Number Conservation Law Research Articles

Efficient Local Classical Shadow Tomography with Number Conservation.

Shadow tomography aims to build a classical description of a quantum state from a sequence of simple random measurements. Physical observables are then reconstructed from the resulting classical shadow. Shadow protocols which use single-body random measurements are simple to implement and capture few-body observables efficiently, but do not apply to systems with fundamental number conservation laws, such as ultracold atoms. We address this shortcoming by proposing and analyzing a new local shadow protocol adapted to such systems. The All-Pairs protocol requires one layer of two-body gates and only poly(V) samples to reconstruct arbitrary few body observables. Moreover, by exploiting the permutation symmetry of the protocol, we derive a linear time postprocessing algorithm which applies to both hardcore bosons and spinless fermions in any spatial dimension. We provide a proof-of-principle reference implementation and demonstrate the reconstruction of two- and four-point functions in a paired Luttinger liquid of hardcore bosons.

Darboux Transformation and Soliton Solutions of the Generalized Sasa–Satsuma Equation

The Sasa-Satsuma equation, a higher-order nonlinear Schr\"{o}dinger equation, is an important integrable equation, which displays the propagation of femtosecond pulses in optical fibers. In this paper, we investigate a generalized Sasa-Satsuma(gSS) equation. The Darboux transformation(DT) for the focusing and defocusing gSS equation is constructed. By using the DT, various of soliton solutions for the generalized Sasa-Satsuma equation are derived, including hump-type, breather-type and periodic soliton. Dynamics properties and asymptotic behavior of these soliton solutions are analyzed. Infinite number conservation laws and conserved quantities for the gSS equation are obtained.

Number conservation in odd-particle number random phase approximation and extensions

Abstract The number conservation law in the odd-particle number random-phase approximation (oRPA) and its extension (EoRPA) is studied by applying them to a pairing model and 16O. It is found in the application to 16O that the number conservation law is not fulfilled in oRPA or EoRPA and that it is drastically improved in EoRPA due to the inclusion of ground-state correlation effects. PACS numbers: 21.60.Jz

Double Beta Decay: A Shell Model Approach

Studies of weak interaction in nuclei are important tools for testing different aspects of the fundamental symmetries of the Standard Model. Neutrinoless double beta decay offers an unique venue of investigating the possibility that neutrinos are Majorana fermions and that the lepton number conservation law is violated. Here, I use a shell model approach to calculate the nuclear matrix elements needed to extract the lepton-number-violating parameters of a few nuclei of experimental interest from the latest experimental lower limits of neutrinoless double beta decay half-lives. The analysis presented here could reveal valuable information regarding the dominant neutrinoless double beta decay mechanism if experimental half-life data become available for different isotopes. A complementary shell model analysis of the two-neutrino double beta decay nuclear matrix elements and half-lives is also presented.

Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field.

The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in d-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective nonintegrable model with d≥2 as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for nonequilibrium dynamics of the Ising models with a weak transverse field.

Global Entropy Solutions and Newtonian Limit for the Relativistic Euler Equations

We analyze the relativistic Euler equations of conservation laws of baryon number and momentum with a general pressure law. The existence of global-in-time bounded entropy solutions for the system is established by developing a compensated compactness framework. The proof relies on a careful analysis of the entropy and entropy-flux functions, which are represented by the fundamental solutions of the entropy and entropy-flux equations for the relativistic Euler equations. Based on a careful entropy analysis, we establish the compactness framework for sequences of both exact solutions and approximate solutions of the relativistic Euler equations. Then we construct approximate solutions via the vanishing viscosity method and employ our compactness framework to deduce the global-in-time existence of entropy solutions. The compactness of the solution operator is also established. Finally, we apply our techniques to establish the convergence of the Newtonian limit from the entropy solutions of the relativistic Euler equations to the classical Euler equations.

