Parity Reversal Research Articles

Absence of topological insulator phases in non-HermitianPT-symmetric Hamiltonians

In this work, we consider a generalization of the symmetry classification of topological insulators to non-Hermitian Hamiltonians, which satisfy a combined $PT$ symmetry (parity and time reversal). We show via examples and explicit proofs from separate bulk and gapless boundary-state perspectives that the typical paradigm of forming topological insulator states from Dirac Hamiltonians is not compatible with the construction of non-Hermitian $PT$-symmetric Hamiltonians. The topological insulator states are $PT$-breaking phases and have energy spectra that are complex (not real) and, thus, are not consistent quantum theories.

Holographic fermionic fixed points in d=3

We present a top-down string theory holographic model of strongly interacting relativistic 2+1-dimensional fermions, paying careful attention to the discrete symmetries of parity and time reversal invariance. Our construction is based on probe $D7$-branes in $AdS_5 \times S^5$, stabilized by internal fluxes. We find three solutions, a parity and time reversal invariant conformal field theory which can be viewed as a particular deformation of Coulomb interacting graphene, a parity and time reversal violating but gapless field theory and a system with a parity and time reversal violating charge gap. We show that the Chern-Simons-like electric response function, which is generated perturbatively at one-loop order by parity violating fermions and which is protected by a no-renormalization theorem at orders beyond one loop, indeed appears with the correctly quantized coefficient in the charge gapped theory. In the gapless parity violating solution, the Chern-Simons response function obtains quantum corrections which we compute in the holographic theory.

Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio

Physical laws are believed to be invariant under the combined transformations of charge, parity and time reversal (CPT symmetry). This implies that an antimatter particle has exactly the same mass and absolute value of charge as its particle counterpart. Metastable antiprotonic helium (pHe(+)) is a three-body atom consisting of a normal helium nucleus, an electron in its ground state and an antiproton (p) occupying a Rydberg state with high principal and angular momentum quantum numbers, respectively n and l, such that n ≈ l + 1 ≈ 38. These atoms are amenable to precision laser spectroscopy, the results of which can in principle be used to determine the antiproton-to-electron mass ratio and to constrain the equality between the antiproton and proton charges and masses. Here we report two-photon spectroscopy of antiprotonic helium, in which p(3)He(+) and p(4)He(+) isotopes are irradiated by two counter-propagating laser beams. This excites nonlinear, two-photon transitions of the antiproton of the type (n, l) → (n - 2, l - 2) at deep-ultraviolet wavelengths (λ = 139.8, 193.0 and 197.0 nm), which partly cancel the Doppler broadening of the laser resonance caused by the thermal motion of the atoms. The resulting narrow spectral lines allowed us to measure three transition frequencies with fractional precisions of 2.3-5 parts in 10(9). By comparing the results with three-body quantum electrodynamics calculations, we derived an antiproton-to-electron mass ratio of 1,836.1526736(23), where the parenthetical error represents one standard deviation. This agrees with the proton-to-electron value known to a similar precision.

Metric operators for non-Hermitian quadratic su(2) Hamiltonians

A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different realizations for this type of symmetry are obtained, including the natural occurrence of charge conjugation together with parity and time reversal. Once specified, the underlying anti-linear symmetry of the Hamiltonian, the former, if unbroken, leads to a purely real spectrum and the latter can be mapped to a Hermitian counterpart by, amongst other possibilities, a similarity transformation. Here, Lie-algebraic methods which were used to investigate the generalized Swanson Hamiltonian (Assis and Fring 2009 J. Phys. A: Math. Theor. 42 015203) are employed to identify the class of quadratic Hamiltonians that allow for such a mapping to the Hermitian counterpart. Whereas for the linear su(2) system, every Hamiltonian of this type can be mapped to a Hermitian counterpart by a transformation which is itself an exponential of a linear combination of su(2) generators, the situation is more complicated for quadratic Hamiltonians. Therefore, the possibility of more elaborate similarity transformations, including quadratic exponents, is also explored in detail. The existence of finite-dimensional representations for the su(2) Hamiltonian, as opposed to the su(1, 1) studied before, allows for comparison with explicit diagonalization results for finite matrices. Finally, the similarity transformations constructed are compared with the analogue of Swanson's method for exact diagonalization of the problem, establishing a simple relation between both approaches.

κ-DEFORMED DIRAC EQUATION

We construct a Dirac equation in κ-Minkowski spacetime and analyze its implications. This κ-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, a. We show that the κ-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the hydrogen atom spectrum is modified due to the κ-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter a, which are a few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.

