超导体中库珀对的SU(2)与Glauber相干态——库珀对与约瑟夫森超流性的量子特性研究

本文利用类自旋算符证明BCS超导基态波函数是单个库珀对SU(2)相干态波函数的直积、且在一定条件下为库珀对体系的SU(2)相干态波函数。若两块处在BCS超导基态的超导体耦合在一起,则体系仍处在SU(2)相干态,且在一定条件下为定态超辐射态。在SU(2)群到谐振子群的收缩下,库珀对的SU(2)相干态变为Glauber相干态。讨论了两种情形下库珀对与约瑟夫森超流性的量子噪声、分布及二阶相关特性。     

Deformation properties of osmium,platinum, mercury isotopes from self-consistent calculations: Influence of the pairing treatment

The deformation properties of several isotopes of the elements Os, Pt and Hg have been computed by means of Hartree-Fock plus BCS calculations. The Hartree-Fock potential has been derived from the Skyrme interaction SIII. Two approximations have been used for the treatment of pairing correlations: the constant (versus deformation) gap method and the constant (versus deformation) pairing matrix element method. A good agreement with experimental data is obtained for ground state deformation properties except for the exact location of the prolate-oblate transition as a function of the neutron number. For one nucleus ¹⁸⁴Hg, the pairing matrix elements have been calculated from the Gogny interaction D1, in order to study their single-particle state — and deformation — dependence. From these results, the validity of the two approximations used for pairing correlations is discussed.     

中子物质中超流性的自能色散效应

利用扩展的 Brueckner- Hartree- Fock理论与推广的 BCS方法研究了自能的色散效应和基态关联对中子物质中超流性和能隙的影响 .研究结果表明 ,自能的色散效应使中子物质中能隙减小;考虑基态关联后 ,超流性将进一步减弱. The effects of the dispersion and ground state correlation of the single particle self-energy on neutron matter superfluidity have been investigated in the framework of the Extended Brueckner-Hartree-Fock and the generalized BCS approaches. A sizable reduction of the energy gap is found due to the energy dependence of the self-energy. And the inclusion of the ground state correlations in the self-energy suppresses further the neutron matter superfluidity.     

Quantum phases in a doped Mott insulator on the Shastry-Sutherland lattice

We propose the projected BCS wave function as the ground state for the doped Mott insulator SrCu2(BO3)2 on the Shastry-Sutherland lattice. At half filling this wave function yields the exact ground state. Adding mobile charge carriers, we find a strong asymmetry between electron and hole doping. Upon electron doping an unusual metal with strong valence bond correlations forms. Hole doped systems are d-wave resonating valence bond superconductors in which superconductivity is strongly enhanced by the emergence of spatially varying plaquette bond order.     

Effects of electron correlation on superconductivity in the Hatsugai–Kohmoto model

Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm. We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space. The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory. The self-consistent equation for the pair potential is derived and solved. Somewhat contrary to expectation, a weak attractive U comparable to the pair potential can destroy the superconductivity, whereas for weak to intermediate repulsive U, the pair potential can be enhanced. The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation. We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors, in contrast to the uncorrelated BCS limit.     

The ground state and the thermodynamics of an extended BCS model of superconductivity

The thermodynamics of an extended BCS model of superconductivity is investigated. A physical system is described by a Hamiltonian containing the BCS interaction and an attractive four-fermion interaction. The four-fermion potential is caused by attractions between Cooper pairs mediated by the phonon field. The weakness of this potential allows the use of perturbation theory. The perturbation expansion was restricted to the first order because in the ground state the second order terms are not larger than 0.5 percent of first order correction for parameters used for calculations. The BCS Hamiltonian is an unperturbed one. The ground state and the thermal properties are examined. As a result the jump in the specific heat is higher than that in the BCS case. Moreover, the squared critical field is larger than the corresponding one in the BCS theory. Additionally, we show connections with the Bogolyubov's mean field approach used earlier in order to investigate general physical consequences of the model.     

