Majorana Transformation for Differential Equations

We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed to reduce the degree of nonlinearity of the lower order equation. Some applications of these methods are carried out and, in particular, we show that second-order Emden–Fowler equations can be transformed into first-order Abel equations. The work presented here is a generalization of a method used by Majorana in order to solve the Thomas–Fermi equation.     

Ettore Majorana and his heritage seventy years later

The physicists working in several areas of research know quite well the name of Ettore Majorana, since it is currently associated to fundamental concepts like Majorana neutrinos in particle physics and cosmology or Majorana fermions in condensed matter physics. But, probably, very few is known about other substantial contributions of that ingenious scholar, and even less about his personal background. For non specialists, instead, the name of Ettore Majorana is usually intimately related to the fact that he disappeared rather mysteriously on March 26, 1938, just seventy years ago, and was never seen again. The life and the work of this Italian scientist is the object of the present review, which will also offer a summary of the main results achieved in recent times by the historical and scientific researches on his work.     

Majorana: From Atomic and Molecular, to Nuclear Physics

In the centennial of Ettore Majorana’s birth (1906–1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi’s solution of the celebrated Thomas–Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana’s seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg–Majorana forces) in his later works on theoretical nuclear physics. In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed.     

Equation of State of Al Based on the Thomas–Fermi Model

A wide‐range semiempirical equation of state for aluminum applicable both at near‐normal conditions and in dense plasma is presented. The finite‐temperature Thomas–Fermi model is used for the thermal contribution of electrons thus diminishing the number of fitting parameters and giving information about a mean ion charge. The constructed equation of state agrees with majority of available shock‐wave data (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ettore Majorana’s Forgotten Publication on the Thomas-Fermi Model

We analyze the forgotten communication of Ettore Majorana (1906–1938?) on the Thomas-Fermi statistical model of the atom, which he presented on December 29, 1928, during the XXII General Meeting of the Italian Physical Society in Rome, and which was published in Il Nuovo Cimento, the Society’s journal, in 1929. His communication was not mentioned subsequently in any of the numerous publications of Enrico Fermi (1901–1954) and his group in Rome, nor in any of the later accounts of Majorana’s life and work. We place Majorana’s contribution within the context of contemporary research on the subject, point out its influence on the final formulation of the Thomas-Fermi statistical model by Fermi and Edoardo Amaldi (1908–1989) in 1934, and discuss Majorana’s other scientific contributions before his mysterious disappearance in 1938. Francesco Guerra is Professor of Theoretical Physics in the Department of Physics at the University of Rome “La Sapienza.” His main fields of research are quantum-field theory, statistical mechanics of complex systems, and the history of nuclear physics. Nadia Robotti is Professor of History of Physics in the Department of Physics at the University of Genoa. Her main fields of research are the history of atomic physics, quantum mechanics, and nuclear physics.     

Asphericity in the Fermi Surface and Fermi Energy of Na-K, Na-Rb and Na-Cs Binary Alloys

Detailed theoretical investigations into asphericity in the Fermi surface (FS) and Fermi energy (FE) ofNa1_xKx, Na1_xRbx, and Na1_xCsx binary solid solutions are carried out for the first time. The alloying behavior ofthe K, Rb, and Cs with the Na generates the Fermi surface distortion (FSD) of bce simple metals. The FS of Na-K,Na-Rb, and Na-Cs solid solution is a distorted sphere with the largest deviation along [110]. We have found that theimpact of local-field correction function on FSD is maximun at [100] point and minimum at [111] point. The exchangeand correlation effect is found to suppress the value of FE.     

Statistical Properties of the Polarized Radiation of a Dye–Solution Laser

Within the framework of the method of polarization components we obtained the Fokker–Planck equation for the intensity–distribution function of an individual component. Solutions for the Ornstein–Uhlenbeck process show that the experimentally observed special features in the behavior of the distribution function of the intensity and degree of polarization of laser radiation in the vicinity of the threshold are well described in the approximation of statistical independence of polarization components. However, since the Ornstein–Uhlenbeck process includes states not realizable physically for the given case, an exact solution of the Fokker–Planck equation is constructed by the method of expansion in eigenstates. It is shown that this solution is totally correct physically and yields virtually the same values for the distribution functions of the intensity and degree of polarization of radiation as the dependences obtained earlier for the Ornstein–Uhlenbeck process.     

