In memory of Igor’ Il’ich Sobel’man

Miscellaneous

In memory of Igor’ Il’ich Sobel’man Member of the Editorial Board of JETP Letters from 1969 to 1988     

Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujans modulus 5 modular equation from his Lost Notebook (p. 139 in [R]). Furthermore, we obtained an infinite list of q-identities for all odd moduli; thus, we generalized the result of Ramanujan.Acknowledgements It was indeed hard to trace all the known proofs of (1.1), (1.2) and (1.3). We apologize if some important references are omitted. We would like to thank Jim Lepowsky for conversations on many related subjects. A few years ago Lepowsky and the author were trying to relate classical Rogers-Ramanujan identities and Zhus work [Z]. We also thank Bruce Berndt for pointing us to [BrO] and Steve Milne for bringing [Mi] to our attention.     

SAC-CI方法研究甲基乙烯基硅酮分子激发态1 1A’’, 1 1A’, 2 1A’’结构与性质

采用对称性匹配簇/组态相互作用(symmetry adapted cluster－configuration interaction, SAC－CI)方法, 在6-311++g**基组水平上优化了甲基乙烯基硅酮分子的前三个单激发态1 1A’’, 1 1A’, 2 1A’’的平衡几何结构, 比较三个激发态的电荷分布, 最高占据轨道, 最低空轨道, 能隙等结构特性. 研究发现, 1 1A’ 态能隙差最小, 电子容易发生跃迁. 计算了三个单重激发态相应的振动光谱, 得出其振动模式. 从甲基乙烯基硅酮分子激发态结构特性, 电荷分布, 极强位置振动模式等方面分析了其断键机制.     

紫外干涉滤光片2280A’2537A’

一、前言紫外滤光片在生物化学,分析研究中有广泛的应用,目前国内制备还处在实验室阶段。对于2600～4000A波段可以采用和可见区相同的常规制作方法,即用PbF_2、Na_3AlF_6等材料镀出全介质滤光片,再加上紫外滤光玻璃UG5、UG11(德)或ZWB_2(中)组合而成。透过率国外报导可达50%,但由于环氧树脂在低于3700A     

CLEO’92和QELS’92会议介绍

由美国IEEE激光、光电子学会和美国光学学会举办的第十二届激光和光电子会议(CLEO’92),第三届量子电子学和激光科学会议(QELS’92)于1992年5月10日～15日在美国加州Anaheim举行。出席会议人数达6916人。CLEO’92会议上共发表文章685篇,特邀论文65篇,内容涉及各种激光器、元器件、系统及其应用。QELS’92会议上总共有288篇论文,77篇特邀论文,会议强调激光科学和量子电子学的基础研究。另外还有一个大型展览会,展出商用、工业用激光器,光电子元器件。     

Stern-Gerlach Experiment’s Interpretations and Noether’s Theorem

In this paper we suggest that theories treating two interacting objects in a different manner (for instance electromagnetic field of a laser classically, and the interacting atom as a quantum object) should be called “mixed”. Mixed theories are not so rare in Physics. One just should look at the whole area of Atomic, Molecular and Optical Physics in which mixed theories are often used, and, also, theories including quantum object interacting with classical surroundings that are the subject of our present discussion: the field of Quantum decoherence, when applied to resolving the dilemma should classical trajectories be used in explaining the Stern-Gerlach experiment or not. Consequently we are proving one improved corollary to Noether’s theorem, stating that mixed theories are not supporting the law of conservation of angular momentum and spin, as they are not based on the isotropy of space-time.     

Minkowski’s tensor or Abraham’s tensor?

It is proved that the question in the article title has an unambiguous answer, i.e., Abraham’s tensor.     

O + NH反应在3A’’和1A’’势能面上的量子含时波包动力学研究

对于O + NH反应,在3A’’和1A’’ 势能面（Guadagnini R, Schatz G C, Walch S P. Global potential energy surface for the lowest 1A’, 3A’’, and 1A’’ states of HNO [J]. J. Chem. Phys., 1995,10:774）上,我们运用coupled state or centrifugal sudden (CS)近似和close coupling or Coriolis coupled (CC)方法进行了量子动力学计算。通过比较两种方法得到的总的反应几率,我们发现对于两个势能面上的标题反应,CS近似是失效的。我们还讨论了用CS和CC方法得到的速率常数,并进行了结果比较。     

Relative entropy of entanglement of two-qubit ’X’ states

Two closest single-qubit states could be diagonalised by the same unitary matrix,which helps to find the relative entropy of entanglement of a two-qubit ’X’ state.We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ’X’ state.This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states,such as pure states,Werner states,and so on.     

