Spin-orbit effects on Knight shift - a new contribution

We derive an expression for the Knight shift (K) including spin-orbit and many-body effects using fite temperature Green function method. We obtain a new contribution to K which is non-zero only when spin-orbit interaction is taken into account. For p-type PbTe, we find that this contribution is of the same order of magnitude as other contributions which have been considered in the past. The effect of exchange and correlation on this new contribution is discussed briefly.     

Correlations between potentials and observables in the NN interaction

We study the effects of the components of the soft-core and velocity-dependent Paris nucleon-nucleon potential on the scattering observables for laboratory energies, T_L, between 10 and 350 MeV. Knowledge of these correlations is useful to indicate constraints on components of the nucléon-nucléon force. The velocity-dependent component, attractive at low energy and repulsive at high energy, plays a role at all energies. The polarisation P, the depolarisation D and the parameters D_t, A, R, C_KP and C_NN are good tests for the tensor, spin-orbit and, to a smaller extent, quadratic spin-orbit forces. The isovector tensor force contribution is important at low energy and that of the isovector spin-orbit at high energy. The isoscalar tensor force effect is large at all energies and that of the isoscalar spin-orbit force rather small. The potential without quadratic spin-orbit term reproduces well the experimental data for T_L < 150 MeV.     

Approximate eigensolutions of Dirac equation for the superposition Hellmann potential under spin and pseudospin symmetries

The Hellmann potential is simply a superposition of an attractive Coulomb potential ?a/r plus a Yukawa potential be^{?δ r} /r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.     

f(R,L m ) gravity

We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L _m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.     

Experimental constraints on heavy fermions in Higgsless models

Using an effective Lagrangian approach we analyse a generic Higgsless model with composite heavy fermions, transforming as SU(2) _L+R doublets. Assuming that the Standard Model fermions acquire mass through mixing with the new heavy fermions, we constrain the free parameters of the effective Lagrangian studying Flavour Changing Neutral Current processes. In doing so we obtain bounds that can be applied to a wide range of models characterised by the same fermion mixing hypothesis.     

K+N spin-orbit interaction in the constituent quark model

We calculate p-wave phase shifts of the KN system in the framework of the non-relativistic constituent-quark model. We show that the symmetric spin-orbit potential from gluon exchange between quarks leads to KN spin-orbit potentials for the I = 0 and I = 1 states with the correct sign and magnitude. We also discuss the spin-orbit contributions from the naive confinement potential which give the wrong behaviour for the hadron-hadron spin-orbit potential.     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Collective modes in asymmetric ultracold Fermi systems

We derive the long wavelength effective action for the collective modes in systems of fermions interacting via a short-range s-wave attraction, featuring unequal chemical potentials for the two fermionic species (asymmetric systems). As a consequence of the attractive interaction, fermions form a condensate that spontaneously breaks the U(1) symmetry associated with total number conservation. Therefore at sufficiently small temperatures and asymmetries, the system is a superfluid. We reproduce previous results for the stability conditions of the system as a function of the four-fermion coupling and asymmetry. We obtain these results analyzing the coefficients of the low energy effective Lagrangian of the modes describing fluctuations in the magnitude (Higgs mode) and in the phase (Nambu-Goldstone, or Anderson-Bogoliubov, mode) of the difermion condensate. We find that for certain values of parameters, the mass of the Higgs mode decreases with increasing mismatch between the chemical potentials of the two populations, if we keep the scattering length and the gap parameter constant. Furthermore, we find that the energy cost for creating a position dependent fluctuation of the condensate is constant in the gapped region and increases in the gapless region. These two features may lead to experimentally detectable effects. As an example, we argue that if the superfluid is put in rotation, the square of the radius of the outer core of a vortex should sharply increase on increasing the asymmetry, when we pass through the relevant region in the gapless superfluid phase. Finally, by gauging the global U(1) symmetry, we relate the coefficients of the effective Lagrangian of the Nambu-Goldstone mode with the screening masses of the gauge field.     