Quirino Majorana’s Experiments on the Speed of Light and Gravitational Absorption

Quirino Majorana (1871–1957) was an outstanding Italian experimental physicist who investigated a wide range of phenomena during his long career in Rome,Turin, and Bologna. We focus on his experiments in Turin during 1916–1921 and in Bologna during 1921–1934 to test the validity of Albert Einstein’s postulate on the constancy of the speed of light and to detect gravitational absorption. These experiments required extraordinary skill, patience, and dedication, and all of them confirmed Einstein’s postulate and Isaac Newton’s law of universal gravitation to high precision. Had they not done so, Majorana’s fame among historians and physicists no doubt would be much greater than it is today. Giorgio Dragoni is Professor of History of Physics at the University of Bologna. Giulio Maltese is a Roman member of the Italian Society for the History of Physics and Astronomy. Luisa Atti is a Bolognese member of the Association for the Teaching of Physics.     

Gaudin Model,KZ Equation and an Isomonodromic Problem on the Tours

This Letter presents a construction of isospectral problems on the torus. The construction starts from an SU(n) version of the XYZ Gaudin model recently studied by Kuroki and Takebe within the context of a twisted WZW model. In the classical limit, the quantum Hamiltonians of the generalized Gaudin model turn into classical Hamiltonians with a natural r-matrix structure. These Hamiltonians are used to build a nonautonomous multi-time Hamiltonian system, which is eventually shown to be an isomonodromic problem on the torus. This isomonodromic problem can also be reproduced from an elliptic analogue of the KZ equation for the twisted WZW model. Finally, a geometric interpretation of this isomonodromic problem is discussed in the language of a moduli space of meromorphic connections.     

费米共振对分子振动能级和光谱的影响

费米共振相互作用对多原子分子具有相同对称类的近简并振动能级及其光谱产生影响,利用定态微扰理论,分析了五阶近似下费米共振对三个振动能级的影响,应用于CO2分子的(0400),(1200)和(2000)三个近简并能级,计算结果与实验观测值符合较好,并讨论了费米共振对(0400),(1200)和(2000)向(0110)能级跃迁时光谱线强度的影响.     

Soliton solutions,travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

Many physical systems can be successfully modelled using equations that admit the soliton solutions. In addition, equations with soliton solutions have a significant mathematical structure. In this paper, we study and analyze a three-dimensional soliton equation, which has applications in plasma physics and other nonlinear sciences such as fluid mechanics, atomic physics, biophysics, nonlinear optics, classical and quantum fields theories. Indeed, solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour. We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time. Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function, elliptic functions, elementary trigonometric and hyperbolic functions solutions of the equation. Besides, various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique. These solutions comprise dark soliton, doubly-periodic soliton, trigonometric soliton, explosive/blowup and singular solitons. We further exhibit the dynamics of the solutions with pictorial representations and discuss them. In conclusion, we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula. We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.     

Fermi–Pasta–Ulam Recurrence Interaction with Fluctuations of the Medium

It is shown in numerical study that the simultaneous influence of discrete and continuous random processes on the Fermi–Pasta–Ulam (FPU) recurrence dynamics in chains of vibrators having both fixed and open ends leads to a widening of the FPU spectrum and to its permanent evolution. These phenomena are much more markedly manifested in the chain with open ends. Taking into account that the FPU recurrence takes place in distributed oscillatory systems one of which is a laser, the present research can be promising in developing multimode lasers exhibiting the recurrence phenomena.     

