Parity Reversal Research Articles

UOTe: Kondo-Interacting Topological Antiferromagnet in a Van der Waals Lattice.

Since the initial discovery of 2D van der Waals (vdW) materials, significant effort has been made to incorporate the three properties of magnetism, band structure topology, and strong electron correlations-to leverage emergent quantum phenomena and expand their potential applications. However, the discovery of a single vdW material that intrinsically hosts all three ingredients has remained an outstanding challenge. Here, the discovery of a Kondo-interacting topological antiferromagnet is reported in the vdW 5f electron system UOTe. It has a high antiferromagnetic (AFM) transition temperature of 150K, with a unique AFM configuration that breaks the combined parity and time reversal (PT) symmetry in an even number of layers while maintaining zero net magnetic moment. This angle-resolved photoemission spectroscopy (ARPES) measurements reveal Dirac bands near the Fermi level, which combined with the theoretical calculations demonstrate UOTe as an AFM Dirac semimetal. Within the AFM order, the presence of the Kondo interaction is observed, as evidenced by the emergence of a 5f flat band near the Fermi level below 100 K and hybridization between the Kondo band and the Dirac band. The density functional theory calculations in its bilayer form predict UOTe as a rare example of a fully-compensated AFM Cherninsulator.

Anomalous Josephson effect in altermagnet

Abstract Anomalous Josephson current in an s-wave superconductor junction is due to the parity and time reversal symmetry breaking from the spin-orbit coupling (SOC) together with magnetization. Altermagnetism is an emerging magnetic phase with the d-wave type magnetism but zero macroscopic magnetization. Here, we numerically study the Josephson supercurrent in a two-dimensional junction with both the SOC and altermagnetism. It is found that the $0$-$\pi$ transition can appear in the system by modulating the junction's lengths or the SOC strengths despite the zero net magnetization in the system. An anomalous Josephson effect is also identified but dependent on the orientation of magnetization.

Dark matter scattering off H2 and He4 nuclei within chiral effective field theory

We study dark matter, assumed to be composed of weak interacting massive particles (WIMPs), scattering off H2 and He4 nuclei. In order to parametrize the WIMP-nucleon interaction, the chiral effective field theory approach is used. Considering only interactions invariant under parity, charge conjugation, and time reversal, we examine five interaction types: scalar, pseudoscalar, vector, axial, and tensor. Scattering amplitudes between two nucleons and a WIMP are determined up to second order of chiral perturbation theory. We apply this program to calculate the interaction rate as a function of the WIMP mass and of the magnitude of the WIMP-quark coupling constants. From our study, we conclude that the scalar nuclear response functions is much greater than the others due to their large combination of low energy constants. We verify that the leading order contributions are dominant in these low energy processes. We also provide an estimate for the background due to atmospheric neutrinos. Published by the American Physical Society 2024

Dirac Theory in Noncommutative Phase Spaces

Based on the position and momentum of noncommutative relations with a noncanonical map, we study the Dirac equation and analyze its parity and time reversal symmetries in a noncommutative phase space. Noncommutative parameters can be endowed with the Planck length and cosmological constant such that the noncommutative effect can be interpreted as an effective gauge potential or a (0,2)-type curvature associated with the Plank constant and cosmological constant. This provides a natural coupling between dynamics and spacetime geometry. We find that a free Dirac particle carries an intrinsic velocity and force induced by the noncommutative algebra. These properties provide a novel insight into the Zitterbewegung oscillation and the physical scenario of dark energy. Using perturbation theory, we derive the perturbed and nonrelativistic solutions of the Dirac equation. The asymmetric vacuum gaps of particles and antiparticles reveal the particle–antiparticle symmetry breaking in the noncommutative phase space, which provides a clue to understanding the physical mechanisms of particle–antiparticle asymmetry and quantum decoherence through quantum spacetime fluctuation.

