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。     

Quasi spin pairing and the structure of the Lipkin Model

By introducing the concepts of quasi-spin pairing and quasi-spin seniority, the Lipkin model is extended to a variable number of particles. The properties of quasi-spin pairing are seen to be quite similar to those of ordinary pairing. The quasi-spin seniority allows one to obtain a simple classification of excited multiplets. A “pairing plus monopole” model is studied in connection with the Hartree-Fock theory.     

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.     

A model for so(5) = sp(4) lie algebra

The paper is the continuation of a previous one [Physica Scripta22 (1980), 545–555] devoted to quadrupling in the shell model. We consider here a simple model of the ten- dimensional quasi-spin Lie algebra which is spectrum generating for the quadrupling Hamiltonian. The model allows us to investigate many concrete aspects of the theory of linear representations of the quasi-spin algebra. In particular, we present an explicit construction of the irreducible representation module for the finite dimensional representations, and we consider the direct product of the such irreducible modules.     

A density-matrix approach to thermal equilibrium states

Different solutions for thermal equilibrium states arising from both density matrix properties and quasi-spin conservation were examined in a constrained approach, with reference to a nuclear model.     

等价电子耦合波函数的构造和矩阵元计算

按(U,D)L-LSQ-R耦合格式构造等价电子耦合波函数(这里U(D)是自旋向上(向下)电子的轨道角动量,Q是准旋,R是自旋-准旋交换算符),只需对半满壳层计算耦合波函数,其它电子数耦合波函数可通过准旋升、降算符和自旋-准旋交换算符的作用得到.对p,d,f,g壳层进行了耦合波函数和产生-湮没算符约化矩阵元计算.理论分析和实际计算表明,(U,D)L-LSQ-R耦合格式比一般LS耦合格式更便于计算. 关键词：     

Explicit Expression of Seniority Particle Operator and Its Properties in Quasi-spin Theory

The explicit expression of the seniority particle operator and its properties in the quasi-spin theory of nuclear physics is presented in this paper. The seniority particle operator can be used to construct D-pair in the microscopic theory of interacting boson model to avoid the seniority mixing problem.     

The axial ising model for martensitic transformations and pseudoelasticity

A theory based on the Ising axial model for the martensitic transformation between close-packed structures in an external stress field is proposed. The quasi-spin Hamiltonian was derived for a stratified close-packed crystal which under certain limitations has the form of a Hamiltonian of the ANNNI-model wherein “the exchange integrals” are expressed in terms of the interlayer interaction potentials. The dependence of the strain on the shear stress is calculated for alloys showing the pseudoelasticity effect and it is shown that the number of steps in the deformation curve is defined by the radius of the interlayer interaction. The theory proposed is applied to the explanation of the stress-induced martensitic transformations in Cu-Al-Ni alloys.     

Explicit Expression of Seniority Particle Operator and Its Properties in Quasi-spin Theory

The explicit expression of the seniority particle operator and its properties in the quasi-spin theory of nuclear physics is presented in this paper. The seniority particle operator can be used to construct D-pair in the microscopic theory of interacting boson model to avoid the seniority mixing problem.     

Stage-I fatigue crack studies in order to validate the dislocation-free zone model of fracture for bulk materials

Stage-I fatigue cracks are commonly described by the model of Bilby, Cottrell and Swinden (BCS model). However, since several experimental investigations have shown a dislocation-free zone (DFZ) in front of crack-tips, it is necessary to validate the new DFZ model and to examine the deviations to the BCS model. Therefore, the dislocation density distribution is derived from height profiles of slip lines in front of stage-I fatigue cracks in CMSX4® single crystals measured by contact-mode atomic force microscopy. This is possible, because the cracks are initiated at notches milled by focused ion beam technique directly on slip planes with a high Schmid factor. Consequently, the directions of the Burgers vectors are well known; it is possible to calculate the dislocation density distributions from the height profiles. The measured distributions are compared to the calculated distribution function of the DFZ model proposed by Chang et al. The additionally measured microscopic friction stress of the dislocations is then used to calculate the influence of grain boundaries on the dislocation density distribution in front of stage-I cracks. The calculation is done by the extended DFZ model of Shiue et al. and compared with the measured distribution function in polycrystalline specimens. Finally, the crack-tip sliding displacement as a measure for the crack propagation rate is compared for the DFZ model and the BCS model with the experimentally revealed values. The important result: the often used BCS model does not reflect the experimental measurements. On the contrary, the DFZ model reflects the measurements at stage-I cracks qualitatively and quantitatively.     

