Microdynamics and time-evolution of macroscopic non-Markovian systems

The time evolution of the single event probability of macroscopic variables is studied from a microscopic point of view. The explicit consideration of the preparation of the initial microdistribution leads to a unique decomposition of the macrodynamics into two parts, a local and instantaneous one and a nonlocal and retarded one. In this retarded, i.e., non-Markovian master equation no inhomogeneity occurs in contrast to previous approaches. It is shown that the retarded master equation can exactly be transformed into a time-convolutionless and homogeneous form , which generates a substitutive Markov process with the same single event behaviour as the process in question.     

Effective interactions and superconductivity in the t-J model in the large-N limit

The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C_4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature T_c is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. T_c increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. T_c is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of T_c is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively. Received: 16 June 1998 / Accepted: 14 July 1998     

Molecular dynamics of liquid lead near its melting point

The molecular dynamics of liquid lead is simulated at T = 613 K using the following three models of an interparticle interaction potential: the Dzugutov pair potential and two multiparticle potentials (the “glue” potential and the Gupta potential). One of the purposes of this work is to determine the optimal model potential of the interatomic interaction in liquid lead. The calculated structural static and dynamic characteristics are compared with the experimental data on X-ray and neutron scattering. On the whole, all three model potentials adequately reproduce the experimental data. The calculations using the Dzugutov pair potential are found to reproduce the structural properties and dynamics of liquid lead on the nanoscale best of all. The role of a multiparticle contribution to the glue and Gupta potentials is studied, and its effect on the dynamic properties of liquid lead in nanoregions is revealed. In particular, the neglect of this contribution is shown to noticeably decrease the acoustic-mode frequency.     

Nuclear shell structure in the systematics of nuclear properties

Existing experimental data allow us to study the behavior of nuclear shell structure by analyzing characteristics of different nature. In this work, one of the most striking phenomena of nuclear dynamics is examined: nucleon pairing. Nucleon pairing for different nuclei chains as a function of the number of protons or neutrons in a nucleus explains why high numbers of states with positive parity in even-odd nuclei are observed for excitation energies E* < 4 MeV that form the multiplet of a nucleus’s ground state.     

Effect of time-odd fields on odd-even mass differences of semi-magic nuclei

The effect of time-odd fields of Skyrme interaction on neutron odd-even mass differences is studied in the framework of axially deformed Skyrme Hartree-Fock(DSHF)+BCS model. To this end, we take into account both the time-even and time-odd fields to calculate the one-neutron and two-neutron separation energies and pairing gaps of semi-magic Ca, Ni, and Sn isotopic chains. In the calculations, a surface-type pairing interaction(IS pairing) and an isospin dependent contact pairing interaction(IS+IV pairing)are adopted on top of Skyrme interactions SLy4, SLy6 and Sk M*, respectively. We find that the time-odd fields have in general small effects on pairing gaps, but achieve better agreement with experimental data using SLy4 and Sly6 interactions, respectively.It is also shown that the calculations with IS+IV pairing reproduce the one-neutron separation energies of Sn isotopes better than those with the IS pairing interaction when the contributions of the time-odd fields are included.     

基于壳模型对力加四极力研究sd和pf壳偶偶原子核

本文在原子核壳模型框架下基于唯象相互作用(对力加四极力)研究sd壳和pf壳的偶偶核低激发集体态。在提取了USDB和GXPF1相互作用的单粒子能量和单极相互作用的基础上,我们用一套统一参数计算重现了球形核和形变核的低激发谱;将对相互作用中的单极成分扣除后可以得到较好的结合能计算结果。同位旋标量的对相互作用对计算结果影响不大。单极相互作用在经验质子—中子相互作用、原子核对称能和Wigner能中产生重要贡献。     

The 3-band Hubbard-model <Emphasis Type="Italic">versus</Emphasis> the 1-band model for the high-<Emphasis Type="Bold">T</Emphasis><Subscript>c</Subscript> cuprates: Pairing dynamics,superconductivity and the ground-state phase diagram

One central challenge in high-T _c superconductivity (SC) is to derive a detailed understanding for the specific role of the Cu-d _x2-y2 and O-p _x,y orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-T _c cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from “high-energy” excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are “universal”. On the other hand, we expect the differences - and thus, the material dependence to show up in the “non-universal” finite-T phase diagram (T _c-values).     