Diquarks from aU (3) L ×U (3) R invariant quark Lagrangian

An effective Lagrangian involving composite pseudoscalar and scalar mesons as well as scalar and pseudoscalardiquarks is derived from a chiralU(3) _L ×U(3) _R invariant four-quark theory using path integral methods. We obtain mass relations for the diquarks where all free parameters can be fixed in the meson sector. We also calculate weak diquark decay constants, and discuss baryon masses in terms of a quark-diquark model.     

Solutions of Dirac Equation for Generalized Hyperbolical Potential Including Coulomb-Like Tensor Potential with Spin Symmetry

We solved the Dirac equation for the generalized hyperbolical potential including a Coulomb-like tensor potential under spin symmetry with spin-orbit quantum number k. We used the parametric generalization of the Nikiforov–Uvarov method to obtain the energy eigenvalue and the unnormalized wave function.     

Non-minimally coupled quintom model inspired by string theory

In this Letter we consider a quintom model of dark energy with a single scalar field T given by a Lagrangian which inspired by tachyonic Lagrangian in string theory. We consider non-minimal coupling of tachyon field to the scalar curvature, then we obtain the equation of state (EoS), and the condition required for the model parameters when ω crosses over −1.     

Anomalous spin-orbit effects in a strained InGaAs/InP quantum well structure

There is currently a large effort to explore spin-orbit effects in semiconductor structures with the ultimate goal of manipulating electron spins with gates. A search for materials with large spin-orbit coupling is therefore important. We report results of a study of spin-orbit effects in a strained InGaAs/InP quantum well. The spin-orbit relaxation time, determined from the weak antilocalization effect, was found to depend nonmonotonically on gate voltage. The spin-orbit scattering rate had a maximum value of 5×10¹⁰ s^?1 at an electron density of n=3×10¹⁵ m^?2. The scattering rate decreased from this for both increasing and decreasing densities. The smallest measured value was approximately 10⁹ s^?1 at an electron concentration of n=6×10¹⁵ m^?2. This behavior could not be explained by either the Rashba or the bulk Dresselhaus mechanisms but is attributed to asymmetry or strain effects at dissimilar quantum well interfaces.     

The Effect of Spin-Orbit Coupling and Spin-Spin Coupling of Compact Binaries on Chaos

There are spin-orbit interaction and spin-spin interaction in a generic post-Newtonian Lagrangian formu-lation of comparable mass spinning compact binaries. The spin-orbit coupling or the spin-spin coupling plays a quite important role in changing the evolution of the system and may sometime cause chaotic behavior. How do the two types of couplings exert together any influences on chaos in this formulation? To answer it, we simply take the Lagrangian formulation of a special binary system, including the Newtonian term and the leading-order spin-orbit and spin-spin couplings. The key to this question can be found from a Hamiltonian formulation that is completely identical to the Lagrangian formulation. If the Lagrangian does not include the spin-spin coupling, its equivalent Hamiltonian has an additional term (i.e. the next-order spin-spin coupling) as well as those terms of the Lagrangian. The spin-spin coupling rather than the spin-orbit coupling makes the Hamiltonian typically nonintegrable and probably chaotic when two objects spin. When the leading-order spin-spin coupling is also added to the Lagrangian, it still appears in the Hamiltonian. In this sense, the total Hamiltonian contains the leading-order spin-spin coupling and the next-order spin-spin coupling, which have different signs. Therefore, the chaos resulting from the spin-spin interaction in the Legrangian formulations is somewhat weakened by the spin-orbit coupling.     

The gauged O(3) sigma model: Schrödinger representation and Hamilton-Jacobi formulation

We first study a free particle on an (n−1)-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schrödinger representation and a Hamilton-Jacobi formulation of the model. We thereby obtain the free particle energy spectrum corresponding to that of a rigid rotator. We extend these considerations to a modified version of the field theoretical O(3) nonlinear sigma model, and obtain the corresponding energy spectrum as well as BRST Lagrangian.     

