The Buchdahl stability bound in Eddington-inspired Born-Infeld gravity

We give the Buchdahl stability bound in Eddington-inspired Born-Infeld(EiBI)gravity.We show that this bound depends on an energy condition controlled by the model parameter K.From this bound,we can constrain κ≤10~8 m~2 if a neutron star with a mass around 3 M is observed in the future.In addition,to avoid the potential pathologies in EiBI,a Hagedorn-like equation of state associated with κ at the center of a compact star is inevitable,which is similar to the Hagedorn temperature in string theory.     

Influence of dark energy on time-like geodesic motion in Schwarzschild spacetime

In this paper we investigate the influence of the dark energy on the time-like geodesic motion of a particle in Schwarzschild spacetime by analysing the behaviour of the effective potential which appears in an equation of motion. For the non-radial time-like geodesics, we find a bound orbit when the particle energy is in an appropriate range, and also find another possible orbit, which is that the particle drops straightly into the singularity of a black hole or escapes to infinity. For the radial time-like geodesics, we find an unstable circular orbit when the particle energy is the critical value, in which case it is possible for the particle to escape to infinity.     

Influence of multi-photon excitation on the atomic above-threshold ionization

Using the time-dependent pseudo-spectral scheme, we solve the time-dependent Schr ¨odinger equation of a hydrogenlike atom in a strong laser field in momentum space. The intensity-resolved photoelectron energy spectrum in abovethreshold ionization is obtained and further analyzed. We find that with the increase of the laser intensity, the abovethreshold ionization emission spectrum exhibits periodic resonance structure. By analyzing the population of atomic bound states, we find that it is the multi-photon excitation of bound state that leads to the occurrence of this phenomenon, which is in fairly good agreement with the experimental results.     

The D~* interaction with isospin zero in an extended hidden gauge symmetry approach

The D~* interaction via a ρ or ω exchange is constructed within an extended hidden gauge symmetry approach, where the strange quark is replaced by the charm quark in the SU(3) flavor space. With this D~*interaction, a bound state slightly lower than the D~* threshold is generated dynamically in the isospin zero sector by solving the Bethe-Salpeter equation in the coupled-channel approximation, which might correspond to the X(3872)particle announced by many collaborations. This formulism is also used to study the BB~* interaction, and a BB~* bound state with isospin zero is generated dynamically, which has no counterpart listed in the review of the Particle Data Group. Furthermore, the one-pion exchange between the D meson and the ~* is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.     

Is X(3872) a bound state?

All existing experimental evidence for the bound state nature of X(3872) relies on observing its decay products,which are measured with a finite experimental mass resolution that is typically △m≥2 MeV,and much larger than its alleged binding energy,B_X=0.00(18) MeV.On the other hand,we have found recently that there is a clear cancellation in the 1~(++) channel of the invariant DD~*mass around the threshold between continuum and the bound state.This is very much like a similar cancellation in the proton-neutron continuum with the deuteron in the1~(++) channel.Based on comparative fits with a common Tsallis distribution of the experimental cross-sections for prompt production of deuterons and X(3872) in pp collisions with a finite p_T,we find a strong argument for questioning the bound state nature of this state,which also suggests that the large observed production rate could be consistent with a half-bound state.     

Approximate analytical solutions and mean energies of stationary Schr¨odinger equation for general molecular potential

The Schrodinger equation is solved with general molecular potential via the improved quantization rule.Expression for bound state energy eigenvalues, radial eigenfunctions, mean kinetic energy, and potential energy are obtained in compact form. In modeling the centrifugal term of the effective potential, a Pekeris-like approximation scheme is applied. Also, we use the Hellmann–Feynman theorem to derive the relation for expectation values. Bound state energy eigenvalues, wave functions and meanenergies of Woods–Saxon potential, Morse potential, Mobius squared and Tietz–Hua oscillators are deduced from the general molecular potential. In addition, we use our equations to compute the bound state energy eigenvalues and expectation values for four diatomic molecules viz. H_2, CO, HF, and O_2. Results obtained are in perfect agreement with the data available from the literature for the potentials and molecules. Studies also show that as the vibrational quantum number increases, the mean kinetic energy for the system in a Tietz–Hua potential increases slowly to a threshold value and then decreases. But in a Morse potential, the mean kinetic energy increases linearly with vibrational quantum number increasing.     

Localization and recurrence of a quantum walk in a periodic potential on a line

We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker＇s coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.     

