On the shape consistency in the deformed shell-model approach

We show that the shape inconsistency (β^V_λ ? β^ρ_λ) between the average potential and the corresponding nucleonic density is generally small (～? 5%) for λ = 2, 3, 4 in both Nilsson and Woods-Saxon models. The properties of (β^V_λ ? β^?_λ) are analysed in detail and understood in terms of the extended Thomas-Fermi model. Approximate formulas β^ρ_λ = β^ρ_λ(β^V) are given and the microscopic reasons for the shape inconsistency discussed.     

Transformations on Density Operators That Leave the Holevo Bound Invariant

For a given probability distribution λ ₁,…,λ _m we determine the structure of all such maps defined on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy $$S\Biggl(\sum_{k=1}^m \lambda_k \phi(\rho_k)\Biggr)- \sum_{k=1}^m \lambda_k S\bigl(\phi (\rho_k)\bigr)= S\Biggl(\sum _{k=1}^m \lambda_k \rho_k\Biggr)- \sum_{k=1}^m \lambda_k S(\rho_k) $$ for all possible collections ρ ₁,…,ρ _m of density operators.     

Rigorous treatment of metastable states in the van der Waals-Maxwell theory

We consider a classical system, in a ν-dimensional cube Ω, with pair potential of the formq(r) + γ ^v φ(γr). Dividing Ω into a network of cells ω₁, ω₂,..., we regard the system as in a metastable state if the mean density of particles in each cell lies in a suitable neighborhood of the overall mean densityρ, withρ and the temperature satisfying $$f_0 (\rho ) + \tfrac{1}{2}\alpha \rho ^2 > f(\rho ,0 + )$$ and $$f''_0 (\rho ) + 2\alpha > 0$$ wheref(ρ, 0+) is the Helmholz free energy density (HFED) in the limit γ→ 0; α = ∫ φ(r)d ^v r andf ₀ (ρ) is the HFED for the caseφ = 0. It is shown rigorously that, for periodic boundary conditions, the conditional probability for a system in the grand canonical ensemble to violate the constraints at timet > 0, given that it satisfied them at time 0, is at mostλt, whereλ is a quantity going to 0 in the limit $$|\Omega | \gg \gamma ^{ - v} \gg |\omega | \gg r_0 \ln |\Omega |$$ Here,r ₀ is a length characterizing the potentialq, andx ? y meansx/y → +∞. For rigid walls, the same result is proved under somewhat more restrictive conditions. It is argued that a system started in the metastable state will behave (over times ?λ ^?1) like a uniform thermodynamic phase with HFED f₀(ρ) + 1/2αρ², but that having once left this metastable state, the system is unlikely to return.     

Spin content of the bosonic string

A new form is derived for the generating function, χ^[λ](x) = Σ_n=0^∞xⁿχ_n^[λ], which counts the number of times, χ_n^[λ], that the irreducible O(D − 1) rotation group representation [λ] appears at the nth mass level for the bosonic string. The derivation goes through for arbitrary old spatial dimensions, D − 1 = 2v + 1. Simplifications of the results are noted for large v and the relation to a previously obtained formula for χ^[λ](x) is explained.     

Holographic dark energy interacting with dark matter in a closed Universe

A cosmological model of an holographic dark energy interacting with dark matter throughout a decaying term of the form Q=3(λ₁ρDE+λ₂ρm)H$Q=3({\lambda }_1{\rho }_{\mathrm{DE}}+{\lambda }_2{\rho }_m)H$ is investigated. General constraint on the parameters of the model are found when accelerated expansion is imposed and we found a phantom scenario, without any reference to a specific equation of state for the dark energy. The behavior of equation of state for dark energy is also discussed.     