Energy approach to determination of the instantaneous damage level

A kinetic equation similar to the Kachanov-Rabotnov equation is derived from the law of conservation of mass for the case of isotropic damage. The energy balance is used to estimate the initial level of damage (instantaneous damage). The notion of instantaneous damage is akin to the concept of instantaneous deformation, which arises immediately after a load has been applied to a specimen in creep or toughness-elasticity tests. Using instantaneous damage as the initial condition for the standard evolutionary equation of damage like the Kachanov-Rabotnov equation, one can construct a more correct creep rupture diagram of structural materials than those currently available.     

Renormalization of spin polarised itinerant electron bands in the normal state of a model ferromagnetic superconductor

This paper studies the normal state properties of itinerant electrons in a toy model,which is constructed according to the model for coexisting ferromagnetism and superconductivity proposed by Suhl [Suhl H 2001 Phys.Rev.Lett.87 167007].In this theory with ferromagnetic ordering based on localized spins,the exchange interaction J between conduction electrons and localized spin is taken as the pairing glue for s-wave superconductivity.It shows that this J term will first renormalize the normal state single conduction electron structures substantially.It finds dramatically enhanced or suppressed magnetization of itinerant electrons for positive or negative J.Singlet Cooper pairing can be ruled out due to strong spin polarisation in the J > 0 case while a narrow window for s-wave superconductivity is opened around some ferromagnetic J.     

Microscopic description of collective motion in pf shell nuclei

Rotational and vibrational excitations in pf shell nuclei are studied by means of the generator coordinate method. The generator coordinates are the pairing energies and the quadrupole moments of constrained Hartree-Bogoliubov states, projected onto good angular momenta and particle numbers. The Kuo interaction and the one modified by McGrory are used. The vibrational character of the yrast energies appears to be produced by mixing prolate and oblate wave functions. Pairing correlations are essential for this mixing. In contrast to the yrast states the excitation energies of the higher states depend strongly on the interaction used. They show good agreement with experiment, particularly in the case of ⁴⁸Ti with the Kuo force. The calculated B(E2) values exhibit a rotational band structure in general, even if the energies look more vibrational. The force dependence of the excitation energies can qualitatively be understood by inspection of the intrinsic energy surface.     

Scale and space localization in the Kuramoto-Sivashinsky equation

We describe a wavelet-based approach to the investigation of spatiotemporally complex dynamics, and show through extensive numerical studies that the dynamics of the Kuramoto-Sivashinsky equation in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wave number). A projection onto a spline wavelet basis enables good separation of scales, each with characteristic dynamics. At the large scales, one observes essentially slow Gaussian dynamics; at the active scales, structured "events" reminiscent of traveling waves and heteroclinic cycles appear to dominate; while the strongly damped small scales display intermittent behavior. The separation of scales and their dynamics is invariant as the length of the system increases, providing additional support for the extensivity of the spatiotemporally complex dynamics claimed in earlier works. We show also that the dynamics are spatially localized, discuss various correlation lengths, and demonstrate the existence of a characteristic interaction length for instantaneous influences. Our results motivate and advance the search for localized, low-dimensional models that capture the full behavior of spatially extended chaotic partial differential equations. (c) 1999 American Institute of Physics.     

Second Coulomb energy differences of isospin triplets in the 2s-1d shell

Second Coulomb energy differences, which in the present case are proportional to the tensor Coulomb energy, are calculated for 0⁺, T = 1 ground states in the region 18 ≦ A ≦ 42 using a shell model that includes a pairing interaction. The calculation is done with a mathematical formalism that includes p-n pairs as well as p-p and n-n pairs. Besides an enhancement of proton-pair Coulomb energies, the pairing interaction is responsible for lowering the Coulomb energy of N = Z members of isospin triplets and also gives rise to an important term in the second energy difference. Using pairing strengths derived from fitting energy levels for mass-18 and mass-42 nuclei, results of the calculation reproduce experimental second energy differences extremely well.     

