Ground State Energy of the One-Component Charged Bose Gas

The model considered here is the “jellium” model in which there is a uniform, fixed background with charge density −eρ in a large volume V and in which N=ρV particles of electric charge +e and mass m move – the whole system being neutral. In 1961 Foldy used Bogolubov's 1947 method to investigate the ground state energy of this system for bosonic particles in the large ρ limit. He found that the energy per particle is −0.402 in this limit, where . Here we prove that this formula is correct, thereby validating, for the first time, at least one aspect of Bogolubov's pairing theory of the Bose gas. Received: 23 August 2000 / Accepted: 5 October 2000     

A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

Geometric entanglement in valance-bond-solid state

Multipartite entanglement, measured by the geometric entanglement (GE), is discussed for integer spin Valance-Bond-Solid (VBS) state respectively with periodic boundary condition (PBC) and open boundary condition (OBC) in this paper. The optimization in the definition of geometric entanglement can be reduced greatly by exploring the symmetry of VBS state, and then the fully separable state can be determined explicitly. Numerical evaluation for GE by the random simulation is also implemented in order to demonstrate the validity of the reductions. Our calculations show that GE is saturated by a finite value with the increment of particle number, that means that the total entanglement for VBS state would be divergent under the thermodynamic limit. Moreover it is found that the scaling behavior of GE with spin number s is fitted as α log(s + β/s + γ)+δ, in which the values of the parameters α, β, γ, σ are only dependent on the parity of spin s. A comparison with entanglement entropy of VBS state is also made, in order to demonstrate the essential differences between multipartite and bipartite entanglement in this model.     

Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an L ¹ function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to α by the formula α_phys ≃ α(1 + 2α/(3π) log Λ)⁻¹, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is  ≤  2Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Séré and Solovej on the mean-field approximation of no-photon QED.     

Isotopic dependence of the nuclear charge radii and binding energies in the relativistic Hartree-Fock formalism

Relativistic nonlinear models based on the Hartree and Hartree-Fock approximations, including the σ, ω, π, and ρ mesons, are worked out to explore the behavior of the nuclear charge radii and the binding energies of several isotopic chains. We find a correlation between the magnitude of the anomalous kink effect (KE) in the Pb isotopic family and the compressibility modulus (K) of nuclear matter. The KE appears to be sensitive, in particular, to the mechanisms which control the K value. The influence of the symmetry energy on the Ca isotopic chain is also studied. The behavior of the charge radii of single-particle states for some special cases and its repercussion on the nuclear charge radius is analyzed. The effect of pairing correlations on the models improves considerably the quality of the results in both binding energy and KE.     

Equation of state for the Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This method is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise to the equation of state in the form p =-Λ + w ₁ρ(a) + w ₂ a ^β + 0 and energy density ρ = Λ+ρ₀₁ a ^-3(1+w) +ρ₀₂ a ^α +ρ₀₃ a ^-3, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data.We showed that the model with scaling fluid fits well to supernovae data. We found that Ω_m,0 ≃ 0.4 and n ≃ -1 (β = -3n), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that Ω_m,0 = 0.3 then the favoured model is close to concordance ΛCDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in the ΛCDM model, while intermediate distant SNIa should be fainter than in the ΛCDM model. We also investigate whether the model with scaling fluid is actually preferred by data over ΛCDM model. As a result we find from the Akaike model selection criterion: it prefers the model with noninteracting scaling fluid.     

Experimental investigation of the angular dependence of photon-induced differential cross-sections of L X-rays from U,Th and Bi at 59.5 keV

Summary The differential cross-sections for the emission of L_ρ, L_α, L_β and L_γ groups of L X-ray lines from U, Th and Bi have been measured at different angles varying from 45° to 135° at intervals of 15°. The vacancies were created by 59.5 keV γ-rays from²⁴¹Am source and L X-rays were measured using a Si(Li) detector. It is found that the L_γ and L_β groups of L X-rays are isotropic, the L_ρ and L_α groups are anisotropic in the spatial distribution. The authors of this paper have agreed to not receive the proofs for correction.     

A Two-Dimensional One Component Plasma and a Test Charge: Polarization Effects and Effective Potential

We study the effective interactions between a test charge Q and a one-component plasma, i.e. a complex made up of mobile point particles with charge q, and a uniform oppositely charged background. The background has the form of a flat disk, in which the mobile charges can move. The test particle is approached perpendicularly to the disk, along its axis of symmetry. All particles interact by a logarithmic potential. The long and short distance features of the effective potential—the free energy of the system for a given distance between Q and the disk—are worked out analytically in detail. They crucially depend on the sign of Q/q, and on the global charge borne by the discotic complex, that can vanish. While most results are obtained at the intermediate coupling Γ≡βq ²=2 (β being the inverse temperature), we have also investigated situations with stronger couplings: Γ=4 and 6. We have found that at large distances, the sign of the effective force reflects subtle details of the charge distribution on the disk, whereas at short distances, polarization effects invariably lead to effective attractions.     

