society 2024

Field-theoretic approach to neutron noise in nuclear reactors.

An operating nuclear reactor is designed to maintain a sustained fission chain reaction in its core, which results from a delicate balance between neutron creations (i.e., fissions) and total absorptions. This balance is associated with random fluctuations that can have two, very different, origins. A distinction must thus be made between low-power noise, whose origin lies in the inherently stochastic nature of neutron interactions with matter, and high-power noise, whose origin lies in the particular thermomechanical constraints associated with the environment in which neutrons propagate. Modeling the behavior of this noisy neutron population with the help of stochastic differential equations, we first show how the Martin-Siggia-Rose-Janssen-De Dominicis (MSRJD) formalism, providing a field theoretical representation of the problem, reveals a convenient and adapted tool for the calculation of observable consequences of neutron noise. In particular, we show how the MSRJD approach is capable of encompassing both types of neutron noises in the same formalism. Emphasizing then on power noise, it is shown how the self-sustained chain reaction developing in a reactor core might be sensitive to noise-induced transitions. Establishing an unprecedented connection between the neutron population evolving in a reactor core and the celebrated Kardar-Parisi-Zhang (KPZ) equation, we indeed find evidence that a noisy reactor core power distribution might be subject to a process analogous to the roughening transition, well-known to occur in systems described by the KPZ equation.

Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling models.

How robust are socioeconomic agent-based models with respect to the details of the agents' decision rule? We tackle this question by considering an occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of utility functions and decision rules, we pinpoint the nonequilibrium nature of the agent dynamics, while recovering an equilibrium-like phase separation phenomenology. Within the mean-field approximation we show how the model can be mapped, to some extent, onto an active matter field description. Finally, we consider nonreciprocal interactions between two populations and show how they can lead to nonsteady macroscopic behavior. We believe our approach provides a unifying framework to further study geography-dependent agent-based models, notably paving the way for joint consideration of population and price dynamics within a field theoretic approach.

Constraining a relativistic mean field model using neutron star mass–radius measurements I: nucleonic models

ABSTRACT Measurements of neutron star mass and radius or tidal deformability deliver unique insight into the equation of state (EOS) of cold dense matter. EOS inference is very often done using generalized parametric or non-parametric models, which deliver no information on composition. In this paper, we consider a microscopic nuclear EOS model based on a field theoretical approach. We show that current measurements from NICER and gravitational wave observations constrain primarily the symmetric nuclear matter EOS. We then explore what could be delivered by measurements of mass and radius at the level anticipated for future large-area X-ray timing telescopes. These should be able to place very strong limits on the symmetric nuclear matter EOS, in addition to constraining the nuclear symmetry energy that determines the proton fraction inside the neutron star.

Topological dualities via tensor networks

The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable in as much as it connects systems commonly associated to different areas of physics—that of long-range entangled topological order, (topological) band insulators, and classical statistical mechanics, respectively. Connecting fermionic and bosonic systems, the duality construction is intrinsically nonlocal, a complication that has been addressed in a plethora of different approaches, including dimensional reduction to one dimension, conformal field theory methods, and operator algebra. In this paper, we propose a unified approach to this duality, whose main protagonist is a tensor network (TN) assuming the role of an intermediate translator. Introducing a fourth node into the net of dualities offers several advantages: the formulation is integrative in that all links of the duality are treated on an equal footing, (unlike in field theoretical approaches) it is formulated with lattice precision, a feature that becomes key in the mapping of correlation functions, and their possible numerical implementation. Finally, the passage from bosons to fermions is formulated entirely within the two-dimensional TN framework where it assumes an intuitive and technically convenient form. We illustrate the predictive potential of the formalism by exploring the fate of phase transitions, point and line defects, topological boundary modes, and other structures under the mapping between system classes. Having condensed-matter readerships in mind, we introduce the construction pedagogically in a manner assuming only minimal familiarity with the concept of TNs. Published by the American Physical Society 2024

Heavy quark fragmentation function in two-dimensional QCD in Nc→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c\\rightarrow \\infty $$\\end{document} limit

We carry out a comprehensive study of the quark-to-meson fragmentation function in the ’t Hooft model, i.e., the two-dimensional quantum chromodynamics (QCD) in Nc→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c\\rightarrow \\infty $$\\end{document} limit, following the operator definition pioneered by Collins and Soper. We apply the Hamiltonian approach as well as the diagrammatic approach to construct the functional form of the quark-to-meson fragmentation function in terms of the meson’s light-cone wave function. For the sake of comparison, we also investigate the heavy quark fragmentation into quarkonium in two-dimensional QCD within the framework of the nonrelativistic QCD (NRQCD) factorization, at the lowest order in quark velocity. In the heavy quark limit, the quark fragmentation function obtained from the ab initio method agrees well, both analytically and numerically, with that obtained from the NRQCD approach. This agreement might be regarded as a nontrivial justification for the validity of both field-theoretical approaches to compute the heavy quark fragmentation function.

Kerner Equation for Motion in a Non-Abelian Gauge Field

The equations of motion of an isospin-carrying particle in a Yang–Mills and gravitational field were first proposed in 1968 by Kerner, who considered geodesics in a Kaluza–Klein-type framework. Two years later, the flat space Kerner equations were completed by also considering the motion of the isospin by Wong, who used a field-theoretical approach. Their groundbreaking work was then followed by a long series of rediscoveries whose history is reviewed. The concept of isospin charge and the physical meaning of its motion are discussed. Conserved quantities are studied for Wu–Yang monopoles and diatomic molecules by using van Holten’s algorithm.