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Wen-Du Li

Publications and source records attributed to Wen-Du Li.

33 records · Page 2Linked to original sources
arXiv2019

Geodesic dual spacetime

A duality between spacetime manifolds, the geodesic duality, is introduced. Two manifolds are geodesic dual, if the transformation between their metrics is also the transformation between their geodesics. That is, the transformation that transforms the metric to the metric of the dual manifold is also the transformation that transforms the geodesic to the geodesic of the dual manifold. On the contrary, for nondual spacetime manifolds, a geodesic is no longer a geodesic after the transformation between the metrics. We give a general result of the duality between spacetime manifolds with diagonal metrics. The geodesic duality of spherically symmetric spacetime are discussed for illustrating the concept. The geodesic dual spacetime of the Schwarzschild spacetime and the geodesic dual spacetime of the Reissner-Nordström spacetime are presented.

gr-qc↗
arXiv2018

Acoustic scattering theory without large-distance asymptotics

In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the exact result, is used to describe a scattering process. The information of the distance between the target and the observer, however, is lost in the large-distance asymptotic approximation. In this paper, we provide a rigorous theory of acoustic scattering without the large-distance asymptotic approximation. The acoustic scattering treatment developed in this paper provides an improved description for the acoustic wave outside the target. Moreover, as examples, we consider acoustic scattering on a rigid sphere and on a nonrigid sphere. We also illustrate the influence of the near target effect on the angular distribution of outgoing waves. It is shown that for long wavelength acoustic scattering, the near target effect must be reckoned in.

physics.class-ph↗
arXiv2018

Quantum Newton duality

Newton revealed an underlying duality relation between power potentials in classical mechanics. In this paper, we establish the quantum version of the Newton duality. The main aim of this paper is threefold: (1) first generalizing the original Newton duality to more general potentials, including general polynomial potentials and transcendental-function potentials, 2) constructing a quantum version of the Newton duality, including power potentials, general polynomial potentials, transcendental-function potentials, and power potentials in different spatial dimensions, and 3) suggesting a method for solving eigenproblems in quantum mechanics based on the quantum Newton duality provided in the paper. The classical Newton duality is a duality among orbits of classical dynamical systems. Our result shows that the Newton duality is not only limited to power potentials, but a more universal duality relation among dynamical systems with various potentials. The key task of this paper is to construct a quantum Newton duality, the quantum version of the classical Newton duality. The quantum Newton duality provides a duality relations among wave functions and eigenvalues. As applications, we suggest a method for solving potentials from their Newtonianly dual potential: once the solution of a potential is known, the solution of all its dual potentials can be obtained by the duality transformation directly. Using this method, we obtain a series of exact solutions of various potentials. In appendices, as preparations, we solve the potentials which is solved by the Newton duality method in this paper by directly solving the eigenequation.

math-ph↗
arXiv2017

A 1+5-dimensional gravitational-wave solution: curvature singularity and spacetime singularity

We solve a $1+5$-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities.

gr-qc↗
arXiv2017

Why the entropy of spacetime is independent of species of particles -- the species problem

The Hawking radiation emits all species of particles, but the Bekenstein-Hawking entropy is independent of the number of the species of particles. This is the so-called species problem --- a puzzling problem for a long time. In this paper, we suggest a solution to this problem. A result of the scheme is that the black hole atmosphere has a mass equaling 3/8 mass of a classical Schwarzschild black hole, which agrees with 't Hooft's brick wall model.

gr-qc↗
arXiv2016

Renormalization for singular-potential scattering

In the calculation of quantum-mechanical singular-potential scattering, one encounters divergence. We suggest three renormalization schemes, dimensional renormalization, analytic continuation approach, and minimal-subtraction scheme to remove the divergence.

quant-ph↗
arXiv2016

Covariant perturbation expansion of off-diagonal heat kernel

Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In literature, only diagonal heat kernels are calculated based on the covariant perturbation expansion.

