Space Formulation Research Articles

Nearly optimal quasienergy estimation and eigenstate preparation of time-periodic Hamiltonians by Sambe space formalism

Nearly optimal quasienergy estimation and eigenstate preparation of time-periodic Hamiltonians by Sambe space formalism

Unifying Special Relativity and Quantum Mechanics via Adynamical Global Constraints

Abstract Maxwell unified the disparate concepts of electric and magnetic fields with one theory (electromagnetism) and Einstein then unified the disparate theories of electromagnetism and mechanics with one kinematics (Minkowski space of special relativity). In this talk, we will briefly explain how the disparate kinematics of quantum mechanics (finite-dimensional Hilbert space) and special relativity can be unified with one principle (relativity principle). This result follows from the axiomatic reconstruction of quantum mechanics via information-theoretic principles, which has successfully recast quantum mechanics as a principle theory a la Einstein, i.e., the formalism of the theory follows from an empirically discovered fact, just like special relativity. According to the quantum reconstruction program, the empirically discovered fact whence the Hilbert space formalism of quantum mechanics is Information Invariance & Continuity. Of course, the empirically discovered fact whence the Lorentz transformations of special relativity is the light postulate, i.e., everyone measures the same value for the speed of light c, regardless of their relative motions. Obviously, the light postulate can be justified by the relativity principle—the laws of physics are the same in all inertial reference frames—because c is a constant of Nature per Maxwell’s electromagnetism. [We label this “NPRF + c” for short, where NPRF stands for “no preferred reference frame.”] As we will show, Information Invariance & Continuity can also be justified by the relativity principle by first spatializing the quantum reconstruction program’s operational notion of measurement. In that case, Information Invariance & Continuity entails the empirically discovered fact that everyone measures the same value for Planck’s constant h, regardless of their relative spatial orientations or locations (Planck postulate). Since Poincar’e transformations relate inertial reference frames via spatial rotations and translations as well as boosts, and h is a constant of Nature per Planck’s radiation law, the relativity principle justifies the Planck postulate (NPRF + h) just like it justifies the light postulate (NPRF + c). Thus, the kinematics of quantum mechanics and special relativity are unified in that both follow most fundamentally from the relativity principle in the adynamical global constraints NPRF + h and NPRF + c. This approach provides a principle solution to the mystery of quantum entanglement that does not violate locality, statistical independence, intersubjective agreement, or the uniqueness of experimental outcomes and it does not alter quantum mechanics as a principle theory. An ontology consistent with this unification is introduced and we deflate both the ‘big’ and ‘small’measurement problems.

A Bayesian approach to model local and temporal heterogeneity in repeated cross-sectional health surveys

Abstract In several countries, including Italy, a prominent approach to population health surveillance involves conducting repeated cross-sectional surveys at short intervals of time. These surveys gather information on the health status of individual respondents, including details on their behaviours, risk factors, and relevant socio-demographic information. While the collected data provides valuable information, modelling such data presents several challenges. For instance, in health risk models, it is essential to consider behavioural information, local and temporal dynamics, and disease co-occurrence. In response to these challenges, our work proposes a multivariate temporal logistic model for chronic disease diagnoses at local level. Linear predictors are modelled using individual risk factor covariates and a latent individual propensity to diseases. Leveraging a state space formulation of the model, we construct a framework in which temporal heterogeneity in regression coefficients is informed by exogenous information at local level, corresponding to different contextual risk factors that may affect the occurrence of chronic diseases in different ways. To explore the effectiveness of our method, we analyse behavioural and risk factor surveillance data collected in Italy (PASSI), which is well-known as a country characterized by high peculiar administrative, social and territorial diversities reflected on high variability in morbidity among population subgroups.

Extended Operational Space Kinematics, Dynamics, and Control of Redundant Serial Robots

A recently developed differential geometric representation of redundant serial robot kinematics is employed to create a new extended operational space dynamics and control formulation that explicitly accounts for redundant robot degrees of freedom. This formulation corrects deficiencies in kinematics and dynamics of redundant serial robots that have relied for over half a century on error-prone generalized inverse velocity-based kinematics for redundancy resolution. New ordinary differential equations of robot operational space dynamics are obtained, without the need for ad hoc derivation, in terms of task coordinates and self-motion coordinates that represent robot redundancy. A new extended operational space control approach is presented that exploits ordinary differential equations of motion in terms of task and self-motion coordinates, enabling enforcement of desired output trajectories, obstacle avoidance, and performance constraints. Four examples are presented with a one-degree-of-redundancy robot that demonstrate the validity and superior performance of the new formulation, relative to the traditional task space method used for redundant serial robot control. Finally, an example with eight degrees of redundancy is presented that further illustrates superior performance of the new operational space formulation.

