A comment on coherent states of the isotonic oscillator

Landau's theory of density and pair fluctuations in a Fermi liquid is extended to include also fluctuations in the vertex functions, i.e. in the Landau parameters themselves. This is a natural consequence of the higher effective action Г[G, α] which depends explicitly on the full propagator G and the vertex α and whose extreme in G and α determine physical configurations of these quantities.     

The general exact bijective continuous solution of Feigenbaum's functional equation

Solutionsf:?→? of Feigenbaum's functional equationf(f(x))=α^?1 f(αx), where α≠0 is a fixed real number, account for many of the fascinating properties of the behaviour of successive iterates of (one parameter families of) nonlinear maps. In connection with the phenomenon of intermittency, interesting families of exact solutions have recently been found (for α>0). These solutions can all be derived from continuous bijective solutions which are topologically equivalent to translations. In this paper, thegeneral exact continuous bijective solution is found for any α≠0, positive or negative. In particular, it is shown that, forany α≠0, there are solutions which areinequivalent to translations. And it is shown that bijective solutions equivalent to translations exist only when 0<α<1. These results considerably enlarge the stock of available exact solutions of Feigenbaum's equation.     

Tight-binding calculations of the subband structures of zincblende-semiconductor [001] quantum wells

The scattering-theoretic T-matrix method is used to calculate the subband structures of GaAs?ZnSe and ZnSe?ZnS_xSe_1?x [001] quantum wells within an empirical tight-binding model, that includes the bulk Г₆, Г₇ and Г₈ valence- and conduction bands. The resulting confinement energies for vanishing lateral crystal momentumk _‖ are compared with those, that are obtained from a simple effective mass model and effects are found and predicted which the effective mass model cannot account for. The effect of the band nonparabolicity and the influence of the microscopic sequence of atomic layers, which determines the symmetry properties of a quantum well, are studied for the GaAs?ZnSe wells.     

Bose condensation in strongly monideal systems

The possibility of the formation of a condensate with a finite absolute value of the momentum k₀ in a strongly nonideal Bose system is considered. Such a condensate comes into existence when the one-particle spectrum of a normal system touches zero in the point k₀ ≠ 0. The form of a correlation function below the condensation point shows the appearance of a long-range order, but not the infinite long-range one. In the case of liquid ⁴He estimates show that $\text{k}{}_0\text{? 1}\text{A}\text{?}{}^{\mathrm{?1}}$, and at the temperature T>₀ ～ 1 K this unusual condensate with a finite magnitude of the momentum turns into the conventional Bose-Einstein condensate with the zero momentum. The properties of correlation functions in the spaces of different dimensions are discussed.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

On the formation of a random color magnetic quantum liquid in QCD

It is shown that a quantum state consisting of a condensate of color magnetic flux tubes is formed in QCD for a rather weak coupling g²/4π = 0.37. This result is obtained in a systematic search for energy minimizing forms of the QCD unstable magnetic mode. The magnetic field is argued to be of a “random” type with 〈H〉 = 0 and 〈H²〉 ≠ 0 at any point.     

Schrödinger operator with a nonlocal potential whose absolutely continuous and point spectra coexist

We consider the Schrödinger-like operatorH in which the role of a potential is played by the lattice sum of rank 1 operators |v _n 〉〈v _n | multiplied byg tan π[(α,n)+ω],g>0, α∈? ^d ,n∈? ^d , ωε[0, 1]. We show that if the vector α satisfies the Diophantine condition and the Fourier transform support of the functionsv _n (x)=v(x?n),d∈? ^d ,n∈? ^d , is small then the spectrum ofH consists of a dense point component coinciding with [?,∞) and an absolutely continuous component coinciding with [?, ∞), where ? is the radius of the mentioned support. Besides, we find the integrated density of statesN(λ) (it has a jump at λ=?) and zero temperature a.c. conductivity ?, that also has a jump at λ=? and vanishes faster than any power of the external field frequency ν as ν→0 and λ≠?.     

Dielectronic recombination rates for ions of the magnesium sequence at low energies

The dielectronic recombination (DR) rate coefficient α^DR is explicitly calculated for the Si, Ar, Fe and Mo target ions of the Mg isoelectronic sequence with twelve electrons. Both the 3s, Δn ≠ 0 and 3s, Δn = 0 transitions are considered in detail. An explicit LS coupling scheme was applied to all the dominant transitions of these ions. Results of α^DR with different free electron temperatures are also discussed     

Dielectronic recombination rates for ions of the magnesium sequence—II

The dielectronic recombination (DR) rate coefficient α^DR is explicitly calculated for Ar, Fe and Mo target ions of the Mg isoelectronic sequence (12 electrons). The 2p transitions are dominant at high temperatures and are considered in detail with full LS coupling. This work extends our previous study in which both the 3s, Δn = 0 and 3s, Δn ≠ 0 transitions are considered. Scaling of α^DR with free-electron temperature is also discussed.     