Partial widths of fixed generalized seniority spectral distributions

Analytic expressions are derived for the partial widths of the fixed generalized seniority spectral distributions, using an expansion of the hamiltonian in terms of irreducible tensors with respect to both symplectic and quasi-spin groups.     

Coupling of core excitation and single-particle motion in odd-a-nuclei

A physical fractional parentage expansion is presented which can be used to treat the coupling of single-particle and core motion in terms of the physical eigenstates of the core. The antisymmetry requirement is formulated in a subsidiary condition which allows diagonalization of the coupling Hamiltonian in the product space of the core and the extra-core particle. Restriction to a subset of core excitations leads to only approximate fulfillment of the subsidiary condition. The usefulness of the method is tested in the quasi-spin model.     

Generalized Hartree-Fock theory and the Hubbard model

The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn, provide a convenient formulation of a generalized Hartree-Fock variational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we begin by elucidating it. The Hubbard model, with its particle-hole symmetry, is well suited to exploring this theory because BCS states for the attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for nonzero temperature in several cases, notably the half-filled band. For the cases treated here, we can exactly determine all broken and unbroken spatial and gauge symmetries of the Hamiltonian.Dedicated to Philippe Choquard on his 65th birthday.     

Maximum overlap,atomic coherent states and the generator coordinate method

A version of the maximum overlap approach is presented, based on the generator coordinate method. Recourse is made to techniques developed with reference to atomic coherent states. Shape instabilities in quasi-spin two-level models are studied.     

对爆轰CJ模型和ZND模型合理性的讨论

 CJ模型和ZND模型未充分考虑爆轰过程中由于热量瞬时释放所带来的本质变化，它们所确定的爆轰终点状态是所有可能状态中熵值最低的，实现的概率极小。终点状态应该由热力学确定，ZND模型达不到热力学确定的平衡终态。爆轰模型应该同时符合流体力学定律和热力学定律。     

Dynamics of the open BCS model

The dynamics of the strong coupling BCS model, considered as an open system interacting with a thermal bath, is solved rigorously and explicitly in the weak coupling limit and in the infinite-volume limit. The BCS system goes from the normal phase to the ordered phase by bifurcation. Fluctuations around trajectories of intensive observables are Gaussian and Markovian. Thermodynamic phases are global attractors in the physical domain. Structural stability is discussed. The model provides an example of a nonequilibrium statistical mechanical system with phase transition whose irreversible macroscopic dynamics can be calculated exactly from the underlying Hamiltonian quantum mechanics.     

Quantum heat engine cycle working with a strongly correlated electron system

A new model of a quantum heat engine(QHE) cycle is established,in which the working substance consists of an interacting electrons system.One of our purposes is to test the validity of the second law of thermodynamics by this model,which is more general than the spin-1/2 antiferromagnetic Heisenberg model since it would recover the spin model when the on-site Coulomb interaction U is strong enough.On the basis of quantum mechanics and the first law of thermodynamics,we show no violation of the second law of thermodynamics during the cycle.We further study the performance characteristics of the cycle by investigating in detail the optimal relations of efficiency and dimensionless power output.We find that the efficiency of our engine can be expressed as η = 1 - t22/t12 in the large-U limit,which is valid even for a four sites QHE.     

The large-deviation principle and the BCS model

The BCS model is investigated by the functional integrals method and Euclidean quantum field theory technique. It permits us to apply some version of the Large Deviation Principle and get the exact solution which was obtained earlier by the approximation Hamiltonian method.     

The Investigation of Gauge Transformations in the SLq(2) Gauge Field and Thermodynamics Model

Some problems about global transformations in the SLq(2) gauge field and correlative thermodynamics model have been investigated in this paper. We proved that the quantum trace of gauge potential is not gauge-invariant if we compose two GLq(2) gauge transformations. In addition, it has been discovered in SLq(2) thermodynamics model that thermodynamics average of an observable quantity does not satisfy similar gauge invariance. We also found that the thermodynamics average can be only calculated in the case of zero energy gap. This fact shows that the q-deformed energy equation in superconductivity theory is unable to derive naturally from quantum trace model.     

无损贮存及涨罐饱和相热力学模型研究

在低温液体无损贮存及涨罐研究方面,经常采用一种假设容器内气、液相均为饱和相的热力学模型.这种模型比较符合实际,并能够大大简化容器内的热力学状态,是一种比较常用的热力学模型.文中利用一个5m3低温贮罐进行的液氮无损贮存及涨罐试验,对该热力学模型进行了对比研究,讨论了饱和相热力学模型误差产生的原因,对于无损贮存和涨罐研究具...