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.     

‘‘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.     

Simulation of quantum wells with ‘spikes’ and ‘dips’

The use of thin high-bandgap ‘spikes’ or thin low-bandgap ‘dips’ inside conventional rectangular quantum wells (QWs) gives supplementary flexibility in engineering intra- and inter-band energy level separation. The paper presents simulation and experimental studies on the effects of ‘spikes’ and ‘dips’ on the fundamental quantum well properties.     

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.     

Heaven and Earth – ‘Madonne col Bambino’ and ‘Rustiques figulines’

Analyses of the productions of della Robbia and Palissy, two masters of Renaissance ceramics in France and in Italy, have enlightened their contributions to the improvement of the glazed terracotta technique. Della Robbia used very homogeneous materials: marly clay for the bodies, and tin-opacified coloured glazes. The technique is here very robust and very mastered. Palissy used different types of clay with different colours and physical properties, associated with specific productions. So far, we have identified seven pastes. Concerning the glazes, he played with transparency and opacity, with lead glazes and with tin-opacified lead glazes. He added traditional colouring oxides as well as specific pigments (lead–tin yellow, haematite, etc.). The mixed-earth technique is specific to his palette. So, the materials used by both artists are completely different and illustrate their different philosophical approaches. To perform the different analyses, new methodologies have been developed: ICP/AES-MS, petrography and X-ray diffractometry for the bodies, PIXE and micro-PIXE, SEM coupled with EDS and Raman spectrometry for the glazes. PACS 82.80.-d; 81.05.Je; 61.43.Fs     

Undulators and ‘free-electron lasers’

This article outlines the early development of the undulator in which an electron beam travelling through a system of magnetic fields with directions alternating in space emits a species of linearly polarized synchrotron radiation peaked at a wavelength which is short compared to the magnet period when the electron energy is high compared with the rest energy. The conditions of synchronism and the departure from synchronism that leads to gain during a single passage of the beam are examined. In later developments, stemming from this, single pass gain of circularly polarized radiation was experimentally demonstrated by means of a ‘twister’ structure and an optical cavity, obtained by adding mirrors to the magnet assembly, was used to achieve build-up of the radiation in an oscillator device known as the ‘free-electron laser’. Applications of this device and further theoretical developments are discussed.     

Primary Cosmic Ray Energy Spectrum Above the ‘‘Knee’’ Measured with PRISMA-32 Array

Physics of Atomic Nuclei - PRISMA-32 (PRImary Spectrum Measurement Array) is working since 2012 in the Scientific & Educational Center NEVOD (NRNU ‘‘MEPhI’’,...     

Measuring the ‘complexity’ of sound

Sounds in the natural environment form an important class of biologically relevant non-stationary signals. We propose a dynamic spectral measure to characterize the spectral dynamics of such non-stationary sound signals and classify them based on rate of change of spectral dynamics. We categorize sounds with slowly varying spectral dynamics as simple and those with rapidly changing spectral dynamics as complex. We propose rate of spectral dynamics as a possible scheme to categorize sounds in the environment.     

‘Rising Stars of Light’评选

正投稿截止日期:2019年4月10日背景Light Conference 2019国际学术会议将于2019年7月16日-18日在长春召开。为激励青年学者发表重大创新结果,会议特组织"Rising Stars of Light"评选活动。第1轮通知参选条件学术成果是未发表(2019年7月18日之前未发表)且与光学研究相关的原创性工作投稿格式论文全文,pdf格式投稿语种英语     

Interference and ‘which way’ information

An overview is given of typical examples of interference experiments that confirm the general quantum mechanical rule that distinguishability of the paths destroys interference. It will be shown that path information can be gained in different ways: from the screen's or the atom's recoil in Young-type optical experiments; from the spontaneously emitted photon in atom optics; and from the idler photon, in a striking interference experiment with a photon pair being involved. In all cases, the physical mechanism that actually makes the interference pattern disappear is elucidated.     

