Topology of the superconducting order under pairing repulsion

The superconducting state with a large momentum of a pair in a doped insulator is controlled by the features of Coulomb pairing associated with the suppression of small momentum transfers during scattering owing to electron-phonon interaction and of large transfers due to redistribution of the spectral weight among the superconducting or the insulating branches of the elementary excitation spectrum. Superconductivity emerges when the characteristic energy of the pairing interaction has an upper bound. The solutions obtained for a self-consistent equation with a simple structure of the degenerate kernel are antisymmetric and symmetric relative to inversion of the momentum of relative motion of a pair. The orbital symmetry of the singlet superconducting order is analyzed.     

Fate of order parameter in the inflationary universe

We evaluate the friction term of the evolution equation of the order parameter in the new inflationary universe scenario. It is shown that the friction force is too weak so that the order parameter travels many time around minima of the Coleman-Weinberg potential. It causes unwanted large scale inhomogeneities. Reheating of the universe is also discussed.     

Relaxation of the order parameter in the BCS model

Relaxation of the order parameter of a “pure” superconductor due to the electron-phonon interaction is considered in a homogeneous case. The process of relaxation has a simple physical interpretation as the variation of the number of electrons in Cooper pairs due to excitation collisions accompanied by the absorption and emission of phonons. It is shown that, in the neighborhood of the critical temperature, the relaxation time of the modulus of the order parameter is much greater than the time between excitation collisions.     

Topology of smectic order on compact substrates

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of the 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on a torus as well as on a sphere, we find that both systems exhibit many topologically distinct low energy states that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area. For a smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.     

On finite-size scaling of the order parameter in percolation

Finite-size scaling of the order parameter O in the disordered phase is presented for percolation in 2d and 3d and compared to the behavior of the magnetization of the Ising model. We find that the order parameter O grows logarithmically with the system size L for p < p_c and thus the analogy with the Ising model is not complete. Furthermore we find evidence for scaling behavior of the type O ～ L^?y/v (p_c ? p)^β?y where the exponent y is not dv/2 as in the Is ing case.     

Symmetry of the order parameter in the UGe2 superconductor

For the UGe₂ ferromagnetic superconductor, the forms of the order parameter are determined with allowance for the crystal symmetry and with the assumption that a strong spin-orbit interaction is present in the system. The limiting case corresponding to the immediate vicinity of the simultaneous transition to the superconducting and ferromagnetic phases is considered. The opposite limit corresponding to a wide separation of the Fermi surfaces with opposite spin orientations is considered as well. Possible effects of the ferromagnetic domain structure on the properties of UGe₂ in the superconducting state are discussed.     

Supersymmetric representation of order parameter fluctuations

We consider the representation of homogeneous and heterophase fluctuations based on the supersymmetric theory of fields. It is shown that the problem reduces to a mixture of noninteracting Fermi and Bose gases. The thermodynamic features resulting from each type of fluctuations are determined, as well as the correlation functions of the spatial distributions of the order parameter and interphase boundaries.Suma Physicotechnical Institute. RETO Scientific-Industrial Complex. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 49–53, April, 1994.     

Higher order corrections and the scale parameter in QCD

I estimate the influence of the higher order corrections on the determination of the scale parameter Λ². I find a sizeable effect (a reduction of Λ² by a factor 3 to 4). This factor can be relevant in the comparison of Λ² with the characteristic confinement parameters.     

Helicity order: hidden order parameter in URu2Si2

We propose that the "hidden order parameter" in URu2Si2 is a helicity order that must arise if the Pomeranchuk criteria for the spin-antisymmetric Landau parameters with respect to the stability of a Fermi liquid state are violated. In a simple model, we calculate the specific heat, the linear and nonlinear magnetic susceptibilities, and the change of transition temperature in a magnetic field with such an order parameter, and obtain quantitative agreement with experiments in terms of two parameters extracted from the data. The peculiar temperature dependence of the NMR linewidth and the nature of the loss of excitations in the ordered phase seen by neutron scattering are also explained, and experiments are suggested to directly confirm the proposed order parameter.     

The order parameter in a spin glass

Various possible precise definitions of an Edwards-Anderson type of order parameter for an Ising model spin glass are considered, using boundary conditions for a finite system, states of an infinite system, and a duplicate-system approach. Several of these definitions are shown to yield identical results.     

Superconductor order parameter symmetry in UPd Al

The heavy fermion compound UPd₂Al₃ has attracted much interest on account of the coexistence of antiferromagnetism and superconductivity at temperatures below 2 K. The antiferromagnetic fluctuations provide, principally via inelastic neutron scattering, a window on the low frequency dynamics in this material. By an analysis of neutron scattering data, and taking into consideration results from other experimental probes, it is suggested which sheet(s) of the f-electron Fermi surface may play an active role in forming the superconducting state in UPd₂Al₃. The proposed scheme sheds new light on previously reported anomalies in this material. Received 16 July 1999     

On the relaxation of the order parameter in the BCS model

The relaxation of the nonequilibrium order parameter (wave function of pairs) of a “pure” superconductor is considered for the homogeneous case. The relaxation is due to the electron-phonon interaction. The orderparameter relaxation time is shown to be much longer than the time interval between electron-electron collisions. This relation is explained by the smallness of the superconducting transition temperature compared to both the Fermi energy and the Debye energy in the BCS model.     

数量级在物理实验中的应用

介绍了数量级在物理实验设计、实验失败原因分析、误差分析及实验结果判断方面的应用．     

Dynamical vanishing of the order parameter in a fermionic condensate

We analyze the dynamics of a condensate of ultracold atomic fermions following an abrupt change of the pairing strength. At long times, the system goes to a nonstationary steady state, which we determine exactly. The superfluid order parameter asymptotes to a constant value. We show that the order parameter vanishes when the pairing strength is decreased below a certain critical value. In this case, the steady state of the system combines properties of normal and superfluid states -- the gap and the condensate fraction vanish, while the superfluid density is nonzero.     

Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model

We prove that if _N is the Sherrington-Kirkpatrick (SK) Hamiltonian and the quantity converges in the variance to a nonrandom limit asN, then the mean free energy of the model converges to the expression obtained by SK. Since this expression is known not to be correct in the low-temperature region, our result implies the non-self-averaging of the order parameter of the SK model. This fact is an important ingredient of the Parisi theory, which is widely believed to be exact. We also prove that the variance of the free energy of the SK model converges to zero asN, i.e., the free energy has the self-averaging property.See the Remarks after the proof of Theorem 1 on the validity of our results for more general distributions ofJ _ij .