The Effect of Spin-Orbit Coupling and Spin-Spin Coupling of Compact Binaries on Chaos

There are spin-orbit interaction and spin-spin interaction in a generic post-Newtonian Lagrangian formulation of comparable mass spinning compact binaries. The spin-orbit coupling or the spin-spin coupling plays a quite important role in changing the evolution of the system and may sometime cause chaotic behavior. How do the two types of couplings exert together any influences on chaos in this formulation? To answer it, we simply take the Lagrangian formulation of a special binary system, including the Newtonian term and the leading-order spin-orbit and spin-spin couplings. The key to this question can be found from a Hamiltonian formulation that is completely identical to the Lagrangian formulation. If the Lagrangian does not include the spin-spin coupling, its equivalent Hamiltonian has an additional term(i.e. the next-order spin-spin coupling) as well as those terms of the Lagrangian. The spin-spin coupling rather than the spin-orbit coupling makes the Hamiltonian typically nonintegrable and probably chaotic when two objects spin. When the leading-order spin-spin coupling is also added to the Lagrangian, it still appears in the Hamiltonian.In this sense, the total Hamiltonian contains the leading-order spin-spin coupling and the next-order spin-spin coupling,which have different signs. Therefore, the chaos resulting from the spin-spin interaction in the Legrangian formulations is somewhat weakened by the spin-orbit coupling.     

RGM calculation of the NN spin-orbit interaction in a quark model

A quark-cluster model supplemented by an effective-meson-exchange potential (EMEP) is applied to the NN ³P scattering using the resonating group method (RGM). The repulsive central and the attractive spin-orbit NN interactions are obtained from the quark-exchange interaction including the symmetric spin-orbit term in the one-gluon-exchange potential. When the long- and medium-range central and tensor forces between nucleons are introduced as the EMEP, the results obtained seem to explain a considerable part of the empirical spin-orbit effect in the ³P scattering phase shifts.     

Superconductivity in a correlated two-dimensional Hubbard model: A theoretical study

In this work we study the superconductivity within an attractive two-dimensional one-band Hubbard model. We consider a d-wave superconducting gap and a Hubbard-I approximation to describe the strongly correlated superconducting regime. We use Green's function method to obtain the order parameter Δ and the superconducting critical temperature T_c. The results show that for fixed values of the superconducting attractive potential U (U<0), the gap increases for low temperatures, whereas diminishes abruptly as the temperature increases. The effect of pressure can be discussed, varying the next-nearest-neighbors hopping t₂, yielding a change in T_c, and also in Δ₀.     

Effective Lagrangian for quantum black holes

We discuss the most general effective Lagrangian obtained from the assumption that the degrees of freedom to be quantized, in a black hole, are on the horizon. The effective Lagrangian depends only on the induced metric and the extrinsic curvature of the (fluctuating) horizon, and the possible operators can be arranged in an expansion in powers of M_P1/M, where M_P1 is the Planck mass and M the black hole mass. We perform a semiclassical expansion of the action with a formalism which preserves general covariance explicitly. Quantum fluctuations over the classical solutions are described by a single scalar field living in the (2 + 1)-dimensional world-volume swept by the horizon, with a given coupling to the background geometry. We discuss the resulting field theory and we compute the black hole entropy with our formalism.     

Hadronic decays of excited heavy quarkonia

We construct an effective Lagrangian for the hadronic decays of a heavy excited s-wave-spin-one quarkonium Ψ′ into a lower s-wave-spin-one state Ψ. We show that reasonable fits to the measured invariant mass spectra in the charmonium and bottomonium systems can be obtained within this framework. The mass dependence of the various terms in the Lagrangian is discussed on the basis of a quark model.     

Statistical Properties of the Burgers Equation with Brownian Initial Velocity

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its n-point correlations. In the same limit, we derive the n-point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.