Number Non-conservation Research Articles

Optical fibers with a frequency-dependent Kerr nonlinearity: Theory and applications

This review provides a detailed discussion of both the mathematical treatment and the impact of a frequency-dependent Kerr nonlinearity on the propagation of short pulses in optical fibers. We revisit the theoretical framework required to deal with the frequency dependence of the nonlinear response without incurring any physical inconsistencies, such as the non-conservation of the photon number. Then, we point out the role of the zero-nonlinearity wavelength, its interplay with the zero-dispersion wavelength, and their influence on evolution of optical pulses in optical fibers, specifically by looking at soliton propagation and the ensuing generation of Cherenkov radiation. Finally, by means of a space–time analogy involving the collision of a weak control pulse and an intense soliton, we describe an all-optical switching scheme in the presence of a zero-nonlinearity wavelength within a photon-conserving framework.

Rare weak decays and neutrino mass

The question whether neutrinos are Majorana fermions (i.e., their own anti-particles) remains among the most fundamental open questions of subatomic physics. If neutrinos are Majorana particles it would revolutionize our understanding of physics. Although neutrinoless double beta decay, 0νββ, was proposed more than 80 years ago to establish the nature of neutrinos, it remains the most sensitive probe into the non-conservation of lepton number. 0νββ-decay is a postulated extremely slow and yet unobserved radioactive process in which two neutrons (or protons) inside a nucleus transform into two protons (or neutrons) emitting two electrons (or positrons), respectively, but no neutrinos. Its observation would be a breakthrough in the description of elementary particles and would provide fundamental information on the neutrino masses, their nature, and origin. In this paper double beta decay, its connection to neutrino mass, and mechanisms beyond the standard mass mechanism are discussed from a theoretical point of view. The current situation is then addressed by combining theoretical results with recent experimental limits.

Spontaneous flow created by active topological defects.

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.

Baryon number nonconservation as Peccei-Quinn mechanism

Baryon number is an accidental symmetry in the standard model, while Peccei-Quinn symmetry is hypothetical symmetry which is introduced to solve the strong CP problem. We study the possible connections between Peccei-Quinn symmetry and baryon number symmetry. In this framework, an axion is identified as the Nambu-Goldstone boson of baryon number violation. As a result, characteristic baryon number violating processes are predicted. We developed the general method to determine the baryon number and lepton number of new scalar in the axion model.

Theory of supercurrent in superconductors

According to the standard theory of superconductivity, the origin of superconductivity is electron pairing. The induced current by a magnetic field is calculated by the linear response to the vector potential, and the supercurrent is identified as the dissipationless flow of the paired electrons, while single electrons flow with dissipation. This supercurrent description suffers from the following serious problems: (1) it contradicts the reversible superconducting-normal phase transition in a magnetic field observed in type I superconductors; (2) the gauge invariance of the supercurrent induced by a magnetic field requires the breakdown of the global [Formula: see text] gauge invariance, or the nonconservation of the particle number; and (3) the explanation of the ac Josephson effect is based on the boundary condition that is different from the real experimental one. We will show that above problems are resolved if the supercurrent is attributed to the collective mode arising from the Berry connection for many-body wavefunctions. Problem (1) is resolved by attributing the appearance and disappearance of the supercurrent to the abrupt appearance and disappearance of topologically protected loop currents produced by the Berry connection; problem (2) is resolved by assigning the non-conserved number to that for the particle number participating in the collective mode produced by the Berry connection; and problem (3) is resolved by identifying the relevant phase in the Josephson effect is that arising from the Berry connection, and using the modified Bogoliubov transformation that conserves the particle number. We argue that the required Berry connection arises from spin-twisting itinerant motion of electrons. For this motion to happen, the Rashba spin–orbit interaction has to be added to the Hamiltonian for superconducting systems. The collective mode from the Berry connections is stabilized by the pairing interaction that changes the number of particles participating in it; thus, the superconducting transition temperatures for some superconductors is given by the pairing energy gap formation temperature as explained in the BCS theory. The topologically protected loop currents in this case are generated as cyclotron motion of electrons that is quantized by the Berry connection even without an external magnetic field. We also explain a way to obtain the Berry connection from spin-twisting itinerant motion of electrons for a two-dimensional model where the on-site Coulomb repulsion is large and doped holes form small polarons. In this model, the electron pairing is not required for the stabilization of the collective mode, and the supercurrent is given as topologically protected spin-vortex-induced loop currents (SVILCs).