A single-point measurement scheme for quantum work based on the squeezing state

To investigate the role of initial quantum coherence in work-probability distribution, it is necessary to consider an incomplete or partial measurement, in which the energy cannot be fully discriminated by the detector. In this paper, we use a harmonic oscillator with a coherent or squeezing state to realize this incomplete or partial measurement, and propose a unified framework of quantum work statistics for a closed system with an arbitrary initial state. We find that work is proportional to the change of the real part of the coherent state parameter, i.e., quantum work can be estimated by the coherent state parameter. The resulting work-probability distribution includes the initial quantum coherence, and can be reduced to the result of the traditional two projective energy measurement scheme(TPM) by squeezing the state of the harmonic oscillator. Our measurement scheme reveals the fundamental connections between measurement error and coherent work. By introducing a ‘coherent work-to-noise ratio', we find the optimal measurement error, which is determined by the energy difference between the superposed energy levels. As an application, we consider a driven two-level system and investigate the effects of driving velocity on work statistics. We find that only when the driving velocity matches the transition frequency of the system can initial quantum coherence play an important role.     

Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem,an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy,specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.     

Schrdinger Equation of a Particle on a Rotating Curved Surface

We derive the Schrdinger equation of a particle constrained to move on a rotating curved surface S.Using the thin-layer quantization scheme to confine the particle on S,and with a proper choice of gauge transformation for the wave function,we obtain the well-known geometric potential V_g and an additive Coriolis-induced geometric potential in the co-rotational curvilinear coordinates.This novel effective potential,which is included in the surface Schrdinger equation and is coupled with the mean curvature of S,contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian.We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.     

Thermodynamics of the frustrated J<Subscript>1</Subscript>-J<Subscript>2</Subscript> Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

We use the spin-rotation-invariant Green’s function method as well as thehigh-temperature expansion to discuss the thermodynamic properties of the frustratedspin-S J ₁-J ₂ Heisenbergmagnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighborbonds J ₁<0 and antiferromagnetic next-nearest-neighbor bonds J ₂ ≥ 0 andarbitrary spin S. We find that the transition point\hbox{$J_2^c$}J2cbetween the ferromagnetic ground state and theantiferromagnetic one is nearly independent of the spin S, i.e., it is very closeto the classical transition point\hbox{$J_2^{c,{\rm clas}}= \frac{2}{3}|J_1|$}J2c,clas=23|J1|. At finite temperatures we focus on the parameterregime\hbox{$J_2<J_2^c$}J2<J2cwith a ferromagnetic ground-state. We calculate theCurie temperature T _C (S, J ₂)and derive an empirical formula describing the influence of the frustration parameterJ ₂ and spin S on T _C . We find that theCurie temperature monotonically decreases with increasing frustration J ₂, where veryclose to\hbox{$J_2^{c,{\rm clas}}$}J2c,clasthe T _C (J ₂)-curveexhibits a fast decay which is well described by a logarithmic term\hbox{$1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$}1/log(23|J1|?J2). To characterize the magnetic ordering below and aboveT _C , we calculate thespin-spin correlation functions ?S ₀ S _R ?, the spontaneous magnetization, the uniform static susceptibilityχ ₀ as well as the correlation lengthξ.Moreover, we discuss the specific heat C _V and the temperaturedependence of the excitation spectrum. As approaching the transition point\hbox{$J_2^c$}J2csome unusual features were found, such as negativespin-spin correlations at temperatures above T _C even though theground state is ferromagnetic or an increase of the spin stiffness with growingtemperature.     

Biquadratic exchange interaction between Ru5+ ions in (Ru2O9) clusters

The energy levels of a Ru₂O₉ cluster have been calculated, including a higher order spin interaction. The Ru⁵⁺-Ru⁵⁺ coupling is described by the Hamiltonian ?= -2JS₁· S₂ ?j(S₁·S₂)². The temperature dependence of the magnetic susceptibility is used to determine the values of the bilinear J and biquadratic j exchange integrals: J/k = -161K and j/k = 6.6K. The second term in the Hamiltonian corresponds to a fourth order perturbation involving low spin states.     

Semiclassical model for accidental predissociation in diatomic molecules

After a short review of possible quantum treatments, the uniform semiclassical theory of Child (J. Mol. Spectrosc.53, 280 (1974)) is applied to the problem of accidental predissociation in a diatomic molecule where a bound state dissociates into a continuum via a coupling with a near-degenerate second bound state. A complete connection diagram and an analytical expression for the lineshape is provided. This expression is used in the diabatic limit to derive the widths and shifts of the resonances. Checks are made for two test cases for which a simplified quantum model leads to analytical formulas. The familiar case in which each resonance shares the initial width of the perturbing state according to its weight in the configuration interaction wavefunction is verified. In the opposite coupling scheme, the “resonance narrowing” phenomenon predicted by the quantum model is also obtained.     

