Dirac
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Related Articles from SNS
Numerical solution of the nonlinear Dirac equation by a splitting variational quantum algorithm
Announce Type: cross Abstract: In this work, we propose an operator-splitting variational quantum algorithm, termed Dirac-sVQA, for simulating the nonlinear Dirac equation (NLDE). The main difficulty arises from the state-dependent nonlinear interaction, its time-discrete update depends explicitly on the intermediate spinor state and, in general, cannot be implemented as a fixed state-independent unitary circuit. To address this difficulty, we decompose the NLDE evolution into a structured...
An Adaptive Log-Laguerre Spectral Method for the Radial Dirac Equation: Resolving Asymptotic Decay and Core Singularities in Atomic Calculations
arXiv:2604.11063v2 Announce Type: replace Abstract: The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. Capturing both the non-polynomial singularities at the origin and the state-dependent asymptotic decay on semi-infinite domains presents a significant computational challenge. In this work, we propose the Adaptive Log-Laguerre Spectral...
Klein--Gordon and Dirac Oscillators with an Apparent Mass Induced by the Momentum-Space Dual of the Fock--Lorentz Transformations
arXiv:2606.05226v1 Announce Type: new Abstract: We propose a controlled momentum-space dual of the Fock--Lorentz (FL) transformations and use it to derive a deformed relativistic mass shell. Restricting the FL conformal factor to the cosmological-frame world line $\vx=0$, the invariant relation takes the form $(E^{2}-\vp^{2}c^{2})(1+ct/R)^{2}=m_{0}^{2}c^{4}$, which is equivalent to the standard special-relativistic dispersion law with a time-dependent apparent mass $\mapp(t)=m_{0}/(1+ct/R)$....
Quaternion Dirac--Coulomb--Breit Integral Transformation for Relativistic Four-Component Correlated Electronic Structure Theory
Announce Type: new Abstract: High-accuracy correlated four-component relativistic electronic structure methods are typically formulated in terms of integrals over molecular orbital (MO). Consequently, an efficient and scalable strategy is required to deal with the complexity of transforming relativistic two-electron integrals from the atomic orbital (AO) to the MO basis. The transformation bottleneck is particularly acute for approaches that include Breit interaction integrals, whose...
First-Principles-Based Grand Unified Theory (GUT) for Micro-Macro Modal Quantization (MQ)--Part II: Heisenberg-Schrodinger-Dirac Pictures, Act 1
arXiv:1804.09246v2 Announce Type: replace Abstract: This series of papers are devoted to establishing a first-principles-based grand unified theory (GUT) for macroscopic modal quantization (MMQ) or traditionally called eigenmode analysis (EMA) in electrodynamics. This paper focuses on outlining the Schrodinger picture of the GUT. The physical picture and mathematical formalism of the energy-based MMQ are reviewed simply, and an MMQ-oriented numerical method--diagonalizing energy source...
Controlling $\langle \hat{S}^2 \rangle$ in Broken-symmetry Density Functional Theory Calculations via Constrained Optimization
Announce Type: new Abstract: Accurate determination of magnetic exchange coupling constants ($J$) from density functional theory (DFT) remains challenging, particularly for open-shell systems where broken-symmetry (BS) solutions suffer from spurious spin contamination that systematically exaggerates $J$ values. Several methods have been proposed to address this problem by adjusting the mapping scheme from the DFT energies to the Heisenberg-Dirac-van Vleck effective spin Hamiltonian energies....
Relativistic deceleration vs acceleration, Unruh effect observation, and the Schott energy
Announce Type: new Abstract: This article examines finite-time relativistic deceleration and its energy balance within the Lorentz-Abraham-Dirac equation, with special attention to boundary Schott-energy terms. From experimental and kinematical viewpoints, deceleration differs from acceleration. Proper accelerations or decelerations relevant to Unruh-effect observations may be more naturally realized in deceleration than in comparable acceleration scenarios.
Asymptotic Recovery in Fourier Spectral Methods for the Schr\"odinger Equation with Point Singularities
arXiv:2606.01718v1 Announce Type: new Abstract: This paper studies the Fourier spectral method (FSM) for the Schr\"odinger equation with singular potentials $V \in H^{s}$, where $s > \max\{d/2-2,-1\}$ and $d$ denotes the spatial dimension. This setting includes a broad class of singular potentials, such as the 3D Coulomb potential and the 1D Dirac-delta potential.
Analysis of Mixed Radiation Fields at the MoEDAL Experiment Based on Real-Time Data from a Timepix Detector Network
arXiv:2605.05936v2 Announce Type: replace Abstract: The primary objective of this work is the determination of fluences and characteristics of fast neutrons, other hadrons, and highly ionizing particles in the environment of the MoEDAL experiment at the Large Hadron Collider. These particles constitute an experimental background for the passive Nuclear Track Detectors (NTDs) used by MoEDAL to search for tracks potentially produced by Dirac magnetic monopoles, in particular by particles...
Operator learning for solving Fokker-Planck equations with various initial conditions
arXiv:2606.09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics. In this work, we propose a conditional normalizing flow-based physics-informed neural network (PINN) framework for efficiently approximating the solution operator of the FPE for a whole range of initial conditions. Leveraging the Chapman-Kolmogorov equation for Markovian...