Charged <Emphasis Type="Italic">ρ</Emphasis>-meson production in neutrino-induced reactions at &lt;<Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">ν</Emphasis></Subscript>&gt;≈ 10 GeV

The production of charged ρ mesons on nuclei and nucleons is investigated in charged current neutrino interactions at moderate energies (〈E _〉 ≈ 10 GeV), using the data obtained with SKAT bubble chamber. No strong nuclear effects are observed in ρ ⁺ and ρ ^? production. The fractions of charged and neutral pions originating from ρ decays are obtained and compared with higher-energy data. From analysis of the obtained and available data on ρ ⁺ and K*⁺(892) neutrino production, the strangeness suppression factor is extracted: λ _s = 0.18 ± 0.03. Estimation is obtained for cross section of coherent ρ ⁺ neutrino production on nuclei.     

Higher order solutions of Lieb-Liniger integral equation

We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Phase diagrams of bosonic AB<Subscript>n</Subscript> chains

The AB_{N ?1} chain is a system that consists of repeating a unit cell withN siteswhere between the A and B sites there is an energy difference ofλ. Weconsidered bosons in these special lattices and took into account the kinetic energy, thelocal two-body interaction, and the inhomogenous local energy in the Hamiltonian. We foundthe charge density wave (CDW) and superfluid and Mott insulator phases, and constructedthe phase diagram for N =2 and 3 atthe thermodynamic limit. The system exhibited insulator phases for densitiesρ =α/N, with α being an integer. Weobtained that superfluid regions separate the insulator phases for densities larger thanone. For any N value, we found that for integer densitiesρ, thesystem exhibits ρ +1 insulator phases, a Mott insulator phase, and ρ CDW phases. Fornon-integer densities larger than one, several CDW phases appear.     

Interpretation of temperature dependence of the in-plane electrical resistivity in YBa2Cu4O8: Electron–phonon approach

In this paper, we undertake a quantitative analysis of observed temperature-dependent in-plane normal state electrical resistivity of single crystal YBa₂Cu₄O₈. The analysis is within the framework of classical electron–phonon i.e., Bloch-Gruneisen model of resistivity. It is based on the inherent acoustic (low frequency) phonons (ω_ac) as well as high frequency optical phonons (ω_op), the contributions to the phonon resistivity were first estimated. The optical phonons of the oxygen breathing mode yields a relatively larger contribution to the resistivity compared to the contribution of acoustic phonons. Estimated contribution to in-plane electrical resistivity by considering both phonons i.e., ω_ac and ω_op, along with the zero-limited resistivity, when subtracted from single crystal data infers a quadratic temperature dependence over most of the temperature range [80 ? T ? 300]. Quadratic temperature dependence of ρ_diff. = [ρ_exp − {ρ₀ + ρ_e−ph (=ρ_ac + ρ_op)}] is understood in terms of electron–electron inelastic scattering. The relevant energy gap expressions within the Nambu-Eliashberg approach are solved imposing experimental constraints on their solution (critical temperature T_c). It is found that the indirect-exchange formalism provides a unique set of electronic parameters [electron–phonon (λ_ph), electron-charge fluctuations (λ_pl), electron–electron (μ) and Coulomb screening parameter (μ^*)] which, in particular, reproduce the reported value of T_c.     

Algebraic realization of a coupled rotor picture

The relation between the shape variables (β, γ) of the collective model and the (λ, μ) labels which define the irreducible representations of the SU(3) shell model is extended to a coupled rotor picture where one rotor represents protons (π) and the other one neutrons (ν). The joint distribution, (β, γ), emerges as the overlap of the initial distributions, (β _π ,γ _π ) and (β _ν ,γ _ν ), where three Euler angles define the relative orientation of proton and neutron subsystems. It is shown analytically that the rotor construction for triaxial and axially symmetric shapes corresponds to a (λ _π ,μ _π = 0) ? (λ _ν ,μ _ν → (λ, μ) _ρ=1 coupling in the SU(3) model.     

