Hard-Core Bosons on a Two-Dimensional Square Optical Superlattice

In this work,we theoretically study hard-core bosons on a two-dimensional square optical superlattice at T = 0.First of all,we present the mean field phase diagram of this model in terms of the chemical potential μ and the alternating potential strength △.Besides a superfluid(SF) phase at △ = 0 and a charge density wave(CDW)phase in the large △ at half filling,we demonstrate that a supersolid(SS) phase emerges in the moderate △.Then,we focus on the μ = 0,e.g.,half filling case,using large-S semi-classical spin-wave approximation to study the SS to CDW quantum phase transition.In particular,we calculate the ground-state energy and the superfluid density at the level of1/S correction.We then compare the spin-wave results with the large scale quantum Monte Carlo(QMC) simulations using the cluster stochastic series expansion(CSSE) algorithm,and find that while the spin wave method is intuitive with clear physical pictures,the quantum critical point is quite different from that of numerical results which is believed to be accurate.We suggest that as simple as it is,this model still exhibits strong quantum fluctuations near the quantum critical point beyond the power of semiclassical spin-wave approach.

An Original Didactic about Standard Model: “The Particles’ Geometric Model” (Leptons and Bosons)

This work shows a didactic model representative (GPM) of the particles described in the Standard Model (SM). Particles are represented by geometric forms corresponding to geometric structures of coupled quantum oscillators. From the didactic hypotheses of the model emerges an in-depth phenomenology of particles that is fully compatible with that of SM. Thanks to this model, we can calculate “geometrically” the mass of Higgs’s Boson and the mass of the pair “muon and muonic neutrino”, and, by the geometric shapes of leptons and bosons, we can also solve crucial aspects of SM physics as the neutrinos’ oscillations and the intrinsic chirality of the neutrino and antineutrino.

Foundations of the Scale-Symmetric Theory and the Illusory Total Width of the Off-Shell Higgs Bosons

Here we present the foundations of the Scale-Symmetric Theory (SST), i.e. the fundamental phase transitions of the initial inflation field, the atom-like structure of baryons and different types of black holes. Within SST we show that the transition from the nuclear strong interactions in the off-shell Higgs boson production to the nuclear weak interactions causes that the real total width of the Higgs boson from the Higgs line shape (i.e. 3.3 GeV) decreases to 4.3 MeV that is the illusory total width. Moreover, there appear some glueballs/condensates with the energy 3.3 GeV that accompany the production of the off-shell Higgs bosons.

Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.

Energy Spectrum of Ground State and Excitation Spectrum of Quasi-particle for Hard-Core Boson in Optical Lattices

We investigate the energy spectrum of ground state and quasi-particle excitation spectrum of hard-core bosons, which behave very much like spinless noninteracting ferrnions, in optical lattices by means of the perturbation expansion and Bogoliubov approach. The results show that the energy spectrum has a single band structure, and the energy is lower near zero momentum; the excitation spectrum gives corresponding energy gap, and the system is in Mort-insulating state at Tonks limit. The analytic result of energy spectrum is in good agreement with that calculated in terms of Green＇s function at strong correlation limit.

Dynamic of Scalar Bosons in Aharonov-Bohm Magnetic Field

We study the dynamic of scalar bosons in the presence of Aharonov-Bohm magnetic field. First, we give the differential equation that governs this dynamic. Secondly, we use variational techniques to show that the following Schrödinger-Newton equation: , where A is an Aharonov-Bohm magnetic potential, has a unique ground-state solution.

Supersolid Phase in One-Dimensional Hard-Core Boson Hubbard Model with a Superlattice Potential

The ground state of the one-dimensional hard-core boson Hubbard model with a superlattice potential is studied by quantum Monte Carlo methods. We demonstrate that besides the CDW phase and the Mott insulator phase, the supersolid phase emerges due to the presence of the superlattice potential, which reflects the competition with the hopping term. We also study the densities of sublattices and have a clear idea about the distribution of the bosons on the lattice.

The Harmonic Neutron Hypothesis: Prime Number Factor Patterns and Their Relationship to the Hierarchy of the Fundamental Particles and Bosons

The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants including particles and bosons are associated with specific quantum integers, n. These integers define partial harmonic fractional exponents, 1 ± (1/n), of a fundamental frequency, Vf. The goal is to evaluate the prime and composite factors associated with the neutron n0, the quarks, the kinetic energy of neutron beta decay, the Rydberg constant, R, e, a0, H0, h, α, W, Z, the muon, and the neutron gluon. Their pure number characteristics correspond and explain the hierarchy of the particles and bosons. The elements and black body radiation represent consecutive integer series. The relative scale of the constants cluster in a partial harmonic fraction pattern around the neutron. The global numerical organization is related to the only possible prime factor partial fractions of 2/3, or 3/2, as pairs of 3 physical entities with a total of 6 in each group. Many other progressively resonant prime number factor patterns are identified with increasing numbers of smaller factors, higher primes, or larger partial fractions associated with higher order particles or bosons.

