Entropic dimension for completely positive maps

We extend the concept of quantum dynamical entropyh _φ (γ) to cover the case of a completely positive map γ. Forh _φ (γ) = 0 we examine the limit $$h_\phi (N,\gamma ,\beta ) = \mathop {\lim }\limits_n (1/n^\beta )H_\phi (N,\gamma {\rm N},...,\gamma ^{n -- 1} N)$$ calling the turning point β₀ between zero and infiniteh _φ (N, γ, β) the “entropic dimension”D _N (γ). The application of this theory to a solvable irreversible quantum dynamical semigroup on a one-dimensional fermion lattice provides any value ofD _N (γ) between 0 and 1.     

Free Energy as a Dynamical Invariant (or Can You Hear the Shape of a Potential?)

Classical lattice spin systems provide an important and illuminating family of models in statistical physics. An interaction Φ on a lattice L?? ^d determines a lattice spin system with potential A _Φ . The pressure P(A _Φ ) and free energy F _AΦ (β)=?(1/β)P(βA _Φ ) are fundamental characteristics of the system. However, even for the simplest lattice spin systems, the information about the potential that the free energy captures is subtle and poorly understood. We study whether, or to what extent, (microscopic) potentials are determined by their (macroscopic) free energy. In particular, we show that for a one-dimensional lattice spin system, the free energy of finite range interactions typically determines the potential, up to natural equivalence, and there is always at most a finite ambiguity; we exhibit exceptional potentials where uniqueness fails; and we establish deformation rigidity for the free energy. The proofs use a combination of thermodynamic formalism, algebraic geometry, and matrix algebra. In the language of dynamical systems, we study whether a Hölder continuous potential for a subshift of finite type is naturally determined by its periodic orbit invariants: orbit spectra (Birkhoff sums over periodic orbits with various types of labeling), beta function (essentially the free energy), or zeta function. These rigidity problems have striking analogies to fascinating questions in spectral geometry that Kac adroitly summarized with the question ``Can you hear the shape of a drum?''.     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.     

Non-Analyticity and the van der Waals Limit

We study the analyticity properties of the free energy f _γ (m) of the Kac model at points of first order phase transition, in the van der Waals limit γ↘0. We show that there exists an inverse temperature β ₀ and γ ₀>0 such that for all β≥β ₀ and for all γ∈(0,γ ₀), f _γ (m) has no analytic continuation along the path m↘m ^* (m ^* denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure p _γ (h), which is related to the free energy f _γ (m) by a Legendre transform.     

The Kosterlitz-Thouless transitions by the mayer expansion finiteness of the perturbations

The Kosterlitz-Thouless transitions in 2D XY and Coulomb gas models are discussed by the Mayer expansion. After transforming the 2D XY model into a (generalzed) 2D Coulomb gas model by the duality transformation, it is shown that the free energy (pressure) and the two point correlation function 〈cos(θ₀?θ_ζ)〉 are expressed as Σa_N(β) and $\text{exp}\text{[(}\text{2}\text{β}\text{) C}{}_0\text{(ζ) + Σb}{}_{\mathrm{N}}\text{(β:ζ)]}$, respectively, for large inverse temperature β > β_c, where {a_N(β)} are the usual virial coefficients and {a_N, b_N} are the contributions from N-electron system. Moreover C₀(ζ) ? ? (2π)^?1 log(|ζ| + 1), |a_N(β)| ≤ C₁(N) exp[?βK₃N] and |b_N(β:N) ≤ C₂(N) exp[?βK₄N] |C₀(ζ)| (K_i > 0). By comparing this system with the dipole gas system in which these series converge absolutely, it is conjectured that these series converge absolutely for large β.     

Structure of even-even actinides in the interacting boson model and the N = 152 subshell closure

We show that a wide range of deformed actinides can be described in terms of an interacting boson model hamiltonian with three parameters, two of them [including the coefficient of the only SU(3) symmetry breaking term] remaining almost constant over the whole region. In addition to ground γ₁ and β₁ spectra, B(E2:0_g⁺ → 2_g⁺) values are well reproduced with no extra adjustable parameters for nuclei with 136⩽N⩽146, while for nuclei beyond N = 146 an effective boson number has to be considered in order to fit the observed in the B(E2:0⁺_g → 2⁺_g) values, which is due to the presensce of a subshell closure at N = 152. The sensitive dependence of the B(E2:0_g⁺→2_g⁺) values on the effective boson numbers is emphasized. β₁ → ground and β₁ → ground transitions are fitted by breaking the SU(3) symmetry of the E2 transition operator.     