Quantization of the nonstandard propagating gravitational waves in the cosmological background

Detections of gravitational wave (GW) stimulate the discussion of how GWs propagate in the expanding Universe. General relativity predicts that GWs are massless and propagate at the speed of light with no extra friction term, which relates to the attenuation of GWs, while some modified gravities may predict a different behavior. The mass and speed terms can be tightly constrained by the GW150914-like and GW170817/GRB 170817A events, respectively. However, the friction term remaining unconstrained. In this paper, we quantize the nonstandard propagating gravitational waves with nonzero friction term in the cosmological background, and study the influence of the friction term on the GW luminosity distance in quantum level, and the initial conditions of perturbations given by inflation. We find the quantum nature of the difference between GW and electromagnetic luminosity distance is graviton particle number non-conservation. For the initial conditions, we obtain an analytical expression of the power spectrum with nonzero friction term for the de Sitter background. In observations, both the GW luminosity distance and primordial GWs can be used to constrain the friction term.

The Cosmic Distance Duality Relation with Strong Lensing and Gravitational Waves: An Opacity-free Test

Abstract The cosmic distance duality relation (CDDR) is a fundamental rule in cosmological studies. Given the redshift z, it relates luminosity distance D L with angular diameter distance D A through . Many efforts have been made to test CDDR with various observational approaches. However, to the best of our knowledge, those methods are always affected by cosmic opacity, which could violate CDDR owing to the non-conservation of photon number. Such a mechanism is more related to astroparticle physics. In this work, in order to directly study the nature of spacetime, i.e., to disentangle it from astroparticle physics, we propose a new strategy to test CDDR, with strong lensing providing D A and gravitational waves (GWs) providing D L . It is known that the propagation of GWs is unaffected by cosmic opacity. We demonstrate that distances from observations of optical lensing are also opacity-free. These two kinds of distance measurements make it possible to test spacetime. Our results show that the constraints on the deviations of CDDR will be very competitive with current techniques.

Chiral charge dynamics in Abelian gauge theories at finite temperature

We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential μ for the fermionic charge, and monitor its evolution with real-time classical lattice simula- tions. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemi- cal potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral charge dynamics in the presence of an external magnetic field B, and extract its decay rate {varGamma}_5equiv frac{d log mu }{dt} . We provide in this way a new determination of the gauge coupling and magnetic field de- pendence of the chiral rate, which exhibits a best fit scaling as {varGamma}_5{propto}^{raisebox{1ex}{11}!left/ !raisebox{-1ex}{2}right.}{B}^2 . We confirm numerically the fluctuation-dissipation relation between Γ5 and Γdiff , the Chern-Simons diffusion rate, which was obtained in a previous study. Remarkably, even though we are outside the MHD range of validity, the dynamics observed are in qualitative agreement with MHD predictions. The magnitude of the chiral/diffusion rate is however a factor ∼ 10 times larger than expected in MHD, signaling that we are in reality exploring a dif- ferent regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite tempera- ture Abelian gauge theories, though no definite conclusion can be made at this point until hard-thermal-loops are included in the lattice simulations.

Elimination of spurious modes within quasiparticle random-phase approximation

We suggest a generalized method for elimination of spurious admixtures (SA) from intrinsic nuclear excitations described within the Quasiparticle-Random-Phase-Approximation (QRPA). Various kinds of SA-corrections are treated at the same theoretical ground. The known corrections are well reproduced. As relevant cases, we consider subtraction of SA related with i) violation of the translational invariance (isovector E1 and isoscalar toroidal and compression E1 modes), ii) pairing-induced non-conservation of the particle number (E2(K=0) and E0 modes), and iii) rotational invariance (E2(K=1) and M1(K=1) modes). The SA subtraction can be done at the level of QRPA states, electromagnetic responses, and even transition operators. The additional deformation-induced corrections are proposed. The accuracy of the method is demonstrated by Skyrme QRPA calculations for axially-deformed $^{154}$Sm.

Lepton Number Violation: Seesaw Models and Their Collider Tests

The Majorana nature of neutrinos is strongly motivated from the theoretical and phenomenological point of view. A plethora of neutrino mass models, known collectively as Seesaw models, exist that could generate both a viable neutrino mass spectrum and mixing pattern. They can also lead to rich, new phenomenology, including lepton number non-conservation as well as new particles, that may be observable at collider experiments. It is therefore vital to search for such new phenomena and the mass scale associated with neutrino mass generation at high energy colliders. In this review, we consider a number of representative Seesaw scenarios as phenomenological benchmarks, including the characteristic Type I, II, and III Seesaw mechanisms, their extensions and hybridizations, as well as radiative constructions. We present new and updated predictions for analyses featuring lepton number violation and expected coverage in the theory parameter space at current and future colliders. We emphasize new production and decay channels, their phenomenological relevance and treatment across different facilities in $e^+e^-$, $e^-p$ and $pp$ collisions, as well as the available Monte Carlo tools available for studying Seesaw partners in collider environments.

Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature

We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, using both analytical estimates and real-time classical lattice numerical simulations. We investigate the random walk of the Chern-Simons number Qpropto {{displaystyle int d}}^4x{F}_{mu nu }{tilde{F}}^{mu nu } , and show that it has a diffusive behaviour in the presence of an external magnetic field B. This indicates that the mechanism for fermionic number non-conservation for B ≠ 0, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We have determined numerically, with lattice simulations, the rate Γ of chirality non-conservation, extracting it from the diffusion process. We find that it is a factor ∼ 60 larger compared to previous theoretical estimates, what calls for a revision of the implications of Abelian fermion number and chirality non-conservation for baryogenesis, magnetogenesis and chiral symmetry evolution.

Beta-spectrum shapes of forbidden β decays

The neutrinoless [Formula: see text] decay of atomic nuclei continues to attract fervent interest due to its potential to confirm the possible Majorana nature of the neutrino, and thus the nonconservation of the lepton number. At the same time, the direct dark matter experiments are looking for weakly interacting massive particles (WIMPs) through their scattering on nuclei. The neutrino-oscillation experiments on reactor antineutrinos base their analyses on speculations of [Formula: see text]-spectrum shapes of nuclear decays, thus leading to the notorious “reactor antineutrino anomaly.” In all these experimental efforts, one encounters the problem of [Formula: see text]-spectrum shapes of forbidden [Formula: see text] decays, either as unwanted backgrounds or unknown components in the analyses of data. In this work, the problem of spectrum shapes is discussed and illustrated with a set of selected examples. The relation of the [Formula: see text]-spectrum shapes to the problem of the effective value of the weak axial-vector coupling strength [Formula: see text] and the enhancement of the axial-charge matrix element is also pointed out.

Lattice implementation of Abelian gauge theories with Chern–Simons number and an axion field

Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark–gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U(1) gauge sector, a(x)FμνF˜μν, reproducing the continuum limit to order O(dxμ2) and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the topological number densityK=FμνF˜μν that admits a lattice total derivative representation K=Δμ+Kμ, reproducing to order O(dxμ2) the continuum expression K=∂μKμ∝E→⋅B→. If we consider a homogeneous field a(x)=a(t), the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern–Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a(x)=a(x→,t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O(dxμ2) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.

Configuration-constrained cranking Hartree-Fock pairing calculations for sidebands of nuclei

Background: Nuclear collective rotations have been successfully described by the cranking Hartree-Fock-Bogoliubov (HFB) model. However, for rotational sidebands which are built on intrinsic excited configurations, it may not be easy to find converged cranking HFB solutions. The nonconservation of the particle number in the BCS pairing is another shortcoming. To improve the pairing treatment, a particle-number-conserving (PNC) pairing method was suggested. But the existing PNC calculations were performed within a phenomenological one-body potential (e.g., Nilsson or Woods-Saxon) in which one has to deal the double-counting problem.Purpose: The present work aims at an improved description of nuclear rotations, particularly for the rotations of excited configurations, i.e., sidebands.Methods: We developed a configuration-constrained cranking Skyrme Hartree-Fock (SHF) calculation with the pairing correlation treated by the PNC method. The PNC pairing takes the philosophy of the shell model which diagonalizes the Hamiltonian in a truncated model space. The cranked deformed SHF basis provides a small but efficient model space for the PNC diagonalization.Results: We have applied the present method to the calculations of collective rotations of hafnium isotopes for both ground-state bands and sidebands, reproducing well experimental observations. The first up-bendings observed in the yrast bands of the hafnium isotopes are reproduced, and the second up-bendings are predicted. Calculations for rotational bands built on broken-pair excited configurations agree well with experimental data. The band-mixing between two ${K}^{\ensuremath{\pi}}={6}^{+}$ bands observed in $^{176}\mathrm{Hf}$ and the $K$ purity of the $^{178}\mathrm{Hf}$ rotational state built on the famous 31 yr ${K}^{\ensuremath{\pi}}={16}^{+}$ isomer are discussed.Conclusions: The developed configuration-constrained cranking calculation has been proved to be a powerful tool to describe both the yrast bands and sidebands of deformed nuclei. The analyses of rotational moments of inertia help to understand the structures of nuclei, including rotational alignments, configurations, and competitions between collective and single-particle excitations.

Can spin-charge-family theory explain baryon number nonconservation?