A k-Coverage Scheduling Scheme in Wireless Sensor Network Based on Hard-Core Process in Rayleigh Fading Channel

Sensing coverage is a fundamental design issue in wireless sensor networks(WSNs),while sensor scheduling ensures coverage degree to the monitored event and extends the network lifetime.In this paper,we address k-coverage scheduling problem in dense WSNs,we maintain a connected k-coverage energy efficiently through a novel Hard-Core based Coordinated Scheduling(HCCS),in which hardcore is a thinning process in stochastic geometry that inhibits more than one active sensor covering any area redundantly in a minimum distance. As compared with existing coordinated scheduling,HCCS allows coordination between sensors with little communication overhead.Moreover,due to the traditional sensing models in k-coverage analysis is unsuitable to describe the characteristic of transmit channel in dense WSNs,we propose a novel sensing model integrating Rayleigh Fading and Distribution of Active sensors(RFDA),and derive the coverage measure and k-coverage probability for the monitored event under RFDA. In addition,we analyze the influence factors,i.e. the transmit condition and monitoring degree to the k-coverage probability. Finally,through Monte Carlo simulations,it is shown that the k-coverage probability of HCCS outperforms that of its random scheduling counterpart.

Energy Efficiency Optimization for Heterogeneous Cellular Networks Modeled by Matérn Hard-Core Point Process

The Poisson point process(PPP) has been widely used in wireless network modeling and performance analysis due to the independence between its nodes. Therefore, it may not be a suitable model for many of the exclusive networks between the nodes. This paper analyzes the energy efficiency(EE) and optimizes the two-tier heterogeneous cellular networks(Het Nets). Considering the mutual exclusion between macro base stations(MBSs) distribution, the deployment of MBSs is modeled by the Matérn hard-core point process(MHCPP), and the deployment of pico base stations(PBSs) is modeled by the PPP. We adopt a simple approximation method to study the signal to interference ratio(SIR) distribution in two-tier MHCPP-PPP networks and then derive the coverage probabilities, the average data rates and the energy efficiency of Het Nets. Finally, an optimization algorithm is proposed to improve the EE of Het Nets by controlling the transmit power of PBSs. The simulation results show that the EE of a system can be effectively improved by selecting the appropriate transmit power for the PBSs. In addition, two-tier MHCPP-PPP Het Nets have higher energy efficiency than two-tier PPP-PPP Het Nets.

The Accurate Mass Formulas of Leptons, Quarks, Gauge Bosons, the Higgs Boson, and Cosmic Rays

One of the biggest unsolved problems in physics is the particle masses of all elementary particles which cannot be calculated accurately and predicted theoretically. In this paper, the unsolved problem of the particle masses is solved by the accurate mass formulas which calculate accurately and predict theoretically the particle masses of all leptons, quarks, gauge bosons, the Higgs boson, and cosmic rays (the knees-ankles-toe) by using only five known constants: the number (seven) of the extra spatial dimensions in the eleven-dimensional membrane, the mass of electron, the masses of Z and W bosons, and the fine structure constant. The calculated masses are in excellent agreements with the observed masses. For examples, the calculated masses of muon, top quark, pion, neutron, and the Higgs boson are 105.55 MeV, 175.4 GeV, 139.54 MeV, 939.43 MeV, and 126 GeV, respectively, in excellent agreements with the observed 105.65 MeV, 173.3 GeV, 139.57 MeV, 939.27 MeV, and 126 GeV, respectively. The mass formulas also calculate accurately the masses of the new particle at 750 GeV from the LHC and the new light boson at 17 MeV. The theoretical base of the accurate mass formulas is the periodic table of elementary particles. As the periodic table of elements is derived from atomic orbitals, the periodic table of elementary particles is derived from the seven principal mass dimensional orbitals and seven auxiliary mass dimensional orbitals. All elementary particles including leptons, quarks, gauge bosons, the Higgs boson, and cosmic rays can be placed in the periodic table of elementary particles. The periodic table of elementary particles is based on the theory of everything as the computer simulation model of physical reality consisting of the mathematical computation, digital representation and selective retention components. The computer simulation model of physical reality provides the seven principal mass dimensional orbitals and seven auxiliary mass dimensional orbitals for the periodic table of elementary particles.

Density and temperature of fermions and bosons from quantum fluctuations

A novel method to determine the density and temperature of a system constituted by fermions and/or bosons is proposed based on quantum fluctuations.For fermions system,the results in the limit where the reached temperature T is small and where there is no constraint for the reached temperature T compared to the Fermi energy εf at a given density ρ are given,respectively.Quadrupole and multiplicity fluctuation relations are derived in terms of T/εf.We compared the two set results in the limit when T is much smaller compared to Fermi energy εf and they are consistent,as expected.The classical limit is also obtained for high temperatures and low densities.For bosons system,quadrupole and multiplicity fluctuations using Landau's theory of fluctuations near the critical point for a Bose-Einstein condensate(BEC) at a given density ρ are derived.As an example,we apply our approach to heavy ion collisions using the Constrained Molecular Dynamics model(CoMD) which includes the fermionic statistics.The multiplicity fluctuation quenching for fermions is found in the model and confirmed by experimental data.To reproduce the available experimental data better,we propose a modification of the collision term in the approach to include the possibility of α-α collisions.The relevant Bose-Einstein factor in the collision term is properly taken into account.This approach increases the yields of bosons relative to fermions closer to data.Boson fluctuations become larger than one as expected.