Notes on solution phase space and BTZ black hole

In this paper, we use the solution phase space approach based on the covariant phase space formalism to compute the conserved charges of the BTZ black hole, namely mass, angular momentum, and entropy. Furthermore, we discuss the first law of the BTZ black hole and the Smarr relation. For completeness, outer horizon and inner horizon cases have been all included. Additionally, the results of the three-dimensional Kerr-dS spacetime have also been obtained. Our results are consistent with previous investigations. Considering the simplicity of the circumstances, we have presented the most detailed possible information, with the aim of facilitating rsearch in related fields.

Phase Space Formulation of Light Propagation on Tilted Planes

The solution of the Helmholtz equation describing the propagation of light in free space from a plane to another can be described by the angular spectrum operator, which acts in the frequency domain. Many applications require this operator to be generalized to handle tilted source and target planes, which has led to research investigating the implications of these adaptations. However, the frequency domain representation intrinsically limits the understanding the way the signal is transformed through propagation. Instead, studying how the operator maps the space–frequency components of the wavefield provides essential information that is not available in the frequency domain. In this work, we highlight and exploit the deep relation between wave optics and quantum mechanics to explicitly describe the symplectic action of the tilted angular spectrum in phase space, using mathematical tools that have proven their efficiency for quantum particle physics. These derivations lead to new algorithms that open unprecedented perspectives in various domains involving the propagation of coherent light.

An exact implementation of the generalized Zhang-Zhu criterion for elasto-plastic finite element calculations

The generalized Zhang-Zhu (GZZ) strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion. The introduction to mean normal stress results in a non-smooth and non-convex yield surface, which presents a challenge for updating plastic stress. Current research primarily focuses on modified smooth GZZ criteria or approximate solutions, which inevitably lead to increased computational costs or inaccuracies. In this paper, an accurate stress updating algorithm is proposed based on the original GZZ criterion. The algorithm operates entirely in the principal stress space, where numerical singularities at the intersection of yield surfaces are avoided by defining four different types of stress updating. This approach simplifies the GZZ criterion compared to its formulation in general stress space. The return mapping is employed to compute the updated stress and consistent stiffness matrix, facilitating calculations using both finite element implicit and explicit algorithms. Finally, the accuracy of the proposed method is validated using rock true triaxial test data and semi-analytical solutions for stresses and displacement around a circular opening under the GZZ criterion.

Relational Lorentzian Asymptotically Safe Quantum Gravity: Showcase Model

In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or physical) Hamiltonian for the true (observable) degrees of freedom. The resulting reduced phase space is then canonically quantized, and one can construct the generating functional of time-ordered Wightman (i.e., Feynman) or Schwinger distributions, respectively, from the corresponding time-translation unitary group or contraction semigroup, respectively, as a path integral. For the unitary choice, that path integral can be rewritten in terms of the Lorentzian Einstein–Hilbert action plus observable matter action and a ghost action. The ghost action depends on the Hilbert space representation chosen for the canonical quantization and a reduction term that encodes the reduction of the full phase space to the phase space of observables. This path integral can then be treated with the methods of asymptotically safe quantum gravity in its Lorentzian version. We also exemplified the procedure using a concrete, minimalistic example, namely Einstein–Klein–Gordon theory, with as many neutral and massless scalar fields as there are spacetime dimensions. However, no explicit calculations were performed. In this paper, we fill in the missing steps. Particular care is needed due to the necessary switch to Lorentzian signature, which has a strong impact on the convergence of “heat” kernel time integrals in the heat kernel expansion of the trace involved in the Wetterich equation and which requires different cut-off functions than in the Euclidian version. As usual we truncate at relatively low order and derive and solve the resulting flow equations in that approximation.

FRACTIONAL ANALYSIS OF ONE-DIMENSIONAL SCHRÖDINGER MODEL IN THE CONTEXT OF CAPUTO-TYPE FRACTIONAL DERIVATIVES BASED ON RESIDUAL POWER SERIES METHOD

This research presents a novel analytical approach to explore the fractional analysis of the one-dimensional time-fractional Schrödinger model (TFSM) using Caputo fractional derivatives. By integrating the Mohand transform (MT) with the residual power series method (RPSM), we develop the Mohand residual power series method (MT-RPSM) that provides results in the form of convergent series without assumptions on variables. Initially, we employ MT to reduce the fractional order, and then we transfer the fractional problem into the Mohand space formulation. Second, we use the RPSM concept to derive the iterative series formula for the Mohand space formulation. We analyze these findings using visual layouts to show the physical representation of the TFSM, which matches the precise results very well. The results indicate that the proposed technique is a reliable and practical method for identifying and analyzing various nonlinear models of physical phenomena.

