Effective potential of the O(N) linear sigma-model at finite temperature

We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation, which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed. Received: 21 June 2000 / Accepted: 13 September 2000     

ΛΛ 6 hypernucleus in α + 2Λ cluster model

The binding energy of the double hypernucleus _ΛΛ ⁶ is calculated in α + 2Λ cluster model using the method of translation invariant basis TIMO. As regards the required interaction potentials we use a density dependent effective ΛN force and a gaussian form for ΛΛ potential. With these interactions a very reasonable value ofB _ΛΛ is obtained if the oscillator states up to the excitation quantum numberN=12 are taken into account in the expansion of wavefunction of the hypernucleus. This value ofN is much smaller than that obtained in an earlier study. This lowering inN value is attributed to a much better choice of ΛN potential used in the present study.     

Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states

At high densities and low temperatures, the conventional Widom test particle method to compute the chemical potential of a system of particles with excluded volume interactions fails owing to bad statistics. A way to circumvent this problem is the use of expanded ensemble simulation techniques or thermodynamic integration. In this article, we will describe an alternative method to compute the chemical potential which is conceptually much easier, by computing the density of states of systems of N and N + 1 particles directly; and by performing a test particle simulation at very high temperature. The advantage of our technique is that the densities of states of the N and N + 1 particle system are computed in an ensemble in which particles can pass each other, resulting in a more efficient sampling. We will demonstrate our method not only for single particles but also for chain molecules with intramolecular interactions. By using an infinite temperature expansion and an extension of the density of states to very high energies, we will show that it is also possible to compute the chemical potential without having to compute the density of states for the N + 1 particle system.     

Meson loop effect on high density chiral phase transition

We test the stability of the mean field solution in the Nambu-Jona-Lasinio model in a semi-quantitative manner. For stable solutions with respect to both the σ and π directions, we investigate effects of the mesonic loop corrections of 1/N _c , which correspond to the next-to-leading order in the 1/N _c expansion, on the high density chiral phase transition. The corrections weaken the first order phase transition and shift the critical chemical potential to a lower value. At N _c = 3, however, instability of the mean field effective potential prevents us from determining the minimum of the corrected one.      

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

The path-integral approach to the N=2 linear sigma model

In QFT the effective potential is an important tool to study symmetry breaking phenomena. It is known that, in some theories, the canonical approach and the path-integral approach yield different effective potentials. In this paper we investigate this for the Euclidean N=2 linear sigma model. Both the Green’s functions and the effective potential will be computed in three different ways. The relative merits of the various approaches are discussed.     

α-Decay calculations of medium mass nuclei within generalized density-dependent cluster model

The α-decay half-lives of even–even medium mass nuclei have been systematically investigated using a radial wave function within the generalized density-dependent cluster model. The α-decay width is calculated using the overlap integral of the quasi-bound initial state wave function, the scattering final state wave function, and the difference of potentials. The effective α–nucleus potential is constructed using the double-folded integral of realistic nucleon–nucleon interactions with the mass density distributions of α particles and daughter nuclei. For comparison calculations are also carried out for the Woods–Saxon shape potential. The present study is restricted to even–even nuclei with 82<N126, where the shell effect on the α-preformation factor has been taken into account for even–even N=126 isotones. The obtained α-decay half-lives are found to agree with the experimental data with a mean factor of less than 2 for both the double-folded potential and the Woods–Saxon shape potential.     

Spontaneous compactification in quantum Kaluza-Klein theories

We study the one-loop effective action for pure gravity in higher odd-dimensional spaces with a cosmological constant. We develop a method for computing the effective action for backgrounds which are a product of 4-dimensional space-time and an odd-dimensional sphere S^N. For N = 1 in harmonic gauge the potential has an unstable stationary point at which the one-loop corrected Newton constant has a wrong sign. For N > 1 in harmonic gauge there is an imaginary contribution to the effective potential from the Faddeev-Popov ghost. The results for spheres up to N = 17 are presented.     

A law of large numbers and a central limit theorem for the Schrödinger operator with zero-range potentials

We consider the Schrödinger operator with zero-range potentials onN points of three-dimensional space, independently chosen according to a common distributionV(x). Under some assumptions we prove that, whenN goes to infinity, the sequence converges to a Schrödinger operator with an effective potential. The fluctuations around the limit operator are explicitly characterized.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Magnetic moments of <Superscript>33</Superscript>Mg in the time-odd relativistic mean field approach

The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN se...     