On the reaction of muon transfer from protium to neon at low collision energies

The reaction of direct muon transfer from protium to neon at thermal collision energies is considered. The question of whether it is possible to reconstruct the energy dependence of the reaction rate on the basis of available experimental data is discussed. A model based on the following two assumptions is proposed: (i) The reaction in question proceeds within an interaction sphere beyond which the entrance channel and the muon-transfer channel decouple. (ii) For s and p waves, the complex logarithmic derivatives of radial wave functions for the entrance channel at the surface of the interaction sphere are independent of energy at low collision energies. Two logarithmic-derivative values that comply with experimental data on the reaction rate at the temperatures of 20 and 300 К are found upon taking into account the s-wave contribution alone. In this temperature range, the reaction rates calculated at the resulting two values do not differ substantially. Sizable distinctions arise only at temperatures of a few kelvin units. The problem of choosing one specific value of the logarithmic derivative is solved by comparing the energy dependence of the S matrix with the results of an earlier calculation. Thereby, the proposed procedure can be viewed as a means for correcting calculations in the low-energy region.     

The dynamics of quantum discord and entanglement of two atoms coupled to two spatially separate cavities in cavity QED

We demonstrate that a kind of highly excited state of strongly attractive Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in the spin-1/2 Fermi optical lattice system by a sudden switch of interaction from the strongly repulsive regime to the strongly attractive regime. In contrast to the ground state of the attractive Hubbard model, such a state is the lowest scattering state with no pairing between attractive fermions. With the aid of Bethe-ansatz method, we calculate energies of both the Fermi Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2 ultracold fermions and show that both energies approach to the same limit as the strength of the interaction goes to infinity. By exactly solving the quench dynamics of the Hubbard model, we demonstrate that the Fermi super-Tonks-Girardeau state can be transferred from the initial repulsive ground state very efficiently. This allows the experimental study of properties of Fermi super-Tonks-Girardeau gas in optical lattices.     

Corrections to the Casimir–Polder potential arising from electric octupole coupling

ABSTRACT

Molecular QED theory is employed to derive a generalised formula for the dispersion potential between two molecules with mixed electric multipole polarisability tensors of arbitrary order at each centre. This expression is used to readily extract the pair energy shift between an electric dipole polarisable molecule and a mixed electric dipole–octupole polarisable one, and that between two mixed electric dipole–octupole polarisable species. This is done to see whether these interaction energies give rise to higher-order corrections to the Casimir–Polder potential, as was found in the previously calculated case of the dispersion energy shift between an electric dipole polarisable molecule and an electric octupole polarisable one. Interestingly, for orientationally averaged species, both of the computed interaction energies are independent of the octupole weight-3 term, are retarded, and may be interpreted as higher-order corrections in the fine structure constant to the leading dipole–dipole dispersion potential.     

Dynamics of the nucleon pairing and the alpha-correlation in the valence shell

In conventional theories, the origin of the pairing force and the formation of the superfluid state are treated separately. In real nuclei, however, the nucleon responsible for the attractive interaction is identical with the nucleon that stabilizes the superfluid state. Hence, the superfluid state modifies the attractive force, and this attractive force determines the superfluid state, leading to a feedback effect. In this paper, as a preliminary attempt, we incorporate the effective interaction and formation of the superfluid state into a common self-consistency scheme. Furthermore, the alpha-correlation is included into this scheme as well. Applying the Ginzburg-Landau formalism to this scheme, a dynamics of the nucleon pairing and alpha-correlation is studied.     

Multifractal properties of denaturation process based on Peyrard–Bishop model

DNA has attracted the interest of physicists for a long time. One interesting theoretical question is its melting behavior. The Rényi dimension spectrum of the melting transition of DNA, reveals the multifractal nature of the dynamics of the Peyrard–Bishop model. In this Letter, the effects of different parameters involved in the Peyrard–Bishop model on the multifractal nature of the melting dynamics of a DNA chain are investigated in details. As a result, it can be concluded that not only the best multifractality nature of the model arises from the Morse potential term which is taken in the model but also the multifractal nature of the model is independent of the homogeneity, the length of chain, stacking terms, the thermal bath simulation methods and even the potentials which describe the interaction between the two bases in a pair. Furthermore, our results confirm that, the best potential to describe the interactions between the bases in pairs in the PB and PBD models is the Morse potential.