Comparison of various extensions of the QRPA formalism for the double-beta decay

We have used a self-consistent version of the BCS + RQRPA method for a systematic study of the double-beta decay of medium-heavy nuclei with 70 A 100. The results have been compared with the previously used approaches, namely the QRPA and the RQRPA approximations. We have shown that inclusion of the quasiparticle correlations at the BCS level reduces ground state correlations in the particle–particle channel of the proton–neutron interaction, resulting in a systematic reduction of the double-beta-decay matrix elements. We also simplified the RQRPA equations significantly obtaining a low-dimensioned set of linear equations for the quasiparticle densities.     

A semi-empirical correlation energy for nuclei

A semi-empirical interaction is used to calculate higher order corrections to the binding energies of even—even nuclei close to the line of stability. These corrections are taken to come from two phonon configurations and are treated as a perturbation with respect to the BCS nuclear ground state which is obtained from applying the energy density method to finite nuclei. The overall correspondence between theory and experiment for the 60 nuclei calculated between A =52 and A =234 is good, with excellent agreement for the non-deformed nuclei situated within the regions A = 72 to 144 and A = 200 to 212. The large correction enegies (several MeV per nucleus on the average) indicate that these correlations are of importance for explaining nuclear binding energies and that it is necessary to include them within energy functional itself. The fact that these correlations come almost exclusively from nucleons close to the fermi surface is also discussed.     

New BCS and renormalized QRPA formalism with application to double beta decay

A new analysis of the renormalized proton–neutron quasiparticle random phase approximation based on simultaneous recalculation of the one-body density matrix and the pairing tensor has been used to study the double beta decay. We demonstrated that inclusion of the quasiparticle correlations at the BCS level reduces ground state correlations in the particle–particle channel of the proton–neutron interaction. We also simplified the RQRPA equations significantly obtaining a low-dimensioned set of linear equations for the quasiparticle densities. The formalism was applied to the double beta decay of ⁷⁶Ge. Received: 4 January 1999 / Revised version: 29 March 1999     

Quantum entanglement in second quantized fermion systems

In this communication we consider the zero temperature properties of entanglement in free and interacting fermion systems following Bogoliubov’s excitation approach. We investigate spin biparticle entanglement in BCS superconductor ground state of electron gas and in EPS state of ³He atoms. The relation between pair-distribution functions and biparticle quantum entanglement is discussed.     

Theoretical evidence for equivalence between the ground states of the strong coupling BCS Hamiltonian and the antiferromagnetic Heisenberg model

By explicitly computing wave function overlap via exact diagonalization in finite systems, we provide evidence indicating that, in the limit of strong coupling, i.e., Delta/t--> infinity the ground state of the Gutzwiller-projected BCS Hamiltonian (accompanied by proper particle-number projection) is identical to the exact ground state of the 2D antiferromagnetic Heisenberg model on the square lattice. This identity is adiabatically connected to a very high overlap between the ground states of the projected BCS Hamiltonian and the t-J model at moderate doping.     

The pairing model

The consequences of the existence of pairing correlations in nuclei are discussed. Special attention is paid to the dynamical aspects of the pairing degree of freedom, as revealed by two-nucleon transfer reactions. These reactions constitute specific probes of the pairing collective modes.The mathematical framework in which the discussion is carried out is the BCS theory and the Random Phase Approximation.The borderline aspect of the subject, which lies between solid state and nuclear physics is emphasized, pointing out the similarities and differences between analogous phenomena of solid state and nuclear physics.     

Temperature and magnetic field dependence of superconductivity in nanoscopic metallic grains

We study pairing correlations in ultrasmall superconductor in the nanoscopic limit by means of a toy model where electrons are confined in a single, multiply degenerate energy level. We solve the model exactly to investigate the temperature and magnetic field dependence of number parity effect (dependence of ground state energy on evenness or oddness of the number of electrons). We find a different parity effect parameter to critical temperature ratio (4 rather than 3.5) which turns out to be consistent with exact solution of the BCS gap equation for our model. This suggests the equivalence between the parity effect parameter and the superconducting gap. We also find that magnetic field is suppressed as temperature increases.     