The spin-charge-family theory, in which spinors carry besides the Dirac spin also the second kind of the Clifford object, no charges, is a kind of the Kaluza-Klein theories. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest in $d=(3+1)$ at low energies all the properties of quarks and leptons assumed by the standard model. The second kind of spins explains the origin of families. Spinors interact with the vielbeins and the two kinds of the spin connection fields, the gauge fields of the two kinds of the Clifford objects, which manifest in $d=(3+1)$ besides the gravity and the known gauge vector fields also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hyper charge ($\mp \frac{1}{2}, \pm \frac{1}{2}$, respectively), explaining the origin of the Higgs and the Yukawa couplings. It is demonstrated in this paper that the scalar fields with the space index $t\in (9,10,\dots,14)$ carry the triplet colour charges, causing transitions of antileptons and antiquarks into quarks and back, enabling the appearance and the decay of baryons. These scalar fields are offering in the presence of the right handed neutrino condensate, which breaks the ${\cal C}{\cal P}$ symmetry, the answer to the question about the matter-antimatter asymmetry.

Particle simulation of lower hybrid wave propagation in fusion plasmas

Global particle simulations of the lower hybrid (LH) waves have been carried out using fully kinetic ions and drift kinetic electrons with a realistic electron-to-ion mass ratio. The LH wave frequency, mode structure, and electron Landau damping from the electrostatic simulations agree very well with the analytic theory. Linear simulation of the propagation of a LH wave-packet in the toroidal geometry shows that the wave propagates faster in the high field side than the low field side, in agreement with a ray tracing calculation. This poloidal asymmetry arises from the non-conservation of the poloidal mode number due to the non-uniform magnetic field. In contrast, the poloidal mode number is conserved in the cylindrical geometry with the uniform magnetic field.

Cosmological effects of scalar-photon couplings: dark energy and varying-α Models

We study cosmological models involving scalar fields coupled to radiation and discuss their effecton the redshift evolution of the cosmic microwave background temperature, focusing on links withvarying fundamental constants and dynamical dark energy. We quantify how allowing for the couplingof scalar fields to photons, and its important effect on luminosity distances, weakens current and futureconstraints on cosmological parameters. In particular, for evolving dark energy models, joint constraintson the dark energy equation of state combining BAO radial distance and SN luminosity distancedeterminations, will be strongly dominated by BAO. Thus, to fully exploit future SN data one must alsoindependently constrain photon number non-conservation arising from the possible coupling of SNphotons to the dark energy scalar field. We discuss how observational determinations of the backgroundtemperature at different redshifts can, in combination with distance measures data, set tight constraints oninteractions between scalar fields and photons, thus breaking this degeneracy. We also discuss prospectsfor future improvements, particularly in the context of Euclid and the E-ELT and show that Euclid can, evenon its own, provide useful dark energy constraints while allowing for photon number non-conservation.

Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators

We consider a generalization of a recently proposed non-Hermitian model for resonant cavities coupled by a chiral mirror by taking into account number non-conservation and nonlinear interactions. We analyze non-Hermitian quantum dynamics of populations and entanglement of the cavity modes. We find that the interplay between initial coherence and non-Hermitian coupling leads to a counterintuitive population transfer. While an initially coherent cavity mode is depleted, the other empty cavity can be populated more than or less than the initially filled one. Moreover, the presence of nonlinearity yields population collapse and revival as well as bipartite entanglement of the cavity modes. In addition to coupled cavities, we point out that similar models can be found in -symmetric Bose-Hubbard dimers of Bose-Einstein condensates or in coupled soliton-plasmon waveguides. We specifically illustrate the quantum dynamics of populations and entanglement in a heuristic model that we propose for a soliton-plasmon system with soliton amplitude-dependent asymmetric interaction. Degree of asymmetry, nonlinearity and coherence are examined to control plasmon excitations and soliton-plasmon entanglement. Relations to -symmetric lasers and Jahn-Teller systems are pointed out.

Double Beta Decay Experiments: Beginning of a New Era

Interest in neutrinoless double beta decay (0νββ) has seen a significant renewal in the recent 10 years after evidence for neutrino oscillations was obtained from the results of atmospheric, solar, reactor, and accelerator neutrino experiments. These results are impressive proof that neutrinos have a nonzero mass. The detection and study of 0νββ decay may clarify the following problems of neutrino physics: (i) lepton number non-conservation, (ii) neutrino nature: whether the neutrino is a Dirac or a Majorana particle, (iii) absolute neutrino mass scale, (iv) the type of neutrino mass hierarchy (normal, inverted, or quasidegenerate), and (v) CP violation in the lepton sector (measurement of the Majorana CP-violating phases).

FERMION–ANTIFERMION MIXING IN GRAVITATIONAL FIELDS

Mixing of fermion and antifermion states occurs in gravitational interactions, leading to non-conservation of fermion number above temperatures determined by the particle masses. We study the evolution of a [Formula: see text]-system and calculate the cross-sections for the reactions [Formula: see text]. Their values are identical in both directions. However, if [Formula: see text] changes quickly into a lighter antiparticle, then the reaction symmetry is broken, resulting in an increased production of matter over antimatter.