Hamiltonian Analysis Research Articles

Hamiltonian charges on light cones for linear field theories on (A)dS backgrounds

We analyse the Noether charges for scalar and Maxwell fields on light cones on a de Sitter, Minkowski, and anti-de Sitter backgrounds. Somewhat surprisingly, under natural asymptotic conditions all charges for the Maxwell fields on both the de Sitter and anti-de Sitter backgrounds are finite. On the other hand, one needs to renormalise the charges for the conformally-covariant scalar field when the cosmological constant does not vanish. In both cases well-defined renormalised charges, with well-defined fluxes, are obtained. Again surprisingly, a Hamiltonian analysis of a suitably rescaled scalar field leads to finite charges, without the need to renormalise. Last but not least, we indicate natural phase spaces where the Poisson algebra of charges is well defined.

Hamiltonian Analysis of f(Q)$f(\mathbb {Q})$ Gravity and the Failure of the Dirac–Bergmann Algorithm for Teleparallel Theories of Gravity

AbstractIn recent years, gravity has enjoyed considerable attention in the literature and important results have been obtained. However, the question of how many physical degrees of freedom the theory propagates—and how this number may depend on the form of the function f—has not been answered satisfactorily. In this article it is shown that a Hamiltonian analysis based on the Dirac‐Bergmann algorithm—one of the standard methods to address this type of question—fails. The source of the failure is isolated and it is shown that other commonly considered teleparallel theories of gravity are affected by the same problem. Furthermore, it is pointed out that the number of degrees of freedom obtained in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely eight), based on the Dirac‐Bergmann algorithm, is wrong. Using a different approach, it is shown that the upper bound on the degrees of freedom is seven. Finally, a more promising strategy for settling this important question is proposed.

Minimally modified gravity with auxiliary constraints formalism

We investigate the possibility of reducing the number of degrees of freedom (d.o.f.) starting from generic metric theories of gravity by introducing multiple auxiliary constraints (ACs), under the restriction of retaining spatial covariance as a gauge symmetry. Arbitrary numbers of scalar-, vector- and tensor-type ACs are considered a priori, yet we find that no vector- and tensor-type constraints should be introduced, and that scalar-type ACs should be no more than four for the purpose of constructing minimally modified gravity (MMG) theories which propagate only two tensorial d.o.f., like general relativity (GR). Through a detailed Hamiltonian analysis, we exhaust all the possible classifications of ACs and find out the corresponding minimalizing and symmetrizing conditions for obtaining the MMG theories. In particular, no condition is required in the case of four ACs, hence in this case the theory can couple with matter consistently and naturally. To illustrate our formalism, we build a concrete model for this specific case by using the Cayley-Hamilton theorem and derive the dispersion relation of the gravitational waves, which is subject to constraints from the observations.

Monitoring the Molecular Structure of Fibrinogen during the Adsorption Process at the Buried Silicone Oil Interface In Situ in Real Time

Interfacial proteins play important roles in many research fields and applications, such as biosensors, biomedical implants, nonfouling coatings, etc. Directly probing interfacial protein behavior at buried solid/liquid and liquid/liquid interfaces is challenging. We used sum frequency generation vibrational spectroscopy and a Hamiltonian data analysis method to monitor the molecular structure of fibrinogen on silicone oil during the adsorption process in situ in real time. The results showed that the adsorbed fibrinogen molecules tend to adopt a bent structure throughout the entire adsorption process with the same orientation. This is different from the case of adsorbed fibrinogen on CaF2 with a linear structure or on polystyrene with a bent structure but a different orientation. The method introduced herein is generally applicable for following time-dependent molecular structures of many other proteins and peptides at interfaces in situ in real time at the molecular level.

Supercomputers against strong coupling in gravity with curvature and torsion

Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm for curvature and torsion theories is presented. These non-Riemannian or Poincaré gauge theories suffer notoriously from strong coupling. The implementation forms a package (the ‘Hamiltonian Gauge Gravity Surveyor’ – HiGGS) for the xAct tensor manipulation suite in Mathematica. Poisson brackets can be evaluated in parallel, meaning that Hamiltonian analysis can be done on silicon, and at scale. Accordingly HiGGS is designed to survey the whole Lagrangian space with high-performance computing resources (clusters and supercomputers). To demonstrate this, the space of ‘outlawed’ Poincaré gauge theories is surveyed, in which a massive parity-even/odd vector or parity-odd tensor torsion particle accompanies the usual graviton. The survey spans possible configurations of teleparallel-style multiplier fields which might be used to kill-off the strongly coupled modes, with the results to be analysed in subsequent work. All brackets between the known primary and secondary constraints of all theories are made available for future study. Demonstrations are also given for using HiGGS – on a desktop computer – to run the Dirac–Bergmann algorithm on specific theories, such as Einstein–Cartan theory and its minimal extensions.