cond-mat.stat-mech↗
arXiv2015

Thermo field dynamics approach for entropy of spacetime

A thermo field dynamics approach for calculating the entropy of a spacetime is suggested. It is exemplified through the Rindler spacetime, the Milne spacetime, the Boulware spacetime, and the Minkowski spacetime with a moving mirror that the entropy of a spacetime is equal to the entropy of a thermo quantum field with the same temperature of the spacetime we study. This in fact suggests an thermo field dynamics approach of calculating the entropy of a spacetime. In this approach, the entropy of a spacetime is an expectation value of the entropy operator on a thermo vacuum state. The thermo vacuum state is the vacuum state on the maximal manifold which is the maximal analytic extension of the spacetime we study.

gr-qc↗
arXiv2015

Scattering theory without large-distance asymptotics in arbitrary dimensions

In conventional scattering theory, by large-distance asymptotics, at the cost of losing the information of the distance between target and observer, one imposes a large-distance asymptotics to achieve a scattering wave function which can be represented explicitly by a scattering phase shift. In this paper, without large-distance asymptotics, we establish an arbitrary-dimensional scattering theory. Arbitrary-dimensional scattering wave functions, scattering boundary conditions, cross sections, and phase shifts are given without large-distance asymptotics. The importance of an arbitrary-dimensional scattering theory is that the dimensional renormalization procedure in quantum field theory needs an arbitrary-dimensional result. Moreover, we give a discussion of one- and two-dimensional scatterings.

math-ph↗
arXiv2015

Heat-kernel approach for scattering

An approach for solving scattering problems, based on two quantum field theory methods, the heat kernel method and the scattering spectral method, is constructed. This approach converts a method of calculating heat kernels into a method of solving scattering problems. This allows us to establish a method of scattering problems from a method of heat kernels. As an application, we construct an approach for solving scattering problems based on the covariant perturbation theory of heat-kernel expansions. In order to apply the heat-kernel method to scattering problems, we first calculate the off-diagonal heat-kernel expansion in the frame of the covariant perturbation theory. Moreover, as an alternative application of the relation between heat kernels and partial-wave phase shifts presented in this paper, we give an example of how to calculate a global heat kernel from a known scattering phase shift.

hep-th↗
arXiv2015

Scattering theory without large-distance asymptotics: scattering boundary condition

By large-distance asymptotics, in conventional scattering theory, at the cost of losing the information of the distance between target and observer, one arrives at an explicit expression for scattering wave functions represented by a scattering phase shift. In the present paper, together with a preceding paper (T. Liu,W.-D. Li, and W.-S. Dai, JHEP06(2014)087), we establish a rigorous scattering theory without imposing large-distance asymptotics. We show that even without large-distance asymptotics, one can also obtain an explicit scattering wave function represented also by a scattering phase shift, in which, of course, the information of the distance is preserved. Nevertheless, the scattering amplitude obtained in the preceding paper depends not only on the scattering angle but also on the distance between target and observer. In this paper, by constructing a scattering boundary condition without large-distance asymptotics, we introduce a scattering amplitude, like that in conventional scattering theory, depending only on the scattering angle and being independent of the distance. Such a scattering amplitude, when taking large-distance asymptotics, will recover the scattering amplitude in conventional scattering theory. The present paper, with the preceding paper, provides a complete scattering theory without large-distance asymptotics.

math-ph↗
arXiv2014

Statistical problem of ideal gas in general 2-dimensional regions

In this paper, based on the conformal mapping method and the perturbation theory, we develop a method to solve the statistical problem within general 2-dimensional regions. We consider some examples and the numerical results and fitting results are given. We also give the thermodynamic quantities of the general 2-dimensional regions, and compare the thermodynamic quantities of the different regions.

physics.gen-ph↗
arXiv2014

Scattering theory without large-distance asymptotics

In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function and the Bessel function with the sine functions so that one can achieve an explicit result. Nevertheless, after such a treatment, the information of the distance between target and observer is inevitably lost. In this paper, we show that such a precondition is not necessary: without losing any information of distance, one can still obtain an explicit result of a scattering rigorously. In other words, we give an rigorous explicit scattering result which contains the information of distance between target and observer. We show that at a finite distance, a modification factor --- the Bessel polynomial --- appears in the scattering amplitude, and, consequently, the cross section depends on the distance, the outgoing wave-front surface is no longer a sphere, and, besides the phase shift, there is an additional phase (the argument of the Bessel polynomial) appears in the scattering wave function.

math-ph↗