Effective ionization coefficients and electron drift velocities in gasmixtures of CF3I with N2 and CO2 obtained from Boltzmannequation analysis

The electron swarm parameters including the density-normalized effective ionization coefficients (α-η)/N and the electron drift velocities V_e are calculated for the gas mixture of CF₃I with N₂ and CO₂ by solving the Boltzmann equation in the condition of steady-state Townsend (SST) experiment. The overall density-reduced electric field strength is from 100 Td to 1000 Td (1 Td=10^-17 V·cm²), while the CF₃I content k in the gas mixture can be varied over the range from 0% to 100%. From the variation of (α-η)/N with the CF₃I mixture ratio k, the limiting field strength (E/N)_lim for each CF₃I concentration is derived. It is found that for the mixtures with 70% CF₃I, the values of (E/N)_lim are essentially the same as that for pure SF₆. Additionally, the global warming potential (GWP) and the liquefaction temperature of the gas mixtures are also taken into account to evaluate the possibility of applying in the gas insulation of power equipment.     

The Uphill Turtle Race; On Short Time Nucleation Probabilities

The short time behavior of nucleation probabilities is studied by representing nucleation as a diffusion process in a potential well with escape over a barrier. If initially all growing nuclei start at the bottom of the well, the first nucleation time on average is larger than the inverse nucleation frequency. Explicit expressions are obtained for the short time probability of first nucleation. For very short times these become independent of the shape of the potential well. They agree well with numerical results from an exact enumeration scheme. For a large number N of growing nuclei the average first nucleation time scales as 1/log N in contrast to the long-time nucleation frequency, which scales as 1/N. For linear potential wells closed form expressions are given for all times.     

On the nature of the phase transition in <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>), <Emphasis Type="Italic">Sp</Emphasis>(2) and <Emphasis Type="Italic">E</Emphasis>(7) Yang–Mills theory

We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in Phys. Lett. B 684, 262 (2010). We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,…,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang–Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition.     

New Criterion for Designing Silica Multimode Interference Power Splitters

We introduce a new criterion for designing 1 × N silica multimode interference power splitters using overlapping-image multimode interference analysis. This criterion requires that widths of multimode waveguides in the devices should be greater than 2 times the product of port number N and effective widths of output waveguides. Better device uniformity can be achieved when the new criterion is satisfied.     

Superconductivity in Supersymmetric Theories

The study of superconductivity has been undertaken through the breaking of supersymmetric gauge theories which automatically incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the effective Lagrangian near a singularity in moduli space for N=2 supersymmetric theory with SU(2) gauge group, it has been shown that when a mass term is added to this Lagrangian, the N=2 Supersymmetry is reduced to N=1 supersymmetry yielding the dyonic condensation which leads to confinement and superconductivity as the consequence of generalized Meissner effect. In the Coulomb phase of N=2 SU(3) Yang–Mills theory the gauge symmetry has been broken down to SU(2)×U(l) and it has been shown that on perturbing it by suitable tree-level superpotential this supersymmetry theory breaks to N=1 SU(2) Yang-Mills theory described by Higgs field in confining phase incorporating superconductivity.     

Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary Number of Dimensions

No Heading Some aspects of the N dimensional Kratzer-Fues potential are discussed, which is an extension of the combined Coulomb-like potential with inverse quadratic potential in N dimensions. The analytical solutions obtained (eigenfunctions and eigenvalues) are dimensionally dependent, so also, the solutions depend on the value of the coefficient of the inverse quadratic term. The expectation values for < r^–2 >, < r^–1 > and the virial theorem for this potential are obtained and the values are also dimensions and parameter dependent.     

Multicenter Higgs oscillators and Calogero model

We show that the spherical part of N-particle Calogero model describes, after exclusion of the center of mass, the motion of the particle on (N − 2)-dimensional sphere interacting with N(N − 1)/2 force centers with Higgs oscillator potential. In the case of four-particle system these force centers are located at the vertexes of cuboctahedron. The geometry of the five-particle case is also investigated.     

Effective actions and large-N limits

The saddlepoint action for a large-N theory is given as an effective action for composite operators. This effective action is computed explicitly forO(N) models and as a series in large-N invariants for matrix models. In the latter case, the use of the first term of the series is found to give good numerical agreement with the exact solutions of the solvable models.     

Functional renormalization group for quantized anharmonic oscillator

Functional renormalization group methods formulated in the real-time formalism are applied to the O(N) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.