The Concept of Particle-Antiparticle and the Baryon Asymmetry of the Universe

Following the results of our publications, in the first part of this letter, we explain that quantum theory based on finite mathematics (FQT) is more general (fundamental) than standard quantum theory based on Poincare invariance. Standard concept of particle-antiparticle is not universal because it arises as a result of symmetry breaking from FQT to standard quantum theory based on Poincare or standard anti-de Sitter symmetries. In FQT one irreducible representation of the symmetry algebra describes a particle and its antiparticle simultaneously, and there are no conservation laws of electric charge and baryon quantum number. Poincare and standard anti-de Sitter symmetry are good approximations at the present stage of the universe but in the early stages they cannot take place. Therefore, the statement that in such stages the numbers of baryons and antibaryons were the same, does not have a physical meaning, and the problem of baryon asymmetry of the universe does not arise. Analogously, the numbers of positive and negative electric charges at the present stage of the universe should not be the same, i.e., the total electric charge of the universe should not be zero.

Singularity-free stable black holes, holding the baryon conservation law in the periodic waveguided multiverse

Black holes (BHs) are three-dimensional (3D) singularity-free macroscopic defects in the superfluid-crystal-like four-dimensional (4D) periodic waveguided multiverse (PWM) concept by the author, like edge-dislocations in 3D smectic-A liquid crystals. The PWM-co-emergent intrinsically identical ordinary matter (OM), antimatter (AM), dark matter (DM), dark antimatter (DAM) arise in the nearest 3D-waveguids–3D-universes with the co-emergent special relativity, weak Newtonian gravity, the expanded equivalence principle–the expanded general relativity (PWM-GR) foundation, predicting gravity mass symmetry–matter-antimatter antigravity. The PWM-BHs have identical Schwarzschild radii, outer gravity potentials as the GR-BHs, but flat-singularity-free gravity potentials inside. Microscopic PWM-fermions—singularity-free defects-holes in the weightless superfluid PWM-vacuum-medium–form singularity-free, intrinsically physically identical macroscopic defects: OM-BHs, DM-BHs, AM-BHs, DAM-BHs in the nearest 3D-waveguides. The smallest free PWM-BHs have 4.3 solar masses (excluding microscopic Hawking’s GR-BHs never experimentally detected), they are stable—too heavy for gravitational Schwinger-like virtual electron-positron pairs decoupling—unable emit gravitationally repulsive virtual positrons; they also unable emit repulsive PWM-antiphotons, electrostatically confined in the gravitationally polarized PWM-vacuum, preserving its decay, holding the fundamental baryon number conservation law, prohibiting Hawking’s-GR-BHs evaporation. Only plasma-eating, growing PWM-BHs emit thermal positrons, simultaneously absorbing attractive virtual particles. The dominating PWM-DM-pulsars explain relativistic galactic positrons flows excess over electrons.

Relativistic BGK model for massless particles in the FLRW spacetime

<p style='text-indent:20px;'>In this paper, we address the Cauchy problem for the relativistic BGK model proposed by Anderson and Witting for massless particles in the Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime. We first derive the explicit form of the Jüttner distribution in the FLRW spacetime, together with a set of nonlinear relations that leads to the conservation laws of particle number, momentum, and energy for both Maxwell-Boltzmann particles and Bose-Einstein particles. Then, we find sufficient conditions that guarantee the existence of equilibrium coefficients satisfying the nonlinear relations and we show that the condition is satisfied through all the induction steps once it is verified for the initial step. Using this observation, we construct explicit solutions of the relativistic BGK model of Anderson-Witting type for massless particles in the FLRW spacetime.</p>

Geometric Flow Appearing in Conservation Law in Classical and Quantum Mechanics

The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional curved surface with thickness $\epsilon$ embedded in $\mathbb E^3$. In such a system, two-dimensional conservation law needs an additional term just like an anomaly. The additional term can be obtained by the $\epsilon$ expansion. This term has a Gaussian and a mean curvature dependence and can be written as the total divergence of geometric flow $J^i_{G}$. This fact holds in both classical and quantum mechanics.

Equilibration in fermionic systems

The time evolution of a finite fermion system towards local statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The solutions of this fermionic diffusion equation are rederived in closed form, evaluated exactly for simplified initial conditions, and applied to hadron systems at low energies in the MeV-range, as well as to quark systems at relativistic energies in the TeV-range where antiparticle production is abundant. Conservation laws for particle number including created antiparticles, and for the energy are discussed.