‘‘Extrinsic’’ and ‘‘Intrinsic’’ Data in Quantum Measurements: Asymptotic Convex Decomposition of Positive Operator Valued Measures

We study the problem of separating the data produced by a given quantum measurement (on states from a memoryless source which is unknown except for its average state), described by a positive operator valued measure (POVM), into a meaningful (intrinsic) and a not meaningful (extrinsic) part. We are able to give an asymptotically tight separation of this form, with the intrinsic data quantified by the Holevo mutual information of a certain state ensemble associated to the POVM and the source, in a model that can be viewed as the asymptotic version of the convex decomposition of POVMs into extremal ones. This result is applied to a similar separation therorem for quantum instruments and quantum operations, in their Kraus form. Finally we comment on links to related subjects: we stress the difference between data and information (in particular by pointing out that information typically is strictly less than data), derive the Holevo bound from our main result, and look at its classical case: we show that this includes the solution to the problem of extrinsic/intrinsic data separation with a known source, then compare with the well–known notion of sufficient statistics. The result on decomposition of quantum operations is used to exhibit a new aspect of the concept of entropy exchange of an open dynamics. An appendix collects several estimates for mixed state fidelity and trace norm distance, that seem to be new, in particular a construction of canonical purification of mixed states that turns out to be valuable to analyze their fidelity.     

‘Twisted’ electrons

Electrons have played a significant role in the development of many fields of physics during the last century. The interest surrounding them mostly involved their wave-like features prescribed by the quantum theory. In particular, these features correctly predict the behaviour of electrons in various physical systems including atoms, molecules, solid-state materials, and even in free space. Ten years ago, new breakthroughs were made, arising from the new ability to bestow orbital angular momentum (OAM) to the wave function of electrons. This quantity, in conjunction with the electron’s charge, results in an additional magnetic property. Owing to these features, OAM-carrying, or twisted, electrons can effectively interact with magnetic fields in unprecedented ways and have motivated materials scientists to find new methods for generating twisted electrons and measuring their OAM content. Here, we provide an overview of such techniques along with an introduction to the exciting dynamics of twisted electrons.     

Rainbow’s stars

In recent years, a growing interest in the equilibrium of compact astrophysical objects like white dwarf and neutron stars has been manifested. In particular, various modifications due to Planck-scale energy effects have been considered. In this paper we analyze the modification induced by gravity’s rainbow on the equilibrium configurations described by the Tolman–Oppenheimer–Volkoff (TOV) equation. Our purpose is to explore the possibility that the rainbow Planck-scale deformation of space-time could support the existence of different compact stars.     

Rovelli’s World

Carlo Rovelli’s inspiring “Relational Quantum Mechanics” serves several aims at once: it provides a new vision of what the world of quantum mechanics is like, and it offers a program to derive the theory’s formalism from a set of simple postulates pertaining to information processing. I propose here to concentrate entirely on the former, to explore the world of quantum mechanics as Rovelli depicts it. It is a fascinating world in part because of Rovelli’s reliance on the information-theory approach to the foundations of quantum mechanics, and in part because its presentation involves taking sides on a fundamental divide within philosophy itself.     

Stoney’s Electron

George Johstone Stony, th man who maned the electron, was led to the concept of a fundamental unit of electic charge by combining electro-chemistry with the kinetic theory of gases. But his understanding was incomplete (so the discovery of the electron is associated wit JJ Thomsons determination of its charge to mass ratio in October 1897)     

High-energy strong interactions: from ‘hard’ to ‘soft’

We discuss the qualitative features of the recent data on multiparticle production observed at the LHC. The tolerable agreement with Monte Carlos based on LO DGLAP evolution indicates that there is no qualitative difference between ‘hard’ and ‘soft’ interactions; and that a perturbative QCD approach may be extended into the soft domain. However, in order to describe the data, these Monte Carlos need an additional infrared cutoff k _min with a value k _min∼2–3 GeV which is not small, and which increases with collider energy. Here we explain the physical origin of the large k _min. Using an alternative model which matches the ‘soft’ high-energy hadron interactions smoothly on to perturbative QCD at small x, we demonstrate that this effective cutoff k _min is actually due to the strong absorption of low k _t partons. The model embodies the main features of the BFKL approach, including the diffusion in transverse momenta, ln k _t , and an intercept consistent with resummed next-to-leading log corrections. Moreover, the model uses a two-channel eikonal framework, and includes the contributions from the multi-Pomeron exchange diagrams, both non-enhanced and enhanced. The values of a small number of physically-motivated parameters are chosen to reproduce the available total, elastic and proton dissociation cross section (pre-LHC) data. Predictions are made for the LHC, and the relevance to ultra-high-energy cosmic rays is briefly discussed. The low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are calculated in this framework, using the parameters which describe the high-energy pp and p[`(p)]p\bar{p} ‘soft’ data. Comparison with the PDFs obtained from the global parton analyses of deep inelastic and related hard scattering data and from diffractive deep inelastic data looks encouraging.