Gentile statistics and restricted partitions

In a recent paper (Tranet al, Ann. Phys.311, 204 (2004)), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for therestricted or coloured partitionsp _k ^s (n), which is the number of partitions of an integern into the summand of sth powers of integers such that each power of a given integer may occur utmostk times. While the method is not rigorous, it reproduces the well-known asymptotic results fors = 1 apart from yielding more general results for arbitrary values ofs.     

Entanglement dynamics in Coriolis coupled rovibrational states of formaldehyde

The entanglement dynamics of two vibrational modes of a polyatomic molecule coupled by Coriolis interaction to overall molecular rotation is studied in terms of two negativities, N(t) and N_s(t), respectively, defined by the minimum of the eigenvalues and by the sum of the negative eigenvalues of the partial transpose of a density matrix. Various initial states are the products of Dicke states and the products of coherent states of vibrations and rotations. Formaldehyde is taken as an example, and the von Neumann entropy s(t) is simulated for the comparison with both negativities. It is shown that negativity N_s(t) is positively correlated with entropy s(t), and the correlated behavior between negativity N(t) and entropy s(t) strongly depends on initial states. However, these three indicators of entanglement display a dominantly positive correlation for the coherent states with small or large parameters. In addition, for the latter state two quantities N(t) and s(t) are nearly unchanged for a long time. This time can be further increased by the increasing of vibrational quantum number so that molecular information processing and quantum computing is allowed. These results are useful in quantum information theory.     

Quasi-Debye response of ion-hopping conduction at lowest frequencies

On the basis of the relaxation mode theory, quasi-Debye response in the dynamic conductivity by hopping ions is theoretically investigated in three-dimensional random lattices with a uniform distribution of activation energies. It is shown at lowest frequencies that the dynamic conductivity is approximately given by σ(ω)∼σ(0)+A″ω^s″, s″=2−n, where n is a non-integer exponent originated from the mode diffusion length and density of states. The numerical analyses give rise to some values of s″<2, for example s″∼1.5, which behaves as s″→2 with increasing temperature.     

Semigroup of positive maps for qudit states and entanglement in tomographic probability representation

Stochastic and bistochastic matrices providing positive maps for spin states (for qudits) are shown to form semigroups with dense intersection with the Lie groups IGL(n,R) and GL(n,R) respectively. The density matrix of a qudit state is shown to be described by a spin tomogram determined by an orbit of the bistochastic semigroup acting on a simplex. A class of positive maps acting transitively on quantum states is introduced by relating stochastic and quantum stochastic maps in the tomographic setting. Finally, the entangled states of two qubits and Bell inequalities are given in the framework of the tomographic probability representation using the stochastic semigroup properties.     

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.     

A field theory model for fixed angle proton-proton scattering

It is argued that the sum of the leading terms to each order in the coupling constant in massive Q.E.D. at fixed angle leads to the elastic cross-section dσ/dt = A(θ)s^?2exp (a ln²s + b(θ)lns). This gives good agreement with the data for wide angle proton-proton scattering.     

Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes

We consider one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in current experiments with ultracold Bose-Fermi mixtures. We apply the Bethe ansatz technique to find the exact ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We use it to prove the absence of the demixing, contrary to prediction of a mean-field approximation. Combining exact solution with local density approximation in a harmonic trap, we calculate the density profiles and frequencies of collective modes in various limits. In the strongly interacting regime, we predict the appearance of low-lying collective oscillations which correspond to the counterflow of the two species. In the strongly interacting regime, we use exact wavefunction to calculate the single particle correlation functions for bosons and fermions at low temperatures under periodic boundary conditions. Fourier transform of the correlation function is a momentum distribution, which can be measured in time-of-flight experiments or using Bragg scattering. We derive an analytical formula, which allows to calculate correlation functions at all distances numerically for a polynomial time in the system size. We investigate numerically two strong singularities of the momentum distribution for fermions at k_f and k_f + 2k_b. We show, that in strongly interacting regime correlation functions change dramatically as temperature changes from 0 to a small temperature ∼E_f/γ ? E_f, where E_f = (π?n)²/(2m), n is the total density and γ = mg/(?²n) ? 1 is the Lieb-Liniger parameter. A strong change of the momentum distribution in a small range of temperatures can be used to perform a thermometry at very small temperatures.     

Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.     

Effective surface potential method for calculating surface states

A novel formalism (the effective surface potential method) is developed for calculating surface states. Like the Green function method of Kalkstein and Soven and the transfer matrix method of Falicov and Yndurain, the technique is exact for simple tight binding Hamiltonians. As well as offering an alternative viewpoint, the present method provides a simple analytic expression describing the surface states. At each point k_s in the surface Brillouin zone the semi-infinite solid is viewed as an effective linear chain where each element of the chain is a planar layer. The solution to the linear chain problem can be expressed in terms of an effective potential h(k_s,E) at each energy E. A number of examples are presented in detail; “sp^d” Hamiltonians for a linear chain (d = 1), the honeycomb lattice (d = 2), the 111 surface of silicon (d = 3), and a dissected Bethe lattice. Various exact results are given, e.g. the extremities of surface state bands and the surface density of states of p-like (delta function) bands. The results of Kalkstein and Soven for the 100 surface of a simple cubic solid with a perturbation on the surface layer are rederived.     

Log-Periodic Oscillations in the Photo Response of Efimov Trimers

The photoassociation of Efimov trimer, composed of three identical bosons, is studied using the long wavelength approximation. It is shown that for identical particles the leading contribution comes from the r ² s-mode operator and from the quadrupole d-mode operator. Log-periodic oscillations are found in the photoassociation response function, both near the energy threshold for the leading s-wave reaction, and in the high frequency tail for all partial waves.     

Transition metal and rare-earth metal atoms on single-layer graphene: Estimations of the charge transfer and adsorption energy

A Hamiltonian accounting for s- and d(f)-states of adatoms has been proposed to describe adsorption of atoms of d- and f-metals on single-sheet graphene. It has been shown that s-electrons mainly contribute to the charge transfer Δn _a between the adatom and graphene substrate. Analytical formulas proposed previously within the M-model of the graphene density of states are used for Δn _a calculations. To estimate the adsorption energy, a simple analytical expression is proposed. Calculations are performed for 3d-, 4d-, 5d-, and 4f-adatoms. The results of calculations are compared with the data obtained by other authors.     

Perturbation of the Laplacian supported by null sets,with applications to polymer measures and quantum fields

We discuss hamiltonians in L²(R^d, dx) of the form H = ?Δ + V, with V a potential supported by a zero measure set C. In particular if C is a path of a brownian motion b such that V(x) = ∫₀¹λ(x, ω)δ(x-b(s, ω)) ds, we show that H exists as a nontrivial, self-adjoint, lower bounded perturbation of ?Δ when d ?5. We must choose λ to be an infinitesimal, negative function for d = 4,5, but for d ? 3 any bounded real-valued function λ will do. The connection with Edward's model of polymers as well as with quantum fields of the ?_d⁴-type is also discussed. The proofs use methods of nonstandard analysis.     

Isometric immersions of pseudo-Riemannian space forms

In this paper we study local isometric immersions f:M_sⁿ(K)→N_s+q²ⁿ⁻¹(c) of a time-like n-submanifold M_sⁿ(K) with constant sectional curvature K and index s into a pseudo-Riemannian space form N_s+q²ⁿ⁻¹(c) with constant sectional curvature c and index s+q, where q≥0, 1≤s≤n−1 and K≠c. We first prove the existence of Chebyshev coordinates of a time-like submanifold M_sⁿ(K) in certain conditions. Afterwards, we generalize the classical Bäcklund theorem for space-like (or time-like) submanifolds in N_n−1²ⁿ⁻¹(c) and N₁²ⁿ⁻¹(c). Finally as an application, in the Chebyshev coordinates, we use the Bäcklund theorem to give a Bäcklund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation.     

Spin and phonon contribution to the superconductivity in La2−xSrxCuO4

Anisotropy of high-energy spin excitations and low-energy conductive electronic excitations in Raman spectra can be interpreted, if quantum spin fluctuation is weak. The low-energy states at (π/2, π/2) in the underdoped phase are composed of insulating states induced by the insulator-metal transition and the conductive states induced by electron-phonon coupling. The superconducting states are created in the latter states and the pairing symmetry is s or d(xy). On the other hand, the electronic states at (π, 0) in the overdoped phase are electron-spin coupled states and the pairing symmetry is d(x²−y²).     