Exact Results for Thermodynamics of the Hydrogen Plasma: Low-Temperature Expansions Beyond Saha Theory

We study hydrogen in the Saha regime, within the physical picture in terms of a quantum proton-electron plasma. Long ago, Saha showed that, at sufficiently low densities and low temperatures, the system behaves almost as an ideal mixture made with hydrogen atoms in their groundstate, ionized protons and ionized electrons. More recently, that result has been rigorously proved in some scaling limit where both temperature and density vanish. In that Saha regime, we derive exact low-temperature expansions for the pressure and internal energy, where density ρ is rescaled in units of a temperature-dependent density ρ ^* which controls the cross-over between full ionization (ρ ≪ ρ ^* ) and full atomic recombination (ρ≫ρ ^* ). Each term reduces to a function of ρ/ρ ^* times temperature-dependent functions which decay exponentially fast when temperature T vanishes. Scaled expansions are ordered with respect to the corresponding decay rates. Leading terms do reduce to ideal contributions obtained within Saha theory. We consistently compute all corrections which are exponentially smaller by a factor exp (β E _H ) at most, where E _H is the negative groundstate energy of a hydrogen atom and β=1/(k _B T). They include all effects arising from both the Coulomb potential and the quantum nature of the particles: excitations of atoms H, formation of molecules H ₂, ions H ₂⁺ and H ⁻, thermal and pressure ionization, plasma polarization, screening, interactions between atoms and ionized charges, etc. Scaled low-temperature expansions can be viewed as partial resummations of usual virial expansions up to arbitrary high orders in the density.     

Connectivity of growing networks with link constraints

We propose a growing network model with link constraint, in which new nodes are continuously introduced into the system and immediately connected to preexisting nodes, and any arbitrary node cannot receive new links when it reaches a maximum number of links k_m. The connectivity of the network model is then investigated by means of the rate equation approach. For the connection kernel A(k)=k^γ, the degree distribution n_k takes a power law if γ≥1 and decays stretched exponentially if 0≤γ< 1. We also consider a network system with the connection kernel A(k)=k^α(k_m-k)^β. It is found that n_k approaches a power law in the α> 1 case and has a stretched exponential decay in the 0≤α< 1 case, while it can take a power law with exponential truncation in the special α=β=1 case. Moreover, n_k may have a U-type structure if α> β.     

Impurity scattering,Friedel oscillations and RKKY interaction in graphene

We investigate Friedel Oscillations (FO) surrounding a point scatterer in graphene. We find that the long-distance decay of FO depends on the symmetry of the scatterer. In particular, the FO of the charge density around a Coulomb impurity show a faster, δρ∼1/ r³, decay than in conventional 2D electron systems. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice decay according to the 1/r² law. We discuss the consequences of these findings for the temperature dependence of the resistivity of the material and the RKKY interaction between magnetic impurities.     

Spin filtering through ballistic nanojunctions, the role of geometry and of spin orbit interaction

We suggest a spin filter scheme using T-stub nanometric crossjunctions patterned in two dimensional electron gases (2DEGs) in the presence of spin orbit interaction (SOI). We compare the effects of SOI arising from vertical confinement of charge carriers in the well, Rashba or α-SOI, with SOI generated by lateral confinement of the wire, β-SOI. We show that β coupling can be more effective in generating a spin polarized current as compared to α-SOI. We also compare the efficiency of the T-stub filter with the one of the X shaped cross junction.     

Asymmetric nuclear matter and Skyrme potential

The binding energy, symmetry energy, pressure, incompressibility, and the velocity of sound are calculated for asymmetric nuclear matter using Skyrme interaction SkO’. The behavior of these physical quantities is studied for different values of the asymmetry parameter α _τ , the density ρ, and the temperature T. Good agreement is obtained in comparison with previous theoretical estimates and experimental data. The text was submitted by the authors in English.     

Guest Charges in an Electrolyte: Renormalized Charge, Long- and Short-Distance Behavior of the Electric Potential and Density Profiles

We complement a recent exact study by L. Šamaj on the properties of a guest charge Q immersed in a two-dimensional electrolyte with charges +1/−1. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Šamaj’s previous work, exact results for arbitrary coulombic coupling β were obtained for a system where all the charges are points, provided β Q < 2 and β < 2. Here, we first focus on the mean field situation which we believe describes correctly the limit β→ 0 but β Q large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value β Q > 2. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Šamaj for the renormalized charge are not valid for β Q > 2, contrary to a hypothesis put forward by Šamaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough (β Q≥ 2−β). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning–Oosawa threshold β Q = 2.     