A study of the bulk phase transitions of the SU(2) lattice gauge theory with mixed action

Using the finite size scaling theory, we reexamine the nature of the bulk phase transition in the fundamental-adjoint coupling plane of the SU(2) lattice gauge theory at β_A = 1.25 where previous finite size scaling investigations of the deconfinement phase transition showed it to be of first order for temporal lattices with four sites. Our simulations on N⁴ lattices with N = 6, 8, 10, 12 and 16 show an absence of a first order bulk phase transition. We find the discontinuity in the average plaquette to decrease approximately linearly with N. Correspondingly, the plaquette susceptibility grows a lot slower with the 4-volume of the lattice than expected from a first order bulk phase transition.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

Mechanical properties and hardness of new carbon-rich superhard C11N4 from first-principles investigations

The structural, mechanical properties and hardness of the new carbon-rich material C₁₁N₄ are studied by first-principles total energy calculations based on the density-functional theory. We use the empirical equations of state (EOS) to investigate the lattice properties and bulk modulus. It is found that the calculated lattice constants and bulk modulus are in good agreement with previous calculations. And the full set elastic constants are calculated using the stress-strain method. The Voigt-Reuss-Hill approximation is used to evaluate the mechanical moduli. The elastic constants show that the two phases of C₁₁N₄ are mechanically stable. The tetragonal-C₁₁N₄ (α-C₁₁N₄) exhibits larger mechanical moduli than the orthorhombic-C₁₁N₄ (β-C₁₁N₄). The mechanical anisotropy is calculated of several different anisotropic indexes and factors, such as universal anisotropic index (A^U), the percent anisotropy (A_G and A_B) and shear anisotropic factors (A₁, A₂ and A₃). Furthermore, the hardness of α-C₁₁N₄ and β-C₁₁N₄ are evaluated according to the intrinsic hardness calculation theory. α-C₁₁N₄ is predicted to be a superhard material with the Vickers hardness of 67.17 GPa, which is slightly higher than that of the cubic boron nitride. And the β-C₁₁N₄ is also a superhard material with the calculated Vickers hardness of 45.63 GPa. C₁₁N₄ can be considered as candidate superhard compounds.     

Renormalization group for network models of quantum Hall transitions

We analyze in detail the renormalization group flows which follow from the recently proposed all orders β functions for the Chalker–Coddington network model. The flows in the physical regime reach a true singularity after a finite scale transformation. Other flows are regular and we identify the asymptotic directions. One direction is in the same universality class as the disordered XY model. The all orders β function is computed for the network model of the spin quantum Hall transition and the flows are shown to have similar properties. It is argued that fixed points of general current–current interactions in 2d should correspond to solutions of the Virasoro master equation. Based on this we identify two coset conformal field theories osp(2N|2N)₁/u(1)₀ and osp(4N|4N)₁/su(2)₀ as possible fixed points and study the resulting multifractal properties. We also obtain a scaling relation between the typical amplitude exponent α₀ and the typical point contact conductance exponent X_t which is expected to hold when the density of states is constant.     

Glueball mass spectrum and mass splitting in 2+1 strongly coupled lattice gauge theories

For a 2+1 strongly coupled (β=2/g ² small) Wilson action lattice gauge theory with complex character we analyze the mass spectrum of the associated quantum field theory restricted to the subspace generated by the plaquette function and its complex conjugate. It is shown that there is at least one but not more than two isolated masses and each mass admits a representation of the formm(β)=?4lnβ+r(β), wherer(β) is a gauge group representation dependent function analytic inβ ^1/2 orβ atβ=0. For the gauge group SU(3) there is mass splitting and the two massesm _± are given by $$m_ \pm (\beta ) = - 41n\beta + 16r^4 + \tfrac{1}{2}(2 \pm 1)\beta + \left( {d_ \pm (\beta )\sum\limits_{n = 2}^\infty {c_n^ \pm } \beta ^n } \right)$$ wherer=3 is the dimension of the representation andd _±(β) is analytic atβ=0.c _n ^± can be determined from a finite number of theβ=0 Taylor series coefficients of finite lattice truncated plaquette-plaquette correlation function at a finite number of points.     

The (γ, p0) reactions in the giant dipole resonance region of 51V and 52Cr nuclei

The differential cross sections at 90° for the ⁵¹V(e, p₀)⁵⁰Ti and ⁵²Cr(e, p₀ + p₁)⁵¹V reactions have been measured over the giant dipole resonance region. These cross sections were used to obtain the differential cross sections of the ⁵¹V(γ, p₀)⁵⁰Ti and ⁵²Cr(γ, p₀ + p₁)⁵¹V reactions. The results show two peaks that appear at the same energies as the main peaks of the (γ, n) and (γ, p) cross section for both nuclei. The angular distributions of protons from the (e, p) reaction have also been measured at several points of the incident electron energy. The coefficients A₂ obtained by fitting with a series of Legendre polynomials, W(θ) = 1 + A₁P₁(cos θ)+A₂P₂(cos θ), varies with excitation energy. These results are discussed in terms of the direct-semidirect process considering isospin effects in the giant dipole resonance.     