On a bound (NΔ(1236))-state and its decay

The possible existence of a bound state of the (NΔ(1236))-system has been investigated. Using a regularized OPE-potential of pure exchange type one finds that the (T = 2, J^P = 2⁺)-state is bound, where the binding energy is rather strongly dependent on the regularization parameter. The decay width of the bound δ is strongly reduced by the binding effect and the Pauli principle, e.g., for a binding energy of 18 MeV the width is only 16 MeV.     

Further analysis of effective Hamiltonians for triply degenerate fundamentals of tetrahedral molecules: Unambiguous fit of q2J5 and q2J6 terms for ν4 of 12CH4

The further study of ambiguities among q²J⁵ and q²J⁶ terms in effective Hamiltonians for triply degenerate fundamentals of tetrahedral molecules is presented. It is shown that, in agreement with theory, q²J⁵ and q²J⁶ diagonal coupling parameters cannot be considered as constants having definite values for a given F₂ vibrational state, just like q²J⁴ terms previously studied [Vl. G. Tyuterev, J. P. Champion, G. Pierre, and V. I. Perevalov, J. Mol. Spectrosc.105, 113–138 (1984)]. The use of reduced Hamiltonians containing fewer (but unambiguous) parameters is suggested and applied to the ν₄ band of ¹²CH₄.     

ΣΛ Conversion in ΛH and in other S-shell hypernuclei

The binding energy of the Λ-particle in the $\text{J =}\text{1}\text{2}\text{and}\text{3}\text{2}$ states of _Λ³H and the doublet and quartet Λ-d scattering lengths are calculated with a separable ΛN-ΣN potential matrix, fitted to experimental data in ΛN and ΣN channels. The dependence of the results on ΛΣ coupling is explained in terms of a perturbative treatment of ΛΣ coupling. This perturbative treatment is also applied in a qualitative discussion of the effects of ΛΣ conversion in the J = 0 and 1 states of _Λ⁴H-_Λ⁴He and in the $\text{J =}\text{1}\text{2}$ state of _Λ⁵He. The importance of three-body ΛNN forces caused by ΣΛ coupling is stressed.     

ρ meson decays of heavy hybrid mesons

We calculate the ρ meson couplings between the heavy hybrid doublets H~h/S~h/M~h/T~h and the ordinary qQˉ doublets in the framework of the light-cone QCD sum rule. The sum rules obtained rely mildly on the Borel parameters in their working regions. The resulting coupling constants are rather small in most cases.     

Reduced exchange coupling and hysteresis loops in two-phased magnetic nanosystem

The reduced exchange coupling has been incorporated in our micromagnetic calculations for the hysteresis loops of Nd₂Fe₁₄B/α-Fe and Sm₄₀Fe₆₀/Ni₈₀Fe₂₀ multilayers. Analysis shows that nucleation and pinning fields are sensitive to the value of the interface coupling constant Jⁱ when the soft layer thickness L^s is small. Hysteresis loops have been obtained for a trilayer system with a soft α-Fe sandwiched between two Nd₂Fe₁₄B layers for different values of L^s and Jⁱ. As Jⁱ decreases, nucleation field decreases while the pinning field increases. In the meantime, the squareness of the loops is deteriorated, which results in smaller energy product. For thick soft layer the coercivity mechanism transforms from pinning to nucleation as the interface coupling decreases, and vice versa. The above calculations have been extended to a Sm₄₀Fe₆₀/Ni₈₀Fe₂₀ bilayer and compared with available experimental data. The theoretical loop is consistent with the experimental one when the value of Jⁱ is taken as 10% of the bulk one, demonstrating that the interface coupling in the experiment is far away from perfect coupling.     

The Effects of Vacuum Fluctuations on ρ Meson Masses in Hot and Dense Matter

Based on the thermo field dynamics, the temperature- and density-dependent effective mass and screening mass of ρ meson in the vector-tensor ρ-meson-nucleon-nucleon coupling model have been calculated. The effects of the vacuum fluctuation corrections through the effective nudeon mass are examined. We have shown that the vacuum fluctuation gives an important correction to the self-energy of ρ meson and leads to a reduction of ρ-meson mass in hot and dense matter.     

THE DECAY ρ→ππ IN LATTICE GAUGE THEORY

The hadronic decays are studied by using an improved Hamiltonian including 2-link interactions. We find that the formulation is effective for studying hadronic decays as well as mass spectrum. In the intermediate coupling region,the decay width of ρ meson is found to be of the right order of magnitude.