Numerical scheme for treatment of Uehling–Uhlenbeck equation for two-particle interactions in relativistic plasma

We present a new efficient method to compute Uehling–Uhlenbeck collision integral for all two-particle interactions in relativistic plasma with drastic improvement in computation time with respect to existing methods. Plasma is assumed isotropic in momentum space. The set of reactions consists of: Moeller and Bhabha scattering, Compton scattering, two-photon pair annihilation, and two-photon pair production, which are described by QED matrix elements. In our method exact energy and particle number conservation laws are fulfilled. Reaction rates are compared, where possible, with the corresponding analytical expressions and convergence of numerical rates is demonstrated.

Phenomenology of cosmological particle creation, Dirac sea and all that

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the “usual” hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by “the particle creation law”, proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel’dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the “empty vacuum”, there may exist the “dynamical vacuum”, which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms. All the vacuum solutions violate the local conformal invariance.

Chiral Anomaly as the Origin of the Planar Hall Effect in Weyl Semimetals.

In condensed matter physics, the term "chiral anomaly" implies the violation of the separate number conservation laws of Weyl fermions of different chiralities in the presence of parallel electric and magnetic fields. One effect of the chiral anomaly in the recently discovered Dirac and Weyl semimetals is a positive longitudinal magnetoconductance. Here we show that chiral anomaly and nontrivial Berry curvature effects engender another striking effect in Weyl semimetals, the planar Hall effect (PHE). Remarkably, the PHE manifests itself when the applied current, magnetic field, and the induced transverse "Hall" voltage all lie in the same plane, precisely in a configuration in which the conventional Hall effect vanishes. In this work we treat the PHE quasiclassically, and predict specific experimental signatures for type-I and type-II Weyl semimetals that can be directly checked in experiments.

Chiral anomaly and longitudinal magnetotransport in type-II Weyl semimetals

In the presence of parallel electric and magnetic fields, the violation of separate number conservation laws for the three dimensional left and right handed Weyl fermions is known as the chiral anomaly. The recent discovery of Weyl and Dirac semimetals has paved the way for experimentally testing the effects of chiral anomaly via longitudinal magneto-transport measurements. More recently, a type-II Weyl semimetal (WSM) phase has been proposed, where the nodal points possess a finite density of states due to the touching between electron- and hole- pockets. It has been suggested that the main difference between the two types of WSMs (type-I and type-II) is that in the latter, chiral anomaly and the associated longitudinal magneto-resistance are strongly anisotropic, vanishing when the applied magnetic field is perpendicular to the direction of tilt of Weyl fermion cones in a type-II WSM. We analyze chiral anomaly in a type-II WSM in quasiclassical Boltzmann framework, and find that the chiral anomaly induced positive longitudinal magneto-conductivity is present along any arbitrary direction.

Toward Understanding the Conformal Gravity

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the usual hydrodynamic description of the particle motion written in the Eulerian coordinates, we substituted the particle number conservation law (which enters the formalism) by the particle creation law, proportional to the square of the Weyl tensor, following the famous result by Ya. B. Zel’dovich and A. A. Starobinsky. Then, demanding the conformal invariance of the whole dynamical system, we have got both the Weyl-conformal gravity and the Einstein–Hilbert dilaton gravity action integral. Thus, we obtained something like the induced gravity suggested first by A. D. Sakharov. It is shown that the resulting system is self-consistent.