Connection dynamics of reduced five-dimensional Kaluza-Klein theory and its deparametrization

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric model of the theory without introducing additional matter fields beyond the 5-dimensional gravity. Thus the physical time evolution and the physical spatial coordinate can be provided by the geometrical degrees of freedom in the higher dimensional spacetime.

The decisive role of electrostatic interactions in transport mode and phase segregation of lithium ions in LiFePO4.

Understanding the mechanism of slow lithium ion (Li+) transport kinetics in LiFePO4 is not only practically important for high power density batteries but also fundamentally significant as a prototypical ion-coupled electron transfer process. Substantial evidence has shown that the slow ion transport kinetics originates from the coupled transfer between electrons and ions and the phase segregation of Li+. Combining a model Hamiltonian analysis and DFT calculations, we reveal that electrostatic interactions play a decisive role in coupled charge transfer and Li+ segregation. The obtained potential energy surfaces prove that ion-electron coupled transfer is the optimal reaction pathway due to electrostatic attractions between Li+ and e- (Fe2+), while prohibitively large energy barriers are required for separate electron tunneling or ion hopping to overcome the electrostatic energy between the Li+-e- (Fe2+) pair. The model reveals that Li+-Li+ repulsive interaction in the [010] transport channels together with Li+-e- (Fe2+)-Li+ attractive interaction along the [100] direction cause the phase segregation of Li+. It explains why the thermodynamically stable phase interface between Li-rich and Li-poor phases in LiFePO4 is perpendicular to [010] channels.

Multi-field Cuscuton cosmology

In this paper, we first introduce a multi-field setup of Cuscuton gravity in a curved field space manifold. Then, we show that this model allows for a regular bouncing cosmology and it does not lead to ghosts or other instabilities at the level of perturbations. More precisely, by decomposing the scalar fields perturbations into the tangential and normal components with respect to the background field space trajectory, the entropy mode perpendicular to the background trajectory is healthy which directly depends on the signature of the field-space metric, whereas the adiabatic perturbation tangential to the background trajectory is frozen. In analogy with the standard Cuscuton theory equipped with an extra dynamical scalar field, the adiabatic field does not have its own dynamics, but it modifies the dynamics of other dynamical fields like entropy mode in our scenario. Finally, we perform a Hamiltonian analysis of our model in order to count the degrees of freedom propagated by dynamical fields.

Geometric action for extended Bondi-Metzner-Sachs group in four dimensions

The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS4 generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS4 Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. Furthermore, the model reproduces the evolution equations of non-radiative asymptotically flat spacetimes at null infinity.

An optimal trajectory planning for automated on‐ramp merging

AbstractThis paper proposes an optimal trajectory planning model for automated on‐ramp merging. The minimum cost path based on the optimal control theory is selected as the optimal trajectory of the on‐ramp merging vehicle, which could avoid potential collisions and satisfy the kinematic constraints on the vehicle motion. Moreover, an optimal control strategy is presented to solve the trajectory planning problem of the facilitating vehicle. An analytical closed‐form solution is derived by using the Hamiltonian analysis and the path information of the merging vehicle. Particularly, the proposed planning process also considers the lateral movement of the on‐ramp merging, which is more efficient in the application. Owing to the location and time that the on‐ramp vehicle merges into the mainline can be obtained endogenously by its planning process, the model has high adaptation to various on‐ramp environments. Solutions to the above two optimal methods are implemented in a model predictive control framework to cope with possible external disturbances. Several numerical simulations and PreScan‐Simulink Co‐Simulation illustrate the effectiveness of the proposed model. Furthermore, this methodology is compared with a typical CACC strategy to demonstrate its potential to reduce fuel consumption, as well as improve passenger comfort.