The analyzing power Aγ(θ) for the elastic scattering of 12 MeV neutrons from deuterons

The analyzing power A_γ(θ) was obtained at 10° intervals between 30° (lab) to 120° (lab) for ²H(n, n)²H at 12.0 MeV. The polarized neutron beam employed in the measurement was obtained by using neutrons emitted at 0° from the polarization transfer reaction ${}^2\text{H}\text{(}\text{d}\text{,}\text{n}\text{)}{}^3\text{He}$. The accuracy in the A_γ(θ) values that was achieved ranged from ± 0.006 to ± 0.013. Comparison of the data to A_γ(θ) results obtained at 12 MeV for the charge symmetric reaction ²H(p, p)²H shows that the two A_γ(θ) distributions are equal to within the above accuracy.     

A path-functional field theory of lattice gauge models and the large-N limit

We transform lattice gauge models to a theory of functional fields defined on a set of closed paths. Some relevant properties of the formalism are discussed in detail, with emphasis on symmetry and topological structure. We then investigate the large-N limit of the U(N) lattice gauge model in arbitrary dimensions using this formalism. Assuming the existence of the limit, we show, to arbitrary order of the strong coupling expansion parameter (g²N)^?, which is kept fixed, that for the leading contribution in the limit: (i) the flow of indices in color space can be represented by planar diagrams; (ii) when the diagrams are immersed in space-time they are random surfaces without handles; (iii) there are interactions of the surfaces which can be depicted as the formation of multisheet bubblesw in the surfaces. This formalism also makes it possible to set up a gauge-invariant mean-field approximation.     

The large-N deconfinement phase transition in a partially reduced Eguchi-Kawal model

We construct generalized twisted Eguchi-Kawai models which for large-N reduce space-time to a lattice of arbitrary size. Large-N lattice gauge theory at finite temperature is investigated in a model on a lattice with L₀ time slices and two lattice points in very time slice. We observe the large-N deconfinement phase transition in the weak coupling region. Assuming asymptotic scaling we find a transition temperature T_c = (101±4)Λ_L.     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Heat capacity of EuMnO3 and Eu0.7A0.3MnO3 (A=Ca,Sr) compounds

We carried out the heat capacity calculation of the magnetoresistance compounds EuMnO₃ and Eu_0.7A_0.3MnO₃ (where A=Ca and Sr) as a function of temperature from 5 to 100 K, using the Rigid Ion Model (RIM). The results on heat capacity for EuMnO₃ and Eu_0.7A_0.3MnO₃ (A=Ca and Sr) obtained by us are in good agreement with the measured values. Although strong electron–phonon interactions are present in these compounds but the lattice part of the specific heat also deserves proper attention. The parent compound EuMnO₃ exhibits two magnetic transitions at 35 and 47 K due to weak ferromagnetic (FM) component and antiferromagnetic (AF) ordering. In addition, we have reported cohesive energy (φ), molecular force constant (f), compressibility (β), Restrahalen frequency (υ₀), Debye temperature (θ_D) and Gruneisen parameter (γ) in the temperature range 5 K?T?100 K.     

Analyticity and renormalization group

We prove the inequalities ψ(y, α) ?α, |α_s(d/dα_s)(β(α_s)/α_s| ? 1 (for the Paterman-Stueckelberg-Gell-Mann-Low functions in QED and QCD) and γ₀(α_s ? 1 (for the anomalous dimension of the gauge-invariant operator O(x)). The consequences of the inequalities are discussed: for modern energies, comparison of theoretical and experimental moments of deep inelastic structure functions has a meaning only for N ? 7 (singlet case) and N ? 50 (non-singlet case); perturbation theory in QCD has a meaning only for α_rms ? 0.45.     

Polymorphism of anhydrous ferrous sulfate

The Mössbauer spectra of α-FeSO₄ and β-FeSO₄ have been measured in the temperature range 4.2 K ? T ? 30 K. The high temperature (β) phase is accompanied by a weak fraction of a third component. In analogy to CoSO₄, the third component of the three-fold polymorphism in anhydrous ferrous-sulfate is named the γ phase. X-ray powder measurements confirm this phase to be isomorphous to the corresponding γ-CoSO₄ structure. The parameters of the hyperfine interaction at 4.2 K of the three phases are evaluated. The magnetic ordering temperatures are T_N (α) = 24.0 K, T_N(β) = 17.0 ± 1.5 K and T_N(γ) = 19.5 ± 1.0 K.