Integrable coupled bosonic massive Thirring model and its nonlocal reductions

A coupled bosonic massive Thirring model (BMTM), involving an interaction between the two independent spinors, is introduced and shown to be integrable. By incorporating suitable reductions between the field components of the coupled BMTM, five novel integrable models with various type of nonlocal interactions are constructed. Lax pairs satisfying the zero curvature condition are obtained for the coupled BMTM and for each of the related nonlocal models. An infinite number of conserved quantities are derived for each of these models which confirms the integrability of the systems. It is shown that the coupled BMTM respects important symmetries of the original BMTM such as parity, time reversal, global U(1)-gauge and the proper Lorentz transformations. Similarly, all the nonlocal models obtained from the coupled BMTM remain invariant under combined operation of parity and time reversal transformations. However, it is found that only one of the nonlocal models is invariant under proper Lorentz transformation and two other models are invariant under global U(1)-gauge transformation. By using ultralocal Poisson bracket relations among the elements of the Lax operator, it is shown that the coupled BMTM and one of the nonlocal models are completely integrable in the Liouville sense.

Conjugations on L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document} Space on the Real Line

Influenced by PT operators (parity and time reversal operators) the general conjugations acting in the L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{L}}^\ extbf{2}$$\\end{document} space on the real line with the Lebesgue measure are studied. The behaviour of conjugations with respect to multiplication operators and translations is investigated. We consider conjugations defined as the convolution of the Fourier transform of a given unimodular (even) function and test functions. We characterize all conjugations commuting (intertwining) with all translation operators on the real line. The conjugations leaving kernels of Toeplitz operators (a generalization of model spaces) on H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{H}}^\ extbf{2}$$\\end{document} space on the upper half plane invariant are also characterized. Analogous results are obtained for conjugations and kernels of Wiener–Hopf operators.

Asymmetric particle-antiparticle Dirac equation: first quantization

We derive a Dirac-like equation, the asymmetric Dirac equation, where particles and antiparticles sharing the same wave number have different energies and momenta. We show that this equation is Lorentz covariant under proper Lorentz transformations (boosts and spatial rotations) and also determine the corresponding transformation law for its wave function. We obtain a formal connection between the asymmetric Dirac equation and the standard Dirac equation and we show that by properly adjusting the free parameters of the present wave equation we can make it reproduce the predictions of the usual Dirac equation. We show that the rest mass of a particle in the theoretical framework of the asymmetric Dirac equation is a function of a set of four parameters, which are relativistic invariants under proper Lorentz transformations. These four parameters are the analog to the mass that appears in the standard Dirac equation. We prove that in order to guarantee the covariance of the asymmetric Dirac equation under parity and time reversal operations (improper Lorentz transformations) as well as under the charge conjugation operation, these four parameters change sign in exactly the same way as the four components of a four-vector. The mass, though, being a function of the square of those parameters remains an invariant. We also extensively study the free particle plane wave solutions to the asymmetric Dirac equation and derive its energy, helicity, and spin projection operators as well as several Gordon’s identities. The hydrogen atom is solved in the present context after applying the minimal coupling prescription to the asymmetric Dirac equation, which also allows us to appropriately obtain its non-relativistic limit.

Asymmetric particle-antiparticle Dirac equation: second quantization

We build the fully relativistic quantum field theory related to the asymmetric Dirac fields first presented in a prequel to this work. These fields are solutions of the asymmetric Dirac equation, a Lorentz covariant Dirac-like equation whose positive and ‘negative’ frequency plane wave solutions’ dispersion relations are no longer degenerate. At the second quantization level, we show that this implies that particles and antiparticles sharing the same wave number have different energies and momenta. In spite of that, we prove that by properly fixing the values of the relativistic invariants that define the asymmetric Dirac free field Lagrangian density, we can build a consistent, fully relativistic, and renormalizable quantum electrodynamics (QED) that is empirically equivalent to the standard QED. We discuss the reasons and implications of this non-trivial equivalence, exploring qualitatively other scenarios in which the asymmetric Dirac fields may lead to beyond the standard model predictions. We give a complete account of how the asymmetric Dirac fields and the corresponding annihilation and creation operators transform under improper Lorentz transformations (parity and time reversal operations) and under the charge conjugation operation. We also prove that the present theory respects the CPT theorem.