Hamiltonian perspective on parquet theory

Understanding collective phenomena calls for tractable descriptions of correlations in assemblies of strongly interacting constituents. Capturing the essence of their self-consistency is central. The parquet theory admits a maximum level of self-consistency for strictly pairwise many-body correlations. While perturbatively based, the core of parquet and allied models is a set of strongly coupled nonlinear integral equations for all-order scattering; tightly constrained by crossing symmetry, they are nevertheless heuristic. Within a formalism due to Kraichnan, we present a Hamiltonian analysis of fermionic parquet's structure. The shape of its constitutive equations follows naturally from the resulting canonical description. We discuss the affinity between the derived conserving scattering amplitude and that of standard parquet. Whereas the Hamiltonian-derived model amplitude is microscopically conserving, it cannot preserve crossing symmetry. The parquet amplitude and its refinements preserve crossing symmetry, yet cannot safeguard conservation at any stage. Which amplitude should be used depends on physics rather than on theoretically ideal completeness.

Photocatalytic and Photocurrent Responses to Visible Light of the Lone-Pair-Based Oxysulfide Sr6Cd2Sb6S10O7.

We present a combined experimental and computational study on the recently reported oxysulfide Sr6Cd2Sb6S10O7. Our spectroscopy and photoelectrochemical measurements and tests for photocatalytic activity indicate the potential of Sr6Cd2Sb6S10O7 for photocatalytic applications. In particular, the transient photocurrent response shows a reproducible photogenerated current which depends on light intensity and which indicates an efficient electron-hole separation upon visible light illumination. Density functional theory calculations, combined with crystal orbital Hamiltonian population analysis, give insights into the electronic structure of Sr6Cd2Sb6S10O7 and the origin of its physical properties. Our comprehensive investigation into Sr6Cd2Sb6S10O7 reveals the roles of its polar structure, polar Sb3+ coordination environments, and the 5s2 lone pair in making this compound a potential candidate for solar water splitting photocatalysis.

Fermions coupled to the Palatini action in n dimensions

We study minimal and nonminimal couplings of fermions to the Palatini action in $n$ dimensions ($n\geq 3$) from the Lagrangian and Hamiltonian viewpoints. The Lagrangian action considered is not, in general, equivalent to the Einstein-Dirac action principle. However, by choosing properly the coupling parameters, it is possible to give a first-order action fully equivalent to the Einstein-Dirac theory in a spacetime of dimension four. By using a suitable parametrization of the vielbein and the connection, the Hamiltonian analysis of the general Lagrangian is given, which involves manifestly Lorentz-covariant phase-space variables, a real noncanonical symplectic structure, and only first-class constraints. Additional Hamiltonian formulations are obtained via symplectomorphisms, one of them involving half-densitized fermions. To confront our results with previous approaches, the time gauge is imposed.

Stabilization of A -site ordered perovskites and formation of spin-half antiferromagnetic lattice: CaCu3Ti4O12 and CaCu3Zr4O12

A-site ordered perovskites, CaCu$_3$B$_4$O$_{12}$, which are derivatives of conventional ABO$_3$ perovskites, exhibit varying electronic and magnetic properties. With the objective of examining the role of Cu in this work, we have studied CaCu$_3$Ti$_4$O$_{12}$ and CaCu$_3$Zr$_4$O$_{12}$ and presented the cause of the crystallization of A-site ordered perovskite from conventional ABO$_3$ perovskite and the underlying mechanism leading to the stabilization of non-trivial and experimentally estabilished G-type antiferromagnetic (G-AFM) ordering in these systems. The first-principles electronic structure calculations supplemented with phonon studies show that the formation of A-site ordered perovskite is driven by Jahn-Teller distortion of the CuO$_{12}$ icosahedron. The crystal orbital Hamiltonian population analysis and magnetic exchange interactions estimated using spin dimer analysis infers that the nearest and next-nearest-neighbor interactions (J$_1$ and J$_2$) are direct and weakly ferromagnetic whereas the third-neighbor interaction (J$_3$) is unusually strong and antiferromagnetic driven by indirect superexchange mechanism. The structural geometry reveals that stabilization of G-AFM requires J$_1$ $<$ 2J$_2$, J$_1$ $<$ 2J$_3$. The experimental and theoretical values of Neel Temperature agrees well for $U$ $\approx$ 7 eV, highlighting the role of strong correlation. The magnetic ordering is found to be robust against pressure and strain.