توظيف التكنولوجيا في تصميم الإعلان الرقمي وتمثلاتها الإبداعية في نتاجات طلبة التربية الفنية

The research dealt with the topic of (employing technology in the design of digital advertising and its creative representations in the products of art education students). The research contained four chapters. The first chapter dealt with: the methodological framework of the research, represented by the research problem that was revealed in the following question: How has technology contributed to employment in the design of digital advertising? They have no role in enriching the creative process and are represented in their artistic productions. The researcher determined the limits of the research, which were represented by the products of the students of the Department of Art Education - First Stage / College of Fine Arts/ University of Baghdad for the academic year (2020-2021), and then the researcher moved to the second semester, which included two sections. The title of the first section was employing technology artistically for advertising, and the section included the second is the creative process and aesthetic standards in the artistic achievement, and the researcher extracted a number of indicators that resulted from the theoretical framework: 1. The use of digital technical methods in employing shapes by following the technique of assembling and composing photographs, and generating a main rhythm between images and color values, served the functional aspect and the creative process of the advertising poster. 2. The computer showed a kind of diversity and excitement in the use of letters and their formal formulation in the design space. Among the most important conclusions is that the use of digital technology in the field of art education for practical academic subjects has given students the ability to diversify the styles of artistic production and facilitate the procedures used in producing these artistic works.

Differential rotation in neutron stars at finite temperatures

IntroductionThis paper investigates the impact of differential rotation on the bulk properties and onset of rotational instabilities in neutron stars at finite temperatures up to 50 MeV.MethodsUtilizing the relativistic Brueckner-Hartree-Fock (RBHF) formalism in full Dirac space, the study constructs equation of state (EOS) models for hot neutron star matter, including conditions relevant for high temperatures. These finite-temperature EOS models are applied to compute the bulk properties of differentially rotating neutron stars with varying structural deformations.ResultsThe findings demonstrate that the stability of these stars against bar-mode deformation, a key rotational instability, is only weakly dependent on temperature. Differential rotation significantly affects the maximum mass and radius of neutron stars, and the threshold for the onset of bar-mode instability shows minimal sensitivity to temperature changes within the examined range.DiscussionThese findings are crucial for interpreting observational data from neutron star mergers and other high-energy astrophysical events. The research underscores the necessity of incorporating differential rotation and finite temperature effects in neutron star models to predict their properties and stability accurately.

The universal multiplicity function: counting haloes and voids

We present a novel combination of the excursion-set approach with the peak theory formalism in Lagrangian space and provide accurate predictions for halo and void statistics over a wide range of scales. The set-up is based on an effective moving barrier. Besides deriving the corresponding numerical multiplicity function, we introduce a new analytical formula reaching the percent level agreement with the exact numerical solution obtained via Monte Carlo realisations down to small scales, ∼ 1012 h -1M⊙. In the void case, we derive the dependence of the effective moving barrier on the void formation threshold, δ v, by comparison against the Lagrangian void size function measured in the DEMNUni simulations. We discuss the mapping from Lagrangian to Eulerian space for both haloes and voids; adopting the spherical symmetry approximation, we obtain a strong agreement at intermediate and large scales. Finally, using the effective moving barrier, we derive Lagrangian void density profiles accurately matching measurements from cosmological simulations, a major achievement towards using void profiles for precision cosmology with the next generation of galaxy surveys.

Moyal deformation of the classical arrival time

The quantum time of arrival (TOA) problem requires the statistics of measured arrival times given only the initial state of a particle. Following the standard framework of quantum theory, the problem translates into finding an appropriate quantum image of the classical arrival time TC(q,p), usually in operator form T̂. In this paper, we consider the problem anew within the phase space formulation of quantum mechanics. The resulting quantum image is a real-valued and time-reversal symmetric function TM(q,p) in formal series of ℏ2 with the classical arrival time as the leading term. It is obtained directly from the Moyal bracket relation with the system Hamiltonian and is hence interpreted as a Moyal deformation of the classical TOA. We investigate its properties and discuss how it bypasses the known obstructions to quantization by showing the isomorphism between TM(q,p) and the rigged Hilbert space TOA operator constructed in Pablico and Galapon [Eur. Phys. J. Plus 138, 153 (2023)], which always satisfy the time-energy canonical commutation relation for arbitrary analytic potentials. We then examine TOA problems for a free particle and a quartic oscillator potential as examples.