Perfect transmission scattering as a [formula omitted]-symmetric spectral problem

We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian quantum mechanical framework from the physical viewpoint. One of the most interesting features of the analysis is that the complex eigenvalues of the underlying non-Hermitian problem, associated with a reflectionless scattering system, lead to the loss of perfect-transmission energies as the parameters characterizing the scattering potential are varied. On the other hand, the scattering data can serve to describe the spectrum of a large class of Schrödinger operators with complex Robin boundary conditions.

PT-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems

Using a scattering matrix formalism, we derive the general scattering properties of optical structures that are symmetric under a combination of parity and time reversal (PT). We demonstrate the existence of a transition between PT-symmetric scattering eigenstates, which are norm preserving, and symmetry-broken pairs of eigenstates exhibiting net amplification and loss. The system proposed by Longhi [Phys. Rev. A 82, 031801 (2010).], which can act simultaneously as a laser and coherent perfect absorber, occurs at discrete points in the broken-symmetry phase, when a pole and zero of the S matrix coincide.

TESTS OF SYMMETRIES WITH NUCLEI

I review here the status of tests of discrete symmetries in nuclear beta decay, including neutron decay. The focus is given on tests of maximal parity violation, tests of time reversal invariance as well as searches for parity and time reversal invariant exotic interactions. Along with the most sensitive results, I present also some recent achievements of precision beta decay experiments as well as selected ongoing project.

Symmetry principles and conservation laws in atomic and subatomic physics — 2

This article is the second part of our review of the important role that symmetry plays in atomic and subatomic physics. We will concentrate on the discrete symmetries — parity, charge conjugation, and time reversal — that have played a significant part in the development of the ‘standard model’ of particle physics during the latter part of the 20th century. The importance of experimental tests of these symmetries, in both atomic and particle physics, and their sensitivity to new phenomena is also discussed. To conclude, we describe how ‘symmetry breaking’ in the standard model leads to the generation of mass via the Higgs mechanism and how the search for evidence of this symmetry violation is one of the principal goals of the Large Hadron Collider, which began operating at CERN, Switzerland in 2009.

Orientifolds of N = 2 gauged linear sigma models

AbstractWe study B‐type parities in the framework of the linear sigma model. Geometrically, B‐type parities correspond to parity reversal combined with a holomorphic involution. The linear sigma model provides a framework to investigate such orientifolds away from the geometric regime.

On domains of symmetric operators related to −y″(x) + (− 1)nx2ny(x)

In recent years a generalization of Hermiticity has been investigated using a complex deformation H = p2 + x2(ix)ϵ of the harmonic oscillator Hamiltonian, where ϵ is a real parameter. These complex Hamiltonians, possessing symmetry (the product of parity and time reversal), can have a real spectrum. We will consider the most simple case: ϵ even. In this paper we describe all self-adjoint (Hermitian) and at the same time symmetric operators associated with H = p2 + x2(ix)ϵ. Surprisingly, it turns out that there is a large class of self-adjoint operators associated with H = p2 + x2(ix)ϵ which are not symmetric.

Relativistic Coupled Cluster (RCC) Computation of the Electric Dipole Moment Enhancement Factor of Francium Due to the Violation of Time Reversal Symmetry

A relativistic many-body theory for the electric dipole moment (EDM) of paramagnetic atoms arising from the electric dipole moment of the electron is presented and implemented. The relativistic coupled-cluster method with single and double excitations (RCCSD) using the Dirac-Coulomb Hamiltonian and a weak parity and time reversal violating interaction to the first-order of perturbation has been employed to obtain the EDM enhancement factor for the ground state of the Fr atom due to the intrinsic EDM of the electron. The trends of different correlation effects and the leading contributions from different physical states are discussed. Our results in combination with that of the Fr EDM experiment that is currently in progress possess the potential to probe the validity of the standard model (SM) of elementary particle physics.

Transformation properties and symmetry behaviour of ELKO spinors

We review the transformation properties of ELKO spinors (Eigenspinoren des Ladungskonjugationsoperators) under charge conjugation, parity, and time reversal. Our calculations confirm that ELKO spinors are not eigenspinors of the helicity operator and satisfy [Formula: see text] which identifies them as a representation of a nonstandard Wigner class. However, we find that ELKO spinors transform symmetrically under parity instead of the previously assumed asymmetry. Furthermore, we demonstrate that ELKO spinors transform asymmetrically under time reversal, which is opposite to the previously reported symmetric behaviour. These changes affect the (anti)commutation relations that are satisfied by the operators acting on ELKO spinors. We are also able to show that ELKO spinors actually satisfy the same (anti)commutation relations as Dirac spinors, even though they belong to two different representations.