Isotopieverschiebungskonstanten von Th,U, Pu und Am

The isotope shifts of unperturbed electron configurations have been determined from isotope shift measurements in the spectra of Th, U, Pu, and Am. The screening of the 7s electron charge density at the nucleus by 6d, 7s, and 7p electrons is discussed. It turns out that the same screening factors as for the 6s electron in lighter elements can be used. The screening of the 7s electron charge density at the nucleus by one 5f electron amounts to about 25%: [δT(f ⁿ s)?δT(f ⁿ )]/[δT(f ⁿ }s)?δ(f ^n} )]=0.7₅. The charge density at the nucleus due to the filleds (andp _1/2) shells is considerabely screened by anf electron. The isotope shiftδT(f^n}-1 d ^m +2)?δT(f ⁿ d ^m ) produced by this effect is of the same order of magnitude as the isotope shiftδT(f ⁿ d ^m s)-δT(f ⁿ d ^m ) due to ans electron. The experimental isotope shift constants are found to be:Β C _exp(Th²³⁰–Th²³²)=880±120;Β C _exp(U²³³–U²³⁵)=1000±180;Β C _exp(U²³⁴–U²³⁶)=1070±200;Β C _exp(U²³⁶–U²³⁸)=1080±180;Β C _exp(Pu²³⁸–Pu²⁴⁰)=1200±120;Β C _exp(Pu²³⁹–Pu²⁴¹)=1060±100;Β C _exp(Pu²⁴⁰–Pu242)=900 ±90;Β C _exp(Am²⁴¹–Am²⁴³)=890±50 [10^?3cm^?1]. The ratiosΒ C _exp/C _th are discussed.     

Electronic structure and magnetic susceptibility of nearly magnetic metals (palladium and platinum)

A self-consistent approach to calculations of the electronic structure and the magnetic susceptibility of nearly magnetic metals, such as palladium and platinum, has been developed in terms of the generalized s(p)d Hubbard model. The energy band structure has been calculated using the ab initio LDA + U + SO method with the additional inclusion of the interstitial s(p)d exchange interaction and spin-fluctuation renormalizations of the electronic spectra, which appear at finite temperatures. The developed approach makes it possible to quantitatively describe the density of states and unusual temperature dependences of the magnetic susceptibility of the nearly magnetic metals under consideration and to evaluate the basic parameters of the electron-electron interactions. The role of the spin-orbit interaction in the formation of the electronic and magnetic properties is enhanced when going from palladium (4d period) to platinum (5d period). The effects of the temperature redistribution of electrons between the s(p) and d states have been revealed.     

Shubnikov-de Haas effect of n-inversion layers in InSb grain boundaries

Hall effect and Shubnikov-de Haas effect have been investigated in a n-inversion layer adjacent to the grain boundary in p-InSb bicrystals. The observed quantum oscillations of the magnetoconductivity result from a superposition of the Shubnikov-de Haas effect in two occupied subbands. The electron densities of the subbands n_si(n_s1=3.5 × 10¹¹cm^-2;n_s0= 1.1 × 10¹²cm^-2) and the effective cyclotron mass of the lower subband m_c0=(0.023 ± 0.002)m₀ have been evaluated.     

Transition energy and dipole oscillator strength of 1s23d-1s2 nf transitions for Sc18+ ion

The transition energies of the 1s²3d-1s² nf (4?n?9) transitions and fine structure splittings of 1s² nf (n?9) states for Sc¹⁸⁺ ion are calculated with the full-core plus correlation method. The quantum defect of 1s² nf series is determined by the single-channel quantum defect theory. The energies of any highly excited states with n?10 for this series can be reliably predicted using the quantum defect as function of energy. Three alternative forms of the dipole oscillator strengths for the 1s²3d-1s² nf (n?9) transitions of Sc¹⁸⁺ ion are calculated with the transition energies and wave functions obtained above. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for 1s²3d-1s² nf (n > 9) transitions and the oscillator strengths densities corresponding to the bound-free transitions are obtained.