Influence of quantum statistical weight on efficiency of electric field ionization of atom

The quantum statistical weight (G) of an atomic energy level is an important spectroscopic parameter, its effect on the atomic ionization process is, however, usually neglected for simplicity. In this work, the influences of the G parameters of the lithium atomic energy levels are taken into account explicitly for the first time in the study on the process of three-step photo-excitation (PE) + electric field ionization (EFI), which yields a significant effect on overall EFI efficiency of the PE+EFI process. With a set of specially designed PE+EFI schemes, the expected results are obtained. First, with a three-step PE scheme, the Li atom is excited by three pulsed lasers with different wavelengths, which are fired simultaneously, to one of the Rydberg states from its ground state, from which the Li atom is ionized by an electric-field pulse with a time delay in order to avoid the Stark effect. Based on the three physical processes the atom experiences the PE, none field, and the EFI processes, and a set of universal rate equations are established according to the conservation law of particle number with the knowledge of physical mechanism of the three different processes and the physical model set up for them, respectively. The G parameters of the four relevant bound energy states are displayed explicitly in the rate equations for the PE process to offer a clear viewabout their effect on the overall EFI efficiency of the PE+EFI process. Secondly, the overall efficiencies of PE+EFI process are calculated with the Matlab programming for the two specified excitation schemes, 2S1/22P1/23S1/225P1/2, 3/2 and 2S1/22P3/23D5/225F5/2, 7/2. The overall EFI efficiency of PE+EFI process is investigated not only by adjusting the laser parameters but also by comparing the results between the two different excitation schemes. In order to establish the relationship between the overall EFI efficiency and external field quantitatively, the dependence of population rate of the relevant bound states on various factors, such as laser and atomic parameters, is calculated systematically. The role of the G parameters of the relevant atomic energy levels played in the population rates is observed to determine which excitation scheme is better in terms of the population rate of the Rydberg state. Meanwhile, the spontaneous emission of the Rydberg state during the time delay between the pulses of electric field and laser is also evaluated to make a balance between avoiding the Stark effect and minimizing the spontaneous emission. Based on the analysis of the calculations, some new results are achieved. An enhancement of the overall EFI efficiency can be obtained by making a sophisticated design on the excitation scheme of the PE+EFI process to optimize the G parameters. The time delay between the pulses of electric field and laser not only lets the atom experience a field-free time period, but also makes an upper limit for the population rate of Rydberg state due to the redistribution of atom among the four relevant bound states in the period. The upper limit is found to be dependent on neither laser parameters nor the absolute values of the G parameters, while only on the branching ratio of the G parameters among those bound states. The overall EFI efficiency is dominated by the population rate of Rydberg state, as the EFI process may ionize all Rydberg atoms once the strength of the EFI field reaches the EFI threshold of the Rydberg state. Hence, the key factor for raising the overall EFI efficiency is to enhance the population rate of Rydberg state in the PE process, which is a hard challenge due to the upper limit for the population rate of Rydberg state.

Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the “usual” hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by “the particle creation law”, proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel'dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the “empty vacuum”, there may exist the “dynamical vacuum”, which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms.

Dual number coefficient octonion algebra, field equations and conservation laws

Starting with octonion algebra, we develop the dual number coefficient octonion (DNCO) algebra having sixteen components. DNCO forms of generalized potential, field and current equations are discussed in consistent manner. We have made an attempt to write the DNCO form of generalized Dirac–Maxwell’s equations in presence of electric and magnetic charges (dyons). Accordingly, we demonstrate the work-energy theorem of classical mechanics reproducing the continuity equation for dyons in terms of DNCO algebra. Further, we discuss the DNCO form of linear momentum conservation law for dyons.

Interplanar coupling-dependent magnetoresistivity in high-purity layered metals.

The magnetic field-induced changes in the conductivity of metals are the subject of intense interest, both for revealing new phenomena and as a valuable tool for determining their Fermi surface. Here we report a hitherto unobserved magnetoresistive effect in ultra-clean layered metals, namely a negative longitudinal magnetoresistance that is capable of overcoming their very pronounced orbital one. This effect is correlated with the interlayer coupling disappearing for fields applied along the so-called Yamaji angles where the interlayer coupling vanishes. Therefore, it is intrinsically associated with the Fermi points in the field-induced quasi-one-dimensional electronic dispersion, implying that it results from the axial anomaly among these Fermi points. In its original formulation, the anomaly is predicted to violate separate number conservation laws for left- and right-handed chiral (for example, Weyl) fermions. Its observation in PdCoO2, PtCoO2 and Sr2RuO4 suggests that the anomaly affects the transport of clean conductors, in particular near the quantum limit.