Mechanical properties of kaolinite ‘macro-crystals’

The mechanical properties of a rare sample of kaolinite macroscopic crystals were evaluated using instrumented indentation. The crystals were also characterized by X-ray diffraction, scanning electron microscopy, atomic force microscopy and Fourier transform infrared spectroscopy before and after heat treatment at 1100°C. The results are explained in terms of the fracture process occurring in the layered structure of kaolinite, and of the effect of roughness on the hardness and elastic modulus. Data analysis using One-way ANOVA (p?<?0.05) showed that the values of hardness and elastic modulus obtained are statistically homogeneous. Before heat treatment, the sample was composed essentially of kaolinite, with hardness of 42?MPa and elastic modulus equal to 1.3?GPa. After calcination at 1100°C, the sample keeps its layered habit and consists of amorphous metakaolinite. The hardness increases to 360?MPa and the elastic modulus increases to 6.9?GPa.     

Mixing and its rate in ‘soft’ and ‘hard’ billiards motivated by the Lorentz process

Billiards corresponding to planar periodic Lorentz processes are considered in the usual (hard) sense and in the case when the hard core potential of the scatterers is replaced by some other circularly symmetric potential. A review on certain important aspects of the history of the subject is given and some new results on exponential decay of correlations are formulated. Both the results from the literature and those of our own mentioned are mathematically rigorous, nevertheless, proofs are only briefly sketched. For further details, see the preprint [Correlation decay in certain soft billiards, Commun. Math. Phys., in press].     

The structure of ‘nearly’ ferroelectric RADP

X-ray scattering techniques have been used to study the structures of two crystals of Rb_1–x (NH₄) _x H₂PO₄ withx0.2, near to the boundary between ferroelectric and structural-glass behavior at low temperature. Below about 83K, both crystals develop shortrange incommensurate correlations with a wavevectorq0.13 a ^* which are presumably related to the glass properties. On cooling below 70 K, the crystal with the slightly larger NH ₄ ⁺ concentrationx, develops the ferroelectric structure in a small fraction of the crystal, while the bulk of the crystal retains the tetragonal structure. The other crystal transforms almost wholly to the ferroelectric phase. The transition to the ferroelectric structure shows considerable hysteresis on heating and cooling, and is spread over about 20 K. The transition is certainly of first order, and the spread in temperature may arise from concentration fluctuations. These results and the structure of the incommensurate modulations are compared with the predictions of a theoretical model for this system.     

‘Measurement of quantum mechanical operators’ revisited

The Wigner-Araki-Yanase (WAY) theorem states a remarkable limitation to quantum mechanical measurements in the presence of additive conserved quantities. Discovered by Wigner in 1952, this limitation is known to induce constraints on the control of individual quantum systems in the context of information processing. It is therefore important to understand the precise conditions and scope of the WAY theorem. Here we elucidate its crucial assumptions, briefly review some generalizations, and show how a particular extension can be obtained by a simple modification of the original proofs. We also describe the evolution of the WAY theorem from a strict no-go verdict for certain, highly idealized, precise measurements into a quantitative constraint on the accuracy and approximate repeatability of imprecise measurements.     

Berry‘’s Phase in Noncommutative Spaces

We discuss the perturbative aspects of noncommutative quantum mechanics.Then we study Berry‘‘s phase within the framework of noncommutative quantum nechanics.The results show deviations from the usual quantum mechanics,which depend on the parameter of space/space noncommutativity.     

A ‘Mixed’ Type Electron Interference Theory

Ａ‘Ｍｉｘｅｄ’ＴｙｐｅＥｌｅｃｔｒｏｎＩｎｔｅｒｆｅｒｅｎｃｅＴｈｅｏｒｙＣＨＥＮＪｉａｎｗｅｎＣＨＥＮＭｉｎＸＩＡＯＴｉｑｉａｏＸＵＺｈｉｚｈａｎ（ＳｈａｎｇｈａｉＩｎｓｔｉｔｕｔｅｏｆＯｐｔｉｃｓａｎｄＦｉｎｅＭｅｃｈａｎｉｃｓ，Ｃｈｉｎｅｓ...     

‘1001’ correlations in random wave fields

Abstract

Correlations in Gaussian speckle patterns are discussed for the intensity and the phase, as well as for the real and imaginary parts of the wavefunction. Application of the sampling theorem to the wave field is described, and five topologically mandated deterministic rules are enumerated that constrain many aspects of the field structure. A brief overview is given of wave-field correlation matrices containing several million coefficients.