Determination of the Scattering Amplitudes of Schrödinger Operators from the Cross-Sections,a New Approach

In this Letter we show how the scattering amplitudes of nonrelativistic one-particle Schrödinger operators with a scalar (not necessarily rotation invariant) potential may be obtained from the scattering cross-sections for the system where a scalar potential is added and whose scattering amplitudes are known explicitly.     

莫比乌斯变换及其物理应用

北京科技大学陈难先教授把数论中的一条古老定理:莫比乌斯变换推广到普通函数并创造性地用之于物理学中许多反问题,取得了巨大成功。在此以更直观和易于理解的方式导出陈氏定理,并通过一些具体实例展示其应用前景。     

On the thermodynamicV-representability of one-particle density matrices

We consider thermodynamicallyV-representable one-matrices, i. e., one-particle density matrices that are obtained by reducing the Gibbs grand canonical density matrix of a quantum mechanical many-particle system subject to a suitable external potential, and show them to obey an inequality lower bounding their eigenvalues in terms of those of the one-particle kinetic energy operator. The result imposes a severe constraint on the asymptotic behavior of the eigenvalues of any one-matrix to beV-representable. For noninteracting particles, the corresponding upper bound is also proven, implying that a one-matrix can be interactionlesslyV-representable for at most one temperature. We expect the upper bound to be valid more generally, as is illustrated by a model of coupled harmonic oscillators where theV-representable one-matrices can be explicitly calculated, and discuss its implications for certain aspects of density-matrix functional theory.     

The Bell Theorem as a Special Case of a Theorem of Bass

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found 10 years earlier by Bass and stated in full generality by Vorob’ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the Bell inequalities may be violated even for objective local random variables.     

Cumulants in perturbation expansions for non-equilibrium field theory

The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally, a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system.     

Scasimir Operator,Scentre and Representations of Uq(osp(1|2))

Recently, Borchers has shown that in a theory of local observables, certain unitary and antiunitary operators, which are obtained from an elementary construction suggested by Bisognano and Wichmann, have the same commutation relations with translation operators as Lorentz boosts and P₁CT operators would have, respectively. It is concluded from this that as soon as the operators considered implement any symmetry, this symmetry can be fixed up to at most some translation. As a symmetry, any unitary or antiunitary operator is admitted under whose adjoint action any algebra of local observables is mapped onto an algebra which can be localized somewhere in Minkowski space.     

Inference in quantum physics

In quantum physics all experimental information is discrete and stochastic. But the values of physical quantities are considered to depict definite properties of the physical world. Thus physical quantities should be identified with mathematical variables which are derived from the experimental data, but which exhibit as little randomness as possible. We look for such variables in two examples by investigating how it is possible to arrive at a value of a physical quantity from intrinsically stochastic data. With the aid of standard probability calculus and elementary information theory, we are necessarily led to the quantum theoretical phases and state vectors as the first candidates for physical quantities.     

Why is \mathcal{CPT} Fundamental?

Lüders and Pauli proved the theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the transform of any relativistic field without calculating , and separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary.     

Multiphoton and tunneling ionization of atoms in an intense laser field

We study the ionization probabilities of atoms by a short laser pulse with three different theoretical methods,i.e.,the numerical solution of the time-dependent Schro¨dinger equation(TDSE),the Perelomov-Popov-Terent’ev(PPT) theory,and the Ammosov-Delone-Krainov(ADK) theory.Our results show that laser intensity dependent ionization probabilities of several atoms(i.e.,H,He,and Ne) obtained from the PPT theory accord quite well with the TDSE results both in the multiphoton and tunneling ionization regimes,while the ADK results fit well to the TDSE data only in the tunneling ionization regime.Our calculations also show that laser intensity dependent ionization probabilities of a H atom at three different laser wavelengths of 600 nm,800 nm,and 1200 nm obtained from the PPT theory are also in good agreement with those from the TDSE,while the ADK theory fails to give the wavelength dependence of ionization probability.Only when the laser wavelength is long enough,will the results of ADK be close to those of TDSE.     

Erratum to “Bayesian methods for parameter estimation in effective field theories” [Ann. Phys. 324 (2009) 682–708]

We have discovered an error in the numerical calculations for the extraction of parameters from the nucleon mass “data” presented in Sections 4 and 5 of our paper [M.R. Schindler, D.R. Phillips, Ann. Phys. 324 (2009) 682. Available from: <hep-ph/0808.3643>]. We present the corrected results and discuss the implications. We stress that the material presented in Sections 1–3 of our paper [M.R. Schindler, D.R. Phillips, Ann. Phys. 324 (2009) 682. Available from: <hep-ph/0808.3643>] is unaffected.     

Application of information theory to the design of line-scan and sensor-array imaging systems

Information theory is used to assess the performance of line-scan and sensor-array imaging systems as a function of their spatial response, sensitivity, and sampling and quantization intervals. Computational results for the statistical properties of random radiance fields provide general guidelines for optimizing the information efficiency of image data acquisition, processing and reconstruction systems.     

Bayesian methods for parameter estimation in effective field theories

We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes’ theorem together with the principle of maximum entropy to account for the prior information that these parameters should be natural, i.e., O(1) in appropriate units. Marginalization can then be employed to integrate the resulting probability density function (pdf) over the EFT parameters that are not of specific interest in the fit. We also explore marginalization over the order of the EFT calculation, M, and over the variable, R, that encodes the inherent ambiguity in the notion that these parameters are O(1). This results in a very general formula for the pdf of the EFT parameters of interest given a data set, D. We use this formula and the simpler “augmented χ²” in a toy problem for which we generate pseudo-data. These Bayesian methods, when used in combination with the “naturalness prior”, facilitate reliable extractions of EFT parameters in cases where χ² methods are ambiguous at best. We also examine the problem of extracting the nucleon mass in the chiral limit, M₀, and the nucleon sigma term, from pseudo-data on the nucleon mass as a function of the pion mass. We find that Bayesian techniques can provide reliable information on M₀, even if some of the data points used for the extraction lie outside the region of applicability of the EFT.