Conventional BCS,unconventional BCS,and non-BCS hidden dineutron phases in neutron matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant λ, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where λ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.     

Density modulation and superconductivity in a system of fermions

An antisymmetrized product of periodic density modulated one particle functions is investigated as a trial wave function for different local twobody forces. The model is compared with a BCS ground state. For some potentials a lower ground state energy has been found for the density modulated state. In lowest order cluster expansion forces with a hard core have been examined. A liquid-solid transition is indicated for³He at a density near the experimental value.     

一维光晶格中超流Fermi气体基态性质的研究

研究了一维光晶格中超流Fermi气体基态解的性质.在平均场理论框架下,利用超流Fermi体系中原子间相互作用能与晶格势能相互平衡的条件,得到了一维光晶格中超流Fermi气体在整个BEC-BCS跨越区的一组基态解,给出了基态的原子数密度空间分布、总原子数和能量.进一步对系统从BEC端转变到BCS端时的基态解性质进行了深入分析和对比.结果表明,一维光晶格中超流Fermi气体基态分布具有一些特殊的性质,由于Fermi压力,相比而言超流Fermi气体在BCS端的基态原子数密度空间分布较为扩展,平均能量明显偏高.     

Pairing in doped inversion-symmetric Weyl semimetals: a finite temperature analysis from Thouless criterion

In doped Weyl semimetal with inversion symmetry, the two pairing states, i.e., the zero momentum BCS pairing and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing are possible in principle. In this paper we use the standard Thouless criterion for the onset of pairings to investigate the leading pairing instability at the finite temperature. Our results suggest that both BCS and FFLO instabilities are possible depending on the on-site attractive interaction. The competition between the BCS pairing and FFLO pairing is driven by the mutual suppression between density of state near the Fermi surface and finite energy band structure in the whole Brillouin zone. For small and intermediate interaction, the former dominates and supports BCS pairing, while for strong interaction, the latter wins and favors FFLO pairing. We expect our results at the finite temperature can provide some important message to identify the true ground state.     

Exchangeable qubit states

We present a characterisation of the two-site marginals of exchangeable and Bose-exchangeable states and provide an elementary proof for the qubit case. A link between the ground state problem for ferromagnetic mean-field models and the additivity of the maximal two-norm for quantum channels is established. We then analyse the corrections on N-particle symmetric states with respect to the exchangeable ones. The finite-size effects on the average ground state energy of the BCS model are explicitly computed.     

Effect of resonant continuum on pairing correlations in the relativistic approach

A proper treatment of the resonant continuum is to take account of not only the energy of the resonant state, but also its width. The effect of resonant states on pairing correlations is presented in the framework of the relativistic mean-field theory plus Bardeen-Cooper-Schrieffer (BCS) approximation with a constant pairing strength. The study is performed in an effective Lagrangian with the parameter set NL3 for neutron-rich even-even Ni isotopes. Results show that the contribution of the proper treatment of the resonant continuum to pairing correlations for those nuclei close to the neutron drip line is important. The pairing gaps, Fermi energies, pairing correlation energies, and binding energies are considerably affected by a proper consideration of the width of resonant states. The problem of unphysical particle gas, which may appear in the calculation of the traditional mean field plus BCS method for nuclei in the vicinity of the drip line could be well overcome when the pairing correlation is performed by using the resonant states instead of the discretized states in the continuum.PACS: 21.60.-n Nuclear-structure models and methods - 24.10.Jv Relativistic modelsZhong-Yu Ma: Also at Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, PRC and Institute of Theoretical Physics, Beijing 100080, PRC.