Roles of zeros of the Green function in Fermi arc and non-Fermi liquid in the two-dimensional Hubbard model

We clarify effects of zeros of the Green function on a Fermi arc and on a non-Fermi liquid behavior in the two-dimensional Hubbard model by means of the cellular dynamical mean-field theory (CDMFT). We study in detail the state with a hole-pocket Fermi surface and zeros of the Green function, which was found for a slightly doped Mott insulator in an earlier CDMFT calculation [T.D. Stanescu, G. Kotliar, Phys. Rev. B 74 (2006) 125110; T.D. Stanescu, M. Civelli, K. Haule, G. Kotliar, Ann. Phys. (N.Y.) 321 (2006) 1682]. As thermal or other extrinsic scatterings of electrons broaden the zeros, regions around the zero surface gain an imaginary part of the self-energy, which strongly suppresses the spectral intensity, especially on the closer side of the hole pocket to the zero surface. Then the rest emerges as a Fermi arc. Quasiparticle weight becomes ill defined on the closer side of the Fermi pocket while it is well defined on the opposite side, which means that a differentiation of electrons occurs in the momentum space, indicating an emergence of a non-Fermi liquid phase.     

Full Fermi–Pasta–Ulam Recurrence Interaction with Fluctuations of the Medium

It is shown in a numerical study that the simultaneous influence of discrete and continuous random processes on the full Fermi–Pasta–Ulam (FPU) recurrence dynamics in two parametrically coupled identical chains of vibrators with open ends and under different initial conditions leads to stabilization of the FPU spectrum. A greater influence on chains of gaussian noise as compared to discrete noise is revealed. An increase in the amplitudes of both noises by one order of magnitude results in considerable parameter changes in their FPU spectrum. The full FPU recurrence interaction in coupled chains with discrete and continuous random noise of the medium manifests itself in extremely low-frequency periodic processes in stochastic dynamics of the medium (with frequency two orders of magnitude lower than the lowest frequency in the initial conditions of the chains).     

Exact solutions of the Boltzmann equation in the VHP model with removal interaction

The linear and nonlinear Boltzmann equation for very hard particles (VHP) is considered in the case when the collision between two particles may lead not only to elastic scattering, but also to a removal event with the disappearance of the molecules. The extended transport equation is solved for arbitrary initial distributions. The computations are carried out explicitly for a special class of initial distributions and for various removal rates. The results are demonstrated graphically. Finally, source terms fulfilling physically reasonable conditions are introduced into the VHP model, and the time-dependent particle number is calculated.     

<原子与分子物理学报>作者群与学科发展现状透析研究

依据文献计量学原理,对１９９０～１９９９年期间《原子与分子物理学报》的论文作者群进行了统计、分析、归纳和研究,从中揭示出我国原子与分子物理学科研究的现状,作者所属系统的分布特点及其规律,确定了该刊核心作者的数量罕比例,同时也对作者的合著率、论文单元数作了统计分析研究。从作者研究的角度肯定了该刊作为本学科核心期刊的合理性,希冀对该学科及该刊的发展提供了可参考的数据。     

CTE Solvability,Exact Solutions and Nonlocal Symmetries of the Sharma-Tasso-Olver Equation

In this letter, we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal symmetries are localized by prolonging the related enlarged system.     

"物理学史和物理学方法论"课程思政教学探索

本文从华东师范大学“物理学史和物理学方法论”课程的教学出发,立足“科学精神和人文素养”的课程基础,通过涵盖“学科历史与思想方法”的教学章节,以期达成“授业解惑和传道育人”、融合思政意识的教学目标.本文希望基于科学与人文的融合,来实践“立德树人”的理念,对于理科院系开展课程思政的建设具有一定的参考和借鉴价值.     

Equation of state in hybrid stars and the stability window of quark matter

Properties of hybrid stars with a mixed phase composed of asymmetric nuclear matter and strange quark matter are studied. The quark phase is investigated by the quark quasiparticle model with a self-consistent thermodynamic and statistical treatment. We present the stability windows of the strange quark matter with respect to the interaction coupling constant versus the bag constant. We find that the appearance of the quark–hadron mixed phases is associated with the meta-stable or unstable regions of the pure quark matter parameters. The mass–radius relation of the hybrid star is dominated by the equation of state of quark matter rather than nuclear matter. The contour plots of the maximum mass of the hybrid star are shown in the plane of the coupling constant and the bag constant.     

Dark Solitons for the Defocusing Cubic Nonlinear Schrödinger Equation with the Spatially Periodic Potential and Nonlinearity

We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.