TPV radical-based multifunctional molecular spintronic device: A first-principles study

We design a multifunctional molecular spintronic device consisting of two 1,3,5-triphenylverdazyl (TPV) radicals with carbon nanotube bridge and electrodes , and investigate its spin-polarized transport properties using the first-principles density functional theory and nonequilibrium Green's function method. The results show that the spin-polarized transport properties depend strongly on the external magnetic field modulation and high-efficiency spin-filtering, giant magnetoresistance , spin-rectifying and low-bias voltage negative differential resistance effects can be realized in this designed device. The mechanisms are proposed for these interesting physical effects based on the bias-dependent spin-resolved transmission function, projected density of states and corresponding molecular projected self-consistent Hamiltonian orbitals analysis. These results hold great potential for the development of high-performance multifunctional molecular spintronic devices. High-efficiency spin-filtering, giant magnetoresistance, spin-rectifying and low-bias voltage negative differential resistance effects are realized in a TPV radical-based molecular spintronic device with carbon nanotube bridge and electrode. • Spin-polarized transport properties of a TPV radical-based molecular spintronic device are investigated. • Spin-polarized transport properties depend strongly on the external magnetic field modulation. • High-efficiency spin-filtering, GMR, spin-rectifying and low-bias voltage NDR effects are realized.

Mechanistic Insight into Hydrocarbon Synthesis via CO2 Hydrogenation on χ-Fe5C2 Catalysts.

Converting CO2 into value-added chemicals and fuels is one of the promising approaches to alleviate CO2 emissions, reduce the dependence on nonrenewable energy resources, and minimize the negative environmental effect of fossil fuels. This work used density functional theory (DFT) calculations combined with microkinetic modeling to provide fundamental insight into the mechanisms of CO2 hydrogenation to hydrocarbons over the iron carbide catalyst, with a focus on understanding the energetically favorable pathways and kinetic controlling factors for selective hydrocarbon production. The crystal orbital Hamiltonian population analysis demonstrated that the transition states associated with O-H bond formation steps within the path are less stable than those of C-H bond formation, accounting for the observed higher barriers in O-H bond formation from DFT. Energetically favorable pathways for CO2 hydrogenation to CH4 and C2H4 products were identified which go through an HCOO intermediate, while the CH* species was found to be the key C1 intermediate over χ-Fe5C2(510). The microkinetic modeling results showed that the relative selectivity to CH4 is higher than C2H4 in CO2 hydrogenation, but the trend is opposite under CO hydrogenation conditions. The major impact on C2 hydrocarbon production is attributed to the high surface coverage of O* from CO2 conversion, which occupies crucial active sites and impedes C-C couplings to C2 species over χ-Fe5C2(510). The coexistence of iron oxide and carbide phases was proposed and the interfacial sites created between the two phases impact CO2 surface chemistry. Adding potassium into the Fe5C2 catalyst accelerates O* removal from the carbide surface, enhances the stability of the iron carbide catalyst, thus, promotes C-C couplings to hydrocarbons.

ADM formulation and Hamiltonian analysis of f(Q) gravity

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity with fixing the coincident gauge condition. Using the standard Dirac-Bergmann algorithm, we show that $f(Q)$ gravity has 8 physical degrees of freedom. This result reflects that the diffeomorphism symmetry of $f(Q)$ gravity is completely broken due to the gauge fixing. Moreover, in terms of the perturbations, we discuss the possible mode decomposition of these degrees of freedom.

On the test of novel constitutive relation of capacitor for electrical circuit analysis: a fractal calculus-based approach

PurposeThe purpose of this paper is to test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor.Design/methodology/approachFor ceteris paribus, the constitutive relations of the resistor and inductor have been reformulated by following the novel constitutive relation of capacitor. The responses of RL, RC, LC and RLC circuits defined on the fractal set described by these definitions have been derived by means of the fractal calculus and fractal Laplace transformation. A comparative Hamiltonian formalism-based analysis has been performed where the circuits described by the conventional and the formerly proposed revisited constitutive relations have also been considered.FindingsThis study has found that the novel constitutive relations give unreasonable results unlike the conventional ones. Like such previous revisited constitutive relations, an odd Hamiltonian has been obtained. On the other hand, the conventional constitutive relations give a reasonable Hamiltonian.Originality/valueTo the best of the author’s knowledge, for the first time, the analysis of fractal set defined electrical circuits by means of unconventional constitutive relations has been performed where the deficiency of the tested capacitive constitutive relation has been pointed out.

Hamiltonian analysis of nonlocal F(R) gravity models

We construct a Hamiltonian for the nonlocal F(R) theory in the present work. By this construction, we demonstrate the nature of the ghost degrees of freedom. Finally, we find conditions that give rise to ghost-free theories.

Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis

We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions D, with a particular emphasis on the case D = 5. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS5, which is realized non linearly, contains a four-fold family of angle- dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincaré subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions D ≥ 6 are also given.