The oscillator frequency in resonating-group-method calculations

For the example α-¹⁶O we present simple RGM calculations with equal (ω = ω′) and different (ω ≠ ω′) oscillator frequencies for the two nuclei. In the case ω ≠ ω′ and ω → ω′ the one-channel RGM space for angular momentum zero contains all ²⁰Ne states with four particles in the s-d shell and total spatial symmetry ($\text{[?] = [4]}$). These states form a basis for low-lying excited 0⁺ states of ²⁰Ne. The ω ≠ ω′ calculation (as well for ω → ω′ as for realistic ω, ω') exhibits, therefore, resonances corresponding to these states. We present also the calculation for ω = ω′ where these physically important resonances are missing.     

Phase transitions (π-condensation) in nuclei and neutron stars

It is shown that in nuclear matter at Z = N for density n < n₀ (n₀ nuclear density) an electrically neutral condensate of π⁺, π^-, π⁰ mesons arises. The results of the calculations for the case of the neutron star (Z ? N) are given.In this case there are two phase transitions: one corresponds to π⁰ condensation and second to the electrically neutral π⁺, π^- condensation. The π^- condensate apparently does not appear even at very high densities.     

Possibility of a phase transition to a pion condensate in neutron stars

We consider the possibility that a pion condensate may arise in an infinite nuclear medium as a consequence of the modification of the pion propagator due to isobar-hole and nucleon-hole excitations, This does not seem likely in a system with N = Z at densities of less than 0.17 fm^?3, but does seem likely to occur at the densities encountered in the interior of neutron stars. We estimate a necessary neutron density of ? 0.38 fm^?3 and a condensate energy density of ? ? 0.25 MeV fm^?3.     

Pairing energy of liquid 4He

The two-particle density matrix of a Bose system described by a Jastrow wave function displays off-diagonal long-range order associated with strong correlations between pairs of bosons with non-zero momenta ?q, -?q. In conjunction with the zero-momentum condensate, these correlations give rise to a finite contribution to the energy expectation value per particle, which is calculated for liquid ⁴He at two values of the density.     

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator (F_μν^a)² can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|(F_μν^a)²|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O(N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.     

Gluonic corrections to quark vacuum condensate contributions to two-point functions in QCD

We present the α _s corrections to quark vacuum condensate contributions to various types of current correlation functions. Their relevance to the first Weinberg sum rule is discussed. A new derivation of the relation between theA ₁-mass and the ?-mass is presented. The higher order corrections to the socalled non-perturbative quark mass are also discussed.     

Improved calculation of the structure functions of the nucleon in the O(4, 2)-infinite multiplet model

A new investigation of the inelastic electon scattering from proton in the O(4, 2) models is presented. The resultant explicit structure functions in the limit satisfy scaling, F₁(ξ) ≠ 0 (σ_T ≠ 0), the Drell-Yan relation F₂(ξ) ～ (1?ξ)³ and, approximately, the Callan-Gross relation F₂(ξ) ≈ 2ξF₁(ξ).     

Higgs phenomenon without symmetry breaking order parameter

We discuss symmetry-breaking order parameters, e.g. 〈?〉, in gauge theories with Higgs scalars, ?, in suitable gauges. We show that, typically, 〈?〉 = 0. A complete set of gauge-invariant, observable composite fields for such theories, local ones and ones localized near strings (paths) is constructed. We then examine the validity of standard perturbation theory, based on assuming that 〈?〉 ≠ 0, and reformulate it in terms of our gauge-invariant fields and without assuming that 〈?〉 ≠ 0. Finally, we classify classical field configurations with non-trivial topology (“defects”) in such theories and propose a defect-gas approach to predict their effects.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

Schrödinger operator with a nonlocal potential whose absolutely continuous and point spectra coexist

We consider the Schrödinger-like operatorH in which the role of a potential is played by the lattice sum of rank 1 operators \(|\left. {v_n } \right\rangle \left\langle {v_n |} \right.\) multiplied by g tan π[(α,n)+ω],g>0, α∈? ^d ,n∈? ^d , ω∈[0, 1]. We show that if the vector α satisfies the Diophantine condition and the Fourier transform support of the functionsv _n (x)=v(x-n),x∈? ^d ,n∈? ^d , is small then the spectrum ofH consists of a dense point component coinciding with? and an absolutely continuous component coinciding with [?, ∞), where ? is the radius of the mentioned support. Besides, we find the integrated density of statesN(λ) (it has a jump at λ=?) and zero temperature a.c. conductivityσ _λ (v), that also has a jump at λ=? and vanishes faster than any power of the external field frequency ν as ν→0 and λ≠?.     

Secure four-site distribution and quantum communication of χ−type entangled states

The research of multi-particle entanglement is a hot topic because of its important applications and far-reaching effects on vast aspects of quantum information. The article is devoted to the χ − type entangled state, a peculiar four-particle entangled state, which is different from a four-particle GHZ or W state under stochastic local operations and classical communication (SLOCC). Secure four-site distribution using decoy particles is proposed. Moreover, applying it, several communication protocols are presented, including four-party hierarchical quantum secret sharing, supervisory three-party asymmetric deterministic secure quantum communication, etc. The security of the four-site distribution and the communication protocols are also analyzed.