Nuclear and Atomic Electric Dipole Moments

The permanent electric dipole moment (EDM) of a particle or system is a separation of charge along the total angular momentum and arises from interactions that directly violate parity and time reversal symmetry, and assuming CPT symmetry, violate CP. EDMs thus probe CP violating interactions in the background of the much stronger strong, weak and electromagnetic interactions. CP violation is also an essential component of Sakharov's mechanism of baryogenesis, but the Standard Model does not provide for CP violation strong enough to account for the observered baryon asymmetry. Currently, only upper limits have been set on EDMs of the neutron and of atoms and molecules, and the Standard Model contributions are many orders of magnitude smaller than these limits. This means that the experimental frontier probes new physics beyond the Standard Model, but also that experiments in at least three systems will be necessary to clarify the soures of CP violating EDMs. This review will describe the motivations and discuss current and near-term experimental endeavors to discover EDMs in a variety of systems.

Enhanced diamagnetism and Nernst signal from a chiral d-density wave state in the pseudogap regime of the cuprates

In this paper we propose an alternative explanation for the pseudogap regime of the cuprate superconductors. Specifically, a solution to this puzzle can be provided by associating at least a part of the pseudogap regime with a chiral dxy +idx2-y2 density wave. As we demonstrate for the first time, violation of parity and time reversal from this unconventional density wave gives rise to the Topological Meissner effect and the concomitant Anomalous Nernst effect. As a matter of fact, the enhanced diamagnetism and Nerst signal, recently observed in the cuprates, could be simultaneously explained in terms of a chiral d-density wave.

Towards a Geometrical Understanding of the CPT Theorem

The CPT theorem of quantum field theory states that any relativistic (Lorentz-invariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which *spacetime* symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, that the existence of a CPT theorem seems to show that it is not possible for a well-formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable --- capable of admitting a temporal orientation --- this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical (rather than quantum) field theory, using a little-known classical analog of the CPT theorem.

Multiconfiguration Dirac-Hartree-Fock calculations for the hyperfine-structure parameters and the scalar-pseudoscalar interaction constant of 133Cs

In this work we investigate the applicability of the multiconfiguration Dirac-Hartree-Fock (MCDHF) method for calculating parity and time reversal symmetry violations in many-electron atoms. As an example we show results from calculations of the scalar-pseudoscalar interaction constant for 133Cs. Calculated limits of this interaction constant are in a good agreement with other theories.

Search for electric dipole moments in atoms of radioactive nuclei

A suggestion to improve upper limits on the existence of dipole moments in atoms is discussed. Parity and time reversal violating components in the nuclear force may produce P, T-odd moments in nuclei which, in turn, induce such moments in atoms. In order to improve the sensitivity, one must use atoms with a high Z. Atoms with nuclei that have both quadrupole and octupole deformations in the ground state have enhanced Schiff moments when there are forces that violate the time reversal and reflection symmetries. These Schiff moments produce enhanced dipole moments in the atom.

A new formulation of the relativistic many-body theory of electric dipole moments of closed shell atoms

The electric dipole moments of closed-shell atoms are sensitive to the parity and time-reversal violating phenomena in the nucleus. The nuclear Schiff moment is one such property, it arises from the parity and time reversal violating quark-quark interactions and the quark-chromo electric dipole moments. We calculate the electric dipole moment of atomic 199Hg arising from the nuclear Schiff moment using the relativistic coupled-cluster theory. This is the most accurate calculation of the quantity to date. Our calculations in combination with the experiment data provide important insights to the P and T violating coupling constants at the elementary particle level. In addition, a new limit on the tensor-pseudo tensor induced atomic EDM, calculated using the relativistic coupled-cluster theory is also presented.

Index Theorem for the Zero Modes of Majorana Fermion Vortices in Chiralp-Wave Superconductors

We show that the Majorana fermion zero modes in the cores of odd winding number vortices of a 2D (p(x)+ip(y))-paired superconductor is due to an index theorem. This theorem is analogous to that proven by Jackiw and Rebbi for the existence of localized Dirac fermion zero modes on the mass domain walls of a 1D Dirac theory. The important difference is that, in our case, the theorem is proven for a two component fermion field theory where the first and second components are related by parity reversal and Hermitian conjugation.