A first experimental approach to the 15O + α elastic scattering

The ¹⁵O(α,α)¹⁵O elastic scattering is investigated using a ¹⁵O radioactive beam and a He gas cell limited by Mylar windows. The width of a ¹⁹Ne state at an excitation energy of 5.35MeV is measured as Γ_α = 3.2±1.6keV, in agreement with charge symmetry estimate.     

The Hume-Rothery rules and phase stabilities in noble metal alloys

Results from martensitic transformations are used to evaluate stabilities of the equilibrium phases in the Hume-Rothery electron compounds based on Cu, Ag and Au, and to give arguments why the electron concentration plays such an important role in the selection of the crystal structures. It is shown that the vibrational entropy difference observed for the martensitic transformation from ordered bcc to the close packed martensite and its e/a dependence can also account for the entropy difference ΔS ^α/β between the equilibrium α and β at high temperatures, and can be made largely responsible for the composition dependence of the (α+β) two phase field. The enthalpy of mixing can be decomposed into a small term which depends on the average periodic lattice, which is different in α and β but which is nearly the same in all alloys studied, and a contribution which is due to the difference in the properties of the atoms and which can be expressed by pair interchange energies. This contribution depends strongly on the specific alloy system, but is independent of structure, which is compatible with a pair interchange energy depending only on pair distance but not on structure, as suggested by simple pseudopotential theory. The same pair interchange energies account also for long range order and the critical ordering temperature. The evaluation for several alloy systems shows a surprisingly good agreement within this picture, and permits to understand better why the electron concentration plays such an important role also for other structures, although the energy contribution of the conduction electrons is only a small part of the total enthalpy of formation of any of the equilibrium structures.     

Clustering of exponentially separating trajectories

It might be expected that trajectories of a dynamical system which has no negative Lyapunov exponent (implying exponential growth of small separations) will not cluster together. However, clustering can occur such that the density ρ(Δx) of trajectories within distance |Δx| of a reference trajectory has a power-law divergence, so that ρ(Δx) ∼ |Δx| ^−β when |Δx| is sufficiently small, for some 0 < β < 1. We demonstrate this effect using a random map in one dimension. We find no evidence for this effect in the chaotic logistic map, and argue that the effect is harder to observe in deterministic maps.     

The Number of Open Paths in an Oriented <Emphasis Type="Italic">ρ</Emphasis>-Percolation Model

We study the asymptotic properties of the number of open paths of length n in an oriented ρ-percolation model. We show that this number is e ^{n α(ρ)(1+o(1))} as n→∞. The exponent α is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n ^−1/2 We ^{n α(ρ)}(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.     

Propagation of mesons in asymmetric nuclear matter in a density-dependent coupling model

We study the propagation of the light mesons σ,ω,ρ, and a₀(980) in dense hadronic matter in an extended derivative scalar coupling model. Within the scheme proposed it is possible to unambiguously define effective density-dependent couplings at the Lagrangian level. We first apply the model to study asymmetric nuclear matter with fixed isospin asymmetry, and then we pay particular attention to hypermatter in β-equilibrium. The equation of state and the potential contribution to the symmetry coefficient arising from the mean-field approximation are investigated. Received: 16 October 2001 / Accepted: 10 January 2002     

q-Gaussian approximants mimic non-extensive statistical-mechanical expectation for many-body probabilistic model with long-range correlations

We study a strictly scale-invariant probabilistic N-body model with symmetric, uniform, identically distributed random variables. Correlations are induced through a transformation of a multivariate Gaussian distribution with covariance matrix decaying out from the unit diagonal, as ρ/r ^α for r =1, 2, ..., N-1, where r indicates displacement from the diagonal and where 0 ⩽ ρ ⩽ 1 and α ⩾ 0. We show numerically that the sum of the N dependent random variables is well modeled by a compact support q-Gaussian distribution. In the particular case of α = 0 we obtain q = (1-5/3 ρ) / (1- ρ), a result validated analytically in a recent paper by Hilhorst and Schehr. Our present results with these q-Gaussian approximants precisely mimic the behavior expected in the frame of non-extensive statistical mechanics. The fact that the N → ∞ limiting distributions are not exactly, but only approximately, q-Gaussians suggests that the present system is not exactly, but only approximately, q-independent in the sense of the q-generalized central limit theorem of Umarov, Steinberg and Tsallis. Short range interaction (α > 1) and long range interactions (α < 1) are discussed. Fitted parameters are obtained via a Method of Moments approach. Simple mechanisms which lead to the production of q-Gaussians, such as mixing, are discussed.