Asymptotically safe — canonical quantum gravity junction

The canonical (CQG) and asymptotically safe (ASQG) approach to quantum gravity share to be both non-perturbative programmes. However, apart from that they seem to differ in several aspects such as: 1. Signature: CQG is Lorentzian while ASQG is mostly Euclidian. 2. Background Independence (BI): CQG is manifesly BI while ASQG is apparently not. 3. Truncations: CQG is apparently free of truncations while ASQG makes heavy use of them.The purpose of the present work is to either overcome actual differences or to explain why apparent differences are actually absent. Thereby we intend to enhance the contact and communication between the two communities. The focus of this contribution is on conceptual issues rather than deep technical details such has high order truncations. On the other hand the paper tries to be self-contained in order to be useful to researchers from both communities.The point of contact is the path integral formulation of Lorentzian CQG in its reduced phase space formulation which yields the formal generating functional of physical (i.e. gauge invariant) either Schwinger or Feynman N-point functions for (relational) observables. The corresponding effective actions of these generating functionals can then be subjected to the ASQG Wetterich type flow equations which serve in particular to find the rigorous generating fuctionals via the inverse Legendre transform of the fixed pointed effective action.

Covariant phase space formalism for fluctuating boundaries

We reconsider formulating D dimensional gauge theories, with the focus on the case of gravity theories, in spacetimes with boundaries. We extend covariant phase space formalism to the cases in which boundaries are allowed to fluctuate. We analyze the symplectic form, the freedoms (ambiguities), and its conservation for this case. We show that boundary fluctuations render all the surface charges integrable. We study the algebra of charges and its central extensions, charge conservation, and fluxes. We briefly comment on memory effects and questions regarding semiclassical aspects of black holes in the fluctuating boundary setup.

A foray on SCFT3 via super spinor-helicity and Grassmann twistor variables

In this paper, we develop a momentum super space formalism for N = 1, 2 superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a “half” Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using this formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in N = 1, 2 theories. We discover interesting double copy relations in N = 1 super-correlators. Further, we discovered super double copy relations that take us from N = 1 to N = 2 super-correlators. We also extend our results to correlators involving scalars as well as to higher points. Further, we comment on the connection of our results with the flat space super amplitudes in one higher dimension.

Dynamical edge modes and entanglement in Maxwell theory

Previous work on black hole partition functions and entanglement entropy suggests the existence of “edge” degrees of freedom living on the (stretched) horizon. We identify a local and “shrinkable” boundary condition on the stretched horizon that gives rise to such degrees of freedom. They can be interpreted as the Goldstone bosons of gauge transformations supported on the boundary, with the electric field component normal to the boundary as their symplectic conjugate. Applying the covariant phase space formalism for manifolds with boundary, we show that both the symplectic form and Hamiltonian exhibit a bulk-edge split. We then show that the thermal edge partition function is that of a codimension-two ghost compact scalar living on the horizon. In the context of a de Sitter static patch, this agrees with the edge partition functions found by Anninos et al. in arbitrary dimensions. It also yields a 4D entanglement entropy consistent with the conformal anomaly. Generalizing to Proca theory, we find that the prescription of Donnelly and Wall reproduces existing results for its edge partition function, while its classical phase space does not exhibit a bulk-edge split.

Efficient real space formalism for hybrid density functionals.

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn-Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space finite-difference Laplacian matrix by leveraging its Kronecker product structure, thereby enabling the time to solution of associated linear systems to be highly competitive with the fast Fourier transform scheme while not imposing any restrictions on the boundary conditions. We implement this formalism for both the unscreened and range-separated variants of hybrid functionals. We verify its accuracy and efficiency through comparisons with established planewave codes for isolated as well as bulk systems. In particular, we demonstrate up to an order-of-magnitude speedup in time to solution for the real space method. We also apply the framework to study the structure of liquid water using abinitio molecular dynamics, where we find good agreement with the literature. Overall, the current formalism provides an avenue for efficient real-space DFT calculations with hybrid density functionals.

GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. This has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$ limit. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies.

Criticality of central charges for Gauss–Bonnet black holes

Employing extended phase space formalism, we study critical phenomenon of A-charge and C-charge for holographic theories dual to Gauss–Bonnet black holes. We find an universal critical Gauss–Bonnet coupling, giving rise to an universal ratio between the two central charges at the critical point. This leads to a new intepretation for critical behavior of Gauss–Bonnet black holes in terms of the boundary degrees of freedoms, although the solutions are electrically neutral. Another novel feature is for either of the central charges, the transition temperature is beyond the critical point but is upper bounded by causality of the boundary theories.