LRS Bianchi Type II Massive String Cosmological Model for Stiff Fluid Distribution with Decaying Vacuum Energy (Λ)

An LRS Bianchi Type II model formed by massive strings with decaying vacuum energy (Λ) for stiff fluid distribution is studied in the context of general relativity. To get the deterministic model, we have assumed that $\frac{\sigma}{\theta} =\mathrm{constant}$ where σ is shear and θ the expansion in the model and decaying vacuum energy (Λ) is proportional to H ² (H is Hubble parameter) as used in Arbab (Gen. Relativ. Gravit. 29:51, 1997). We find that the model represents decelerating and accelerating phases of universe. The decaying vacuum energy (Λ) is proportional to $\frac{1}{\tau^{2}}$ as obtained by Bertolami (Nuovo Cimento B 93:36, 1986) and Hubble parameter is proportional to $\frac{1}{\tau}$ which matches with the observation. The model in general represents anisotropic space-time. However, in special case, it isotropizes. The particle density (ρ _p ) and string tenson (λ) are initially large but decrease due to lapse of time. The model also admits particle horizon and entropy is inversely proportional absolute temperature. Thus the model is in good agreement with present age of universe.     

A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame

We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R_1ρ = 1/T_1ρ) and transverse relaxation rates in the rotating frame (R_2ρ = 1/T_2ρ), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M_1ρ(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M_2ρ(t)) by subtracting M_1ρ(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R_1ρ and R_2ρ from the eigenvalues, and compared them with those obtained numerically from M_1ρ(t) and M_2ρ(t), respectively. There was excellent agreement between them. From the exact solutions for R_1ρ and R_2ρ, R_2ρ was found to be given by R_2ρ = (2R₂ + R₁)/2 − R_1ρ/2, where R₁ and R₂ denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M_1ρ(t) and M_2ρ(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R_1ρ and R_2ρ values obtained from the eigenvalues and those obtained numerically from M_1ρ(t) and M_2ρ(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T_1ρ- and T_2ρ-weighted MRI.     

Inverse solutions to radiative-transfer problems with partially transparent boundaries and diffuse reflection

Analytical techniques are used to solve a class of inverse radiative-transfer problems relevant to finite and semi-infinite plane-parallel media. While the assumption of isotropic scattering is made, diffuse reflection is allowed at the surface, for the semi-infinite case, and at both surfaces for the case of a finite layer. For the general case based on a semi-infinite medium, a cubic algebraic equation is used to define the basic result, but for the specific case of a semi-infinite medium illuminated by a constant incident distribution of radiation, very simple exact expressions are developed for the albedo for single scattering ? and the coefficient for diffuse reflection ρ. Analytical results are also developed (again in terms of a cubic algebraic equation) for the case of a finite layer with equal reflection coefficients relevant to the two surfaces. For the general case of a finite layer with unequal reflection coefficients, two specific formulations are given. The first algorithm is based on a system of three quadratic algebraic equations for the two reflection coefficients ρ₁ and ρ₂ and the single-scattering albedo ?. Secondly, an elimination between these three algebraic equations is carried out to yield two coupled algebraic equations for ρ₁ and ρ₂ plus an explicit expression for ? in terms of ρ₁ and ρ₂. In addition, an exact expression for τ₀, the optical thickness of the finite layer, is developed in terms of ?, ρ₁ and ρ₂. As is typical with the considered class of inverse problems in radiative transfer, all surface quantities are either specified or considered available from experimental measurements. All basic results are tested numerically.     

Non-string two-magnon configurations in the isotropic Heisenberg magnet

By means of the $\text{1}\text{N}$ expansion we study the Bethe-ansatz equations for two-magnon states in the one-dimensional isotropic Heisenberg spin chain of N spins $\text{1}\text{2}$. A qualitative picture of complex solutions for N → ∞ is obtained which substantially disagrees with the string hypothesis. For example, the solutions $\text{λ}{}_{\mathrm{<mtext>1,2</mtext>}}\text{= x ±}\text{i}\text{y, x ～ N,y ～}\text{N}$ are found, whereas according to the string hypothesis $\text{y →}\text{1}\text{2}$ if N → ∞.     

