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Qinghai Wang

Publications and source records attributed to Qinghai Wang.

11 recordsLinked to original sources
arXiv2016

The wage transition in developed countries and its implications for China

The expression "wage transition" refers to the fact that over the past two or three decades in all developed economies wage increases have levelled off. There has been a widening divergence and decoupling between wages on the one hand and GDP per capita on the other hand. Yet, in China wages and GDP per capita climbed in sync (at least up to now). In the first part of the paper we present comparative statistical evidence which measures the extent of the wage transition effect. In a second part we consider the reasons of this phenomenon, in particular we explain how the transfers of labor from low productivity sectors (such as agriculture) to high productivity sectors (such as manufacturing) are the driver of productivity growth, particularly through their synergetic effects. Although rural flight represents only one of these effects, it is certainly the most visible because of the geographical relocation that it implies; it is also the most well-defined statistically. Moreover, it will be seen that it is a good indicator of the overall productivity and attractivity of the non-agricultural sector. Because this model accounts fairly well for the observed evolution in industrialized countries, we use it to predict the rate of Chinese economic growth in the coming decades. Our forecast for the average annual growth of real wages ranges from 4% to 6% depending on how well China will control the development of its healthcare industry.

q-fin.GN↗
arXiv2005

Photons in gapless color-flavor-locked quark matter

We calculate the Debye and Meissner masses of a gauge boson in a material consisting of two species of massless fermions that form a condensate of Cooper pairs. We perform the calculation as a function of temperature, for the cases of neutral Cooper pairs and charged Cooper pairs, and for a range of parameters including gapped quaisparticles, and ungapped quasiparticles with both quadratic and linear dispersion relations at low energy. Our results are relevant to the behavior of photons and gluons in the gapless color-flavor-locked phase of quark matter. We find that the photon's Meissner mass vanishes, and the Debye mass shows a non-monotonic temperature dependence, and at temperatures of order the pairing gap it drops to a minimum value of order sqrt(alpha) times the quark chemical potential. We confirm previous claims that at zero temperature an imaginary Meissner mass can arise from a charged gapless condensate, and we find that at finite temperature this can also occur for a gapped condensate.

hep-ph↗
arXiv2004

The C Operator in PT-Symmetric Quantum Field Theory Transforms as a Lorentz Scalar

A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorentz group as a scalar.

hep-th↗
arXiv2004

Ghost Busting: PT-Symmetric Interpretation of the Lee Model

The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g^2, the square of the renormalized coupling constant, above which g_0^2, the square of the unrenormalized coupling constant, is negative. Thus, for g^2 larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. It was also discovered that in this non-Hermitian regime a new state appears whose norm is negative. This state is called a ghost state. It has always been assumed that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess PT symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having PT symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a new time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this paper the C operator for the Lee model in the ghost regime is constructed exactly in the V/N-theta sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g^2.

hep-th↗
arXiv2004

A Possible Aoki Phase for Staggered Fermions

The phase diagram for staggered fermions is discussed in the context of the staggered chiral Lagrangian, extending previous work on the subject. When the discretization errors are significant, there may be an Aoki-like phase for staggered fermions, where the remnant SO(4) taste symmetry is broken down to SO(3). We solve explicitly for the mass spectrum in the 3-flavor degenerate mass case and discuss qualitatively the 2+1-flavor case. From numerical results we find that current simulations are outside the staggered Aoki phase. As for near-future simulations with more improved versions of the staggered action, it seems unlikely that these will be in the Aoki phase for any realistic value of the quark mass, although the evidence is not conclusive.

hep-lat↗
arXiv2003

Finite-Dimensional PT-Symmetric Hamiltonians

This paper investigates finite-dimensional representations of PT-symmetric Hamiltonians. In doing so, it clarifies some of the claims made in earlier papers on PT-symmetric quantum mechanics. In particular, it is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian.

quant-ph↗
arXiv2002

All Hermitian Hamiltonians Have Parity

It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an eigenstate of P with eigenvalue (-1)^n. Given these properties, it is appropriate to refer to P as the parity operator and to say that H has parity symmetry, even though P may not refer to spatial reflection. Thus, if the Hamiltonian has the form H=p^2+V(x), where V(x) is real (so that H possesses time-reversal symmetry), then it immediately follows that H has PT symmetry. This shows that PT symmetry is a generalization of Hermiticity: All Hermitian Hamiltonians of the form H=p^2+V(x) have PT symmetry, but not all PT-symmetric Hamiltonians of this form are Hermitian.

quant-ph↗
arXiv2002

Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics

In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian PT-symmetric Hamiltonian $H={1\over2}p^2+{1\over2}x^2 +iεx^3$ using perturbative techniques. It is also shown how to construct the operator C for $H={1\over2}p^2+{1\over2}x^2-εx^4$ using nonperturbative methods.

quant-ph↗
arXiv2002

Two-Point Green's Function in PT-Symmetric Theories

The Hamiltonian $H={1\over2} p^2+{1\over2}m^2x^2+gx^2(ix)^δ$ with $δ,g\geq0$ is non-Hermitian, but the energy levels are real and positive as a consequence of ${\cal PT}$ symmetry. The quantum mechanical theory described by $H$ is treated as a one-dimensional Euclidean quantum field theory. The two-point Green's function for this theory is investigated using perturbative and numerical techniques. The Källen-Lehmann representation for the Green's function is constructed, and it is shown that by virtue of ${\cal PT}$ symmetry the Green's function is entirely real. While the wave-function renormalization constant $Z$ cannot be interpreted as a conventional probability, it still obeys a normalization determined by the commutation relations of the field. This provides strong evidence that the eigenfunctions of the Hamiltonian are complete.

hep-th↗
arXiv2001

A Class of Exactly-Solvable Eigenvalue Problems

The class of differential-equation eigenvalue problems $-y''(x)+x^{2N+2}y(x)=x^N Ey(x)$ ($N=-1,0,1,2,3,...$) on the interval $-\infty<x<\infty$ can be solved in closed form for all the eigenvalues $E$ and the corresponding eigenfunctions $y(x)$. The eigenvalues are all integers and the eigenfunctions are all confluent hypergeometric functions. The eigenfunctions can be rewritten as products of polynomials and functions that decay exponentially as $x\to\pm \infty$. For odd $N$ the polynomials that are obtained in this way are new and interesting classes of orthogonal polynomials. For example, when N=1, the eigenfunctions are orthogonal polynomials in $x^3$ multiplying Airy functions of $x^2$. The properties of the polynomials for all $N$ are described in detail.

math-ph↗