A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS

In this article, we consider the dynamics of N two-dimensional boson systems interacting through a pair potential N-1Va（xi -xj） where Va（x） = a^-2V（x/a）. It is well known that the Cross-Pitaevskii （GP） equation is a nonlinear SchrSdinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if ut solves the GP equation, then the family of k-particle density matrices { k ut, k≥1} solves the GP hierarchy. Denote by ψN,t the solution to the N-particle Schrodinger equation. Under the assumption that a = N^-ε for 0 〈 ε 〈 3/4, we prove that as N→∞ the limit points of the k-particle density matrices of CN,t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by f V（x） dx.

Energy spectrum and superfluidity of spin-2 ultracold bosons in optical lattices

This paper studies the superfluidity of ultracold spin-2 Bose atoms with weak interactions in optical lattices by calculating the excitation energy spectrum using the Bogoliubov approach. The energy spectra exhibit the characteristics of the superfluid-phase explicitly and it finds the nonvanishing critical speeds of superfiuid. The obtained results display that the critical speeds of superfiuid are different for five spin components and can be controlled by adjusting the lattice parameters in experiments. Finally it discusses the feasibilities of implementing and measuring superfluid.

Heavy Neutrinos, Z' and Higgs Bosons at the LHC: New Particles from an Old Symmetry

A new era in particle physics is being spurred on by new data from the Large Hadron Collider. Non-vanishing neutrino masses represent firm observational evidence of new physics beyond the Standard Model. An extension of the latter, based on a SU(3)C × SU(2)L × U(1)Y × U(1)B-L symmetry, incorporating an established Baryon minus Lepton number invariance, is proposed as a viable and testable solution to the neutrino mass problem. We argue that LHC data will probe all the new content of this model: heavy neutrinos, an extra gauge boson emerging from spontaneous breaking of the additional gauge group at the TeV scale, onset by a new heavier Higgs boson, also visible at the CERN proton-proton collider. An even more exciting version of this model is the one exploiting Supersymmetry: firstly, it incurporates all its well-known benefits;secondly, it alleviates the flaws of its more minimal realisations. Finally, this model provides a credible cold Dark Matter candidate, the lightest sneutrino, detectable in both underground and collider experiments.

One-Dimensional w-Component Fermions and Bosons with Repulsive Delta Function Interaction

We prove in theorems 2 and 3 that for ID Bosons with repulsive delta function interaction with any number of components and any Young tableau,the energy per particle as N→∞is the same as for spinless Bosons.

Deformed Gauge Invariance with Massive Gauge Vector Bosons

We consider the concept of deformed gauge invariance. The described formalism allows the vector gauge bosons to be massive independently of Higgs mechanism. It also allows the possibility for the variability of gauge coupling constants in space-time.

On the Quantum Statistical Distributions Describing Finite Fermions and Bosons Systems

A century old methodology for deriving statistical distribution using approximate Stirling’s formulation of the factorial becomes questionable. By avoiding the use of exaggerated approximations, a new picture of the energy distribution of fermions and bosons are presented. Energy distribution among fermions (or bosons) in systems with finite degeneracy are found to be degeneracy dependent. The presented point of view explains, successfully, presence of degeneracy pressure in ultra-cooled Fermi gas and predicts the minimum accessible temperature for finite degeneracy fermions system.

<i>H</i>, <i>W</i>, <i>Z</i>Bosons, Dark Matter: Composite Particles?

The present article develops a model initially published in ref. [1]. It is a quasi-classical quantum model of composite particles with ultra-relativistic (UR) constituents (leptons and quarks). The model is used to calculate the mass energy of three composite particles: a UR tauonium, a UR bottomonium and a UR leptoquarkonium. The result is that these three hypothetic particles have masses close to 125 GeV: the Higgs boson mass energy. These results are recalled in the present article. Then the model is extended to calculate the mass energy of pi-mesons, W and Z bosons. Finally, the model provides a hypothesis on dark matter.

Trapped Three Interacting Bosons with a Short-Ranged Interaction

A system of three bosons trapped by a parabolic confinement and interacting with a short-ranged interaction has been investigated by the exact diagonafization of the Hamiltonian matrix. We report a calculation for the energy spectrum of the low-lying states of a system of three interacting bosons. The important feature of the low-lying states of three interacting bosons trapped by a parabolic confinement is obtained via an analysis of the energy spectrum.