Integrable coupled massive Thirring model with field values in a Grassmann algebra

A coupled massive Thirring model of two interacting Dirac spinors in 1 + 1 dimensions with fields taking values in a Grassmann algebra is introduced, which is closely related to a SU(1) version of the Grassmannian Thirring model also introduced in this work. The Lax pair for the system is constructed, and its equations of motion are obtained from a zero curvature condition. It is shown that the system possesses several infinite hierarchies of conserved quantities, which strongly confirms its integrability. The model admits a canonical formulation and is invariant under space-time translations, Lorentz boosts and global U(1) gauge transformations, as well as discrete symmetries like parity and time reversal. The conserved quantities associated to the continuous symmetries are derived using Noether’s theorem, and their relation to the lower-order integrals of motion is spelled out. New nonlocal integrable models are constructed through consistent nonlocal reductions between the field components of the general model. The Lagrangian, the Hamiltonian, the Lax pair and several infinite hierarchies of conserved quantities for each of these nonlocal models are obtained substituting its reduction in the expressions of the analogous quantities for the general model. It is shown that, although the Lorentz symmetry of the general model breaks down for its nonlocal reductions, these reductions remain invariant under parity, time reversal, global U(1) gauge transformations and space-time translations.

Implications of a matter-antimatter mass asymmetry in Penning-trap experiments

The Standard Model (SM) of particle physics, being a local, unitary and Lorentz-invariant quantum field theory, remains symmetric under the combined action of Charge, Parity, and Time Reversal (CPT) symmetry. This automatically implies that fundamental properties of particles and antiparticles should be equal in magnitude. These fundamental tenets of the CPT principle have been put to stringent tests in recent Penning-trap experiments, where the matter-antimatter mass asymmetry has been measured. In light of these recent advances, we compare the bounds arising on CPT invariance from kaon systems with those from Penning-trap experiments. Using a simple yet powerful argument of mass decomposition of hadrons, we show that bounds on quark-antiquark mass differences from kaon oscillations are way beyond the reach of Penning-trap experiments. We lay out a roadmap to discuss possible reformulations of our understanding of the SM in the case of a discovery of CPT violation by these precision experiments.

Symmetries in non-relativistic quantum electrodynamics

We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity, and time reversal symmetry. We collect transformation properties related to these symmetries in Fock space representation as well as in the Schrödinger representation. As an application, we generalize and improve theorems about Kramers’ degeneracy in non-relativistic quantum electrodynamics.

Some special exact solutions in nonlocal Alice-Bob sine-Gordon systems ∗ ∗ The work was sponsored by the National Natural Science Foundation of China (Nos. 11435005, 11975131, 12235007) and K. C. Wong Magna Fund in Ningbo University.

Three nonlocal Alice-Bob sine-Gordon (ABSG) systems with the parity and time reversal nonlocality and/or space-time exchange nonlocality are investigated. For the common local SG equation, two types of N-soliton solutions and three types of periodic solutions are presented. The multiple solutions, breather solution, double kink solution, and periodic solutions of the ABSG systems are obtained from the symmetry reductions of a coupled local sine-Gordon system.

A framework for nonrelativistic isotropic models based on generalized uncertainty principles

The existence of a fundamental length scale in nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so-called generalized uncertainty principles (GUP). In this work we provide such a framework in the context of nonrelativistic quantum mechanics. Our approach is based on very few assumptions: there is a fundamental length scale, space isotropy, invariance under parity and time reversal transformations, and symmetricity of the position and momentum operators. We show that simple dimensional analysis allows building a common framework for isotropic models based on GUP (we call those iGUP models). We discuss some popular GUP models in this context after elaborating on relevant theoretical aspects of the framework. At last, we translate current bounds on three often investigated GUP models into bounds on parameters of such common iGUP framework.