Radial excitations ofp- and π-mesons and their strong decays

Radial (L=0) excitations ofp- and π-mesons are considered in the framework of the quark model. The experimentally observed statesρ′ (1220) andρ″ (1560) are identified with the first and second radial excitations of thep-meson. Within the relativistically generalized model of spontaneous production of a \(q\bar q\) pair from vacuum we explain the dominant (ρ′ →ωπ;ρ″ →ω2π) modes of strong decays of these resonances and find nondominant modes (ρ ′ 2π;ρ″ →ωπ) to be suppressed. An estimation is given for masses of analogous excitations of the pion and partial widths of their decays.     

(p, γ) reaction studies on 60Ni

The γ-ray spectra from the ⁶⁰Ni(p, γ)⁶¹Cu reaction were measured for 27 isolated resonances. From these studies the J^π assignment of the compound states in ⁶¹Cu were made. Moreover, a value for the El photon strength function k(El) = 1.03 × 10^?9 MeV^?3 was obtained from seven l = 0 resonances to the 16 low-lying states. This value was then compared with the theoretical estimates of El strengths as predicted from the s.p. and giant dipole resonance models. The distribution of partial radiative widths about their mean value was determined from a Monte Carlo technique and was found to be consistent with the Porter-Thomas distribution when the Γ_{γ, ij} were divided by the E_γ⁵ energy dependence.Values for the coefficients of the correlation R between Γ_{λ, p} and Γ_{λ, γj} and T between Γ_{λ, yj} and $\text{Γ}{}_{\mathrm{\lambda ,\; \gamma ?}}$ where f ≠ j, were computed with the values R = 0.14 and T = 0.39, respectively. Also the correlation coefficients C(〈 Γ_{λ, yj}〉, I₃He, d, j) and $\text{C(〈Γ}{}_{\mathrm{\lambda ,\; y?}}\text{〉 I}{}_{\mathrm{<mtext>d,\; n</mtext><mtext>,\; ?</mtext>}}\text{)}$ yielded the values ρ = 0.87 and ρ = 0.80 respectively. All these correlations which are found to be statistically significant, imply that the (p, γ) reaction in ⁶⁰Ni is partly due to direct capture such as given by valence and doorway state contributions.     

Quantum phase transition in XY spin chain with three-site interaction studied in terms of Loschmidt echo and Berry phase

By means of the Loschmidt Echo (LE) and Berry Phase (BP) calculations, quantum phase transition (QPT) of an XY spin chain with three-site interaction (α) in a transverse magnetic field (λ) is studied. Both the LE and BP?s λ derivative present anomaly behaviors at the critical regions λ₁,λ₂ and λ₃. The model is in the Ferromagnetic phase as λ>λ₁=1+α and in the Spin Liquid I phase as −1+α<λ<1+α. λ₁ and λ₂ are independent on the anisotropy parameter γ. But, the anisotropy interaction can shift the critical line λ₃ between the Spin Liquid II phase and the Ferromagnetic phase. The present work suggests that QPT of the XY spin chain with three-site interaction can be characterized by exploring the dynamical behaviors of the LE and BP.     

t-channel factorization description of γγ→V 1 V 2

At-channel factorization model is used to estimate cross sections for the processes γγ→V ₁ V ₂. WheneverV=ρ, the width of the ρ has been included in the calculations. The channels γγ→ρ⁰ρ⁰, ρ⁰?, ??, ωω, ρ⁰ω and ρ⁺ρ^? are calculated for two quasi-real photons. Predictions are also given for the process γ^*γ→ρ⁰ρ⁰ for virtual photon mass squaredQ ²<5 GeV². Our results are consistent with all available experimental data.