Faddeev-Jackiw and the improved methods in quantization of the superconductive system

In this paper, we give the overview on Faddeev-Jackiw method and its improved one, as well as the relative studies recently and realize quantization of the superconductive system by the two methods, we get the same results by the two disposal methods. Furthermore, at convenience of the familiar study in this system, we take it as the application example and compare the two methods by dealing with this system from different aspects, demonstrate the improved Faddeev-Jackiw method is effective and significative, and represent the superiorities of the improved Faddeev-Jackiw method. We show that the improved method may simplify investigations of different complicated constrained systems.     

A strategy for multivariate calibration based on modified single-index signal regression: Capturing explicit non-linearity and improving prediction accuracy

In this paper, a modified single-index signal regression (mSISR) method is proposed to construct a nonlinear and practical model with high-accuracy. The mSISR method defines the optimal penalty tuning parameter in P-spline signal regression (PSR) as initial tuning parameter and chooses the number of cycles based on minimizing root mean squared error of cross-validation (RMSECV). mSISR is superior to single-index signal regression (SISR) in terms of accuracy, computation time and convergency. And it can provide the character of the non-linearity between spectra and responses in a more precise manner than SISR. Two spectra data sets from basic research experiments, including plant chlorophyll nondestructive measurement and human blood glucose noninvasive measurement, are employed to illustrate the advantages of mSISR. The results indicate that the mSISR method (i) obtains the smooth and helpful regression coefficient vector, (ii) explicitly exhibits the type and amount of the non-linearity, (iii) can take advantage of nonlinear features of the signals to improve prediction performance and (iv) has distinct adaptability for the complex spectra model by comparing with other calibration methods. It is validated that mSISR is a promising nonlinear modeling strategy for multivariate calibration.     

Constraints on operator ordering from third quantization

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.     

A hidden analytic structure of the Rabi model

The Rabi model describes the simplest interaction between a cavity mode with a frequency ω_c${\omega }_c$ and a two-level system with a resonance frequency ω₀${\omega }_0$. It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to Δ=ω₀/(2ω_c)=0$\Delta ={\omega }_0/\left(2{\omega }_c\right)=0$, which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy ?$?$, which are orthogonal on an equidistant lattice. A non-zero value of Δ$\Delta$ leads to non-classical discrete orthogonal polynomials ?_k(?)${?}_k\left(?\right)$ and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model. The number of ca. 1350 calculable energy levels per parity subspace obtained in double precision (cca 16 digits) by an elementary stepping algorithm is up to two orders of magnitude higher than is possible to obtain by Braak’s solution. Any first n$n$ eigenvalues of the Rabi model arranged in increasing order can be determined as zeros of ?_N(?)${?}_N\left(?\right)$ of at least the degree N=n+n_t$N=n+n_t$. The value of n_t>0$n_t>0$, which is slowly increasing with n$n$, depends on the required precision. For instance, n_t?26$n_t?26$ for n=1000$n=1000$ and dimensionless interaction constant κ=0.2$\kappa =0.2$, if double precision is required. Given that the sequence of the l$l$th zeros x_nl$x_{nl}$’s of ?_n(?)${?}_n\left(?\right)$’s defines a monotonically decreasing discrete flow with increasing n$n$, the Rabi model is indistinguishable from an algebraically solvable model in any finite precision. Although we can rigorously prove our results only for dimensionless interaction constant κ<1$\kappa <1$, numerics and exactly solvable example suggest that the main conclusions remain to be valid also for κ≥1$\kappa \ge 1$.     

Geodesic mode instability driven by the electron current in tokamak plasmas

Effect of the parallel electron current on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current modeled by shifted Maxwell distribution may overcome the phase velocity threshold and ion Landau damping thus resulting in the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity Rqω. The instability occurs due to its cross term of the current with the ion diamagnetic drift. Possible applications to tokamak experiments are discussed.     

Hawking radiation and black hole spectroscopy in Hořava–Lifshitz gravity

Hawking radiation from the black hole in Ho?ava–Lifshitz gravity is discussed by a reformulation of the tunneling method given in Banerjee and Majhi (2009) [17]. Using a density matrix technique the radiation spectrum is derived which is identical to that of a perfect black body. The temperature obtained here is proportional to the surface gravity of the black hole as occurs in usual Einstein gravity. The entropy is also derived by using the first law of black hole thermodynamics. Finally, the spectrum of entropy/area is obtained. The latter result is also discussed from the viewpoint of quasi-normal modes. Both methods lead to an equispaced entropy spectrum, although the value of the spacing is not the same. On the other hand, since the entropy is not proportional to the horizon area of the black hole, the area spectrum is not equidistant, a finding which also holds for the Einstein–Gauss–Bonnet theory.     

Projective Structure,Symplectic Connection and Quantization

Let X be a connected Riemann surface equipped with a projective structure . Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using , this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using , a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed.     

Jackiw-Pi模型的新涡旋解

运用φ映射拓扑流理论研究了Jackiw-Pi模型中的自对偶方程，得到一个静态的自对偶解满足带有δ函数项的刘维尔方程, 从而得到了一个完整的带有拓扑信息的涡旋解,自然给出了磁通量子化.     

Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

Characterization of the Landau expansion equation for SrTiO3 under pressure

This work focuses on the characterization of the expansion of Landau's main equation for Pm3?m structures, which are transformed with symmetry subgroups, associated with M+3 and R+4 special points of the Brillouin zone, under hydrostatic pressure. This solution has been adapted to include the general influence of hydrostatic pressure and the evolution of the order parameter. We present a simple scheme in order to search systematically the ground state of all perovskite structures derivable from octahedral rotations under high pressure. We have applied this adaptation to SrTiO₃ perovskite. Results of the characterization of Landau′s equation for the cubic-tetragonal phase transition under pressure are discussed here.