Magnetized matter effects on dilaton photon mixing

Dilatons [$\ensuremath{\phi}(x)$] are a class of bosonic scalar particles associated with scaling symmetry and its compensation (under the violations of the same). They are capable of interacting gravitationally with other massive bodies. As they have coupling to two photons ($\ensuremath{\gamma}$), they are (also) capable of decaying to the two photons. However, the decay time is long and that makes them a good candidate for dark matter. Furthermore due to two photon coupling, they can produce optical signatures in a magnetic field. In a vacuum or plain matter they couple to one of the transversely polarized states of the photon. But in magnetized matter, they couple to both the transversely polarized state of photons (due to the emergence of a parity violating part of the photon self-energy contribution from magnetized matter). Being spin zero scalar, they could mix with spin zero longitudinal part of photons but they do not. A part of this work is directed towards understanding this issue of mixing the scalar with various polarization states of photons in a medium (magnetized or unmagnetized) due to the constraints from different discrete symmetries, e.g., charge conjugation ($\mathbf{C}$), parity ($\mathbf{P}$) and time reversal ($\mathbf{T}$) associated with the interaction. Based on these symmetry aided arguments, the structure of the mixing matrix is found to be $3\ifmmode\times\else\texttimes\fi{}3$, as in the case of neutrino flavor mixing matrix. Thus there exists nonzero finite probabilities of oscillation between different polarization states of photon to dilaton. Our analytical and numerical analysis show no existence of periodic oscillation length either in temporal or spatial direction for the most general values of the parameters in the theory. Possible astrophysical consequences of these results can be detected through the discussed observations.

The phenomenology of the exotic hybrid nonet with π1(1600) and η1(1855)

We study the decays of the JPC=1−+ hybrid nonet using a Lagrangian invariant under the flavor symmetry, parity reversal, and charge conjugation. We use the available experimental data, the lattice predictions, and the flavor constraints to evaluate the coupling strengths of the π1(1600) to various two-body mesonic states. Using these coupling constants, we estimate the partial widths of the two-body decays of the hybrid pion, kaon and the isoscalars. We find that the hybrid kaon can be nearly as broad as the π1(1600). Quite remarkably, we find also that the light isoscalar must be significantly narrow while the width of the heavy isoscalar can be matched to the recently observed η1(1855).

Precision antihydrogen annihilation reconstructions using the ALPHA-g detector

The ALPHA (Antihydrogen Laser PHysics Apparatus) collaboration aims to test fundamental symmetries with matter and antimatter by testing CPT (charge conjugation, parity reversal, time reversal) theory and observing whether antimatter follows Einstein’s Weak Equivalence Principle (WEP), where the acceleration due to gravity that a body experiences is independent of its structure or composition. A measurement of the gravitational mass of antimatter has never been done before, as previous experiments used charged particles, which meant the experiments were dominated by electromagnetic forces. The ALPHA-g apparatus will use electrically neutral antihydrogen atoms produced in a vertical Penning-Malmberg trap and hold the antihydrogen in a magnetic well. Once the antihydrogen is released, the position of the resulting annihilations can be reconstructed with a radial time projection chamber (rTPC) surrounding the trapping volume. Tracing the annihilation position within the rTPC is imperative to measuring the gravitational mass of antihydrogen. These proceedings will highlight simulations of antihydrogen annihilations, and how to calibrate the detector for z-positions. This data will be used to measure the gravitational mass of antihydrogen; an important measurement in testing the fundamental symmetry of matter and antimatter. The ALPHA-g apparatus is currently being commissioned at CERN, and the first gravitational measurements of antihydrogen are underway.

Enhanced magnetic quadrupole moments in nuclei with octupole deformation and their CP -violating effects in molecules

Nuclei with an octupole deformation have a non-zero electric octupole moment, electric dipole moment (EDM), Schiff moment and magnetic quadrupole moment (MQM) in the intrinsic frame which rotates with the nucleus. In a state with definite angular momentum in the laboratory frame, these moments are forbidden by parity (P) and time reversal invariance (T) conservation, meaning their expectation values vanish due to nuclear rotation. However, nuclei with an octupole deformation have doublets of close opposite parity rotational states with the same spin, which are mixed by T,P-odd nuclear forces. This mixing produces the orientation of the nuclear axis along nuclear spin and all moments existing in the intrinsic frame appear in the laboratory frame (provided the nuclear spin I is sufficiently large to allow such moment). Such a mechanism produces enhanced T,P-violating nuclear moments. This enhancement also takes place in nuclei with a soft octupole vibration mode. Schiff moments in such nuclei have been calculated in previous works. In the present paper we consider the magnetic quadrupole moment which appears in isotopes with nuclear spin $I \geq 1$. Magnetic interaction between the nuclear MQM and electrons produces an atomic EDM and T,P-violating nuclear spin - molecular axis interaction constants for molecules in electronic states with non-zero electron angular momentum. Measurements of these constants may be used to test CP-violation theories and search for axion dark matter in atomic, molecular and solid state experiments. Potential candidate nuclei include 153Eu, 161Dy, 221Fr, 223Fr, 223Ra, 223Rn, 225Ac, 227Ac, 229Th, 229Pa, 233U and 235U. We subsequently consider molecules containing these nuclei (EuO, EuN+, RaF, AcO, AcN+, AcF+, ThO and ThF+).

Multi-Band Parity-Time-Symmetric Wireless Power Transfer Systems for ISM-Band Bio-Implantable Applications

Modern wireless implantable medical devices face escalating demand for lightweight and low-cost wireless solutions exploited to wake up sensors and transfer data. In this paper, we propose and experimentally demonstrate the efficient, multi-band wireless power transfer (WPT) systems that are symmetric with respect to the combined parity ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> ) and time reversal ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ) transformations (i.e., space-time reflection symmetry). In analogy with non-Hermitian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PT</i> -symmetric physical systems that can have branching real eigenfrequencies as a function of the dimensionless non-Hermiticity and the coupling factor, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PT</i> -symmetric WPT system exhibits multi-band and/or wideband operations via adjustment of the non-Hermiticity (i.e., quality-factor of resonant tanks) and their mutual inductive or capacitive coupling strength. Here, we put forward design and implementation for achieving dual-band, tri-band, and wideband <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PT</i> -symmetric WPT systems, capable of operating in the industrial, scientific, and medical (ISM) bands (27.12 MHz and 40.68 MHz) with high transmission efficiency. This compact and low-cost WPT technique may be exploited in many practical applications, such as wireless charging of bioimplants and wearables, as well as interrogation of battery-free medical devices and internet-of-things (IoT) sensors to assist smart healthcare.

Some Aspects About Pushing the CPT and Lorentz Invariance Frontier With Neutrinos

The CPT symmetry, which combines Charge Conjugation, Parity, and Time Reversal, is a cornerstone of our model-building method, and its probable violation will endanger the most extended tool we presently utilize to explain physics, namely local relativistic quantum fields. However, the kaon system’s conservation constraints appear to be rather severe. We will show in this paper that neutrino oscillation experiments can enhance this limit by many orders of magnitude, making them an excellent instrument for investigating the basis of our understanding of Nature. As a result, verifying CPT invariance does not evaluate a specific model, but rather the entire paradigm. Therefore, as the CPT’s status in the neutrino sector, linked or not to Lorentz invariance violation, will be assessed at an unprecedented level by current and future long baseline experiments, distinguishing it from comparable experimental fingerprints coming from non-standard interactions is critical. Whether the entire paradigm or simply the conventional model of neutrinos is at jeopardy is significantly dependent on this.

Truncation-dependent PT phase transition for the edge states of a two-dimensional non-Hermitian system

We consider a bulk system supporting parity and time reversal ($PT$) symmetry, and investigate how the $PT$ phase transition of edge states is influenced by different truncations of the system. As an example, we study a two-dimensional $PT$-symmetric Su--Schrieffer--Heeger lattice with non-Hermitian onsite potentials. We find that when the truncation preserves certain symmetries of the bulk lattice, the edge states can remain in the $PT$-unbroken phase when the non-Hermitian onsite potentials are less than a nonzero critical value. On the other hand, when the truncation removes such symmetries, edge states with complex eigen-energies are observed for infinitesimal non-Hermitian onsite potentials. We develop an analytic theory to account for such behaviors. Our results are important in the manipulation of the gain and loss behaviors of edge states in non-Hermitian systems, with potential applications in the study of topological lasers, quantum sensors, and unidirectional invisibility.