两自由度弱非线性耦合系统的一阶近似Lie对称性与近似守恒量

采用变劲度系数的耦合弹簧构建一实际的两自由度弱非线性耦合系统, 用近似Lie对称性理论研究系统的一阶近似Lie对称性与近似守恒量, 得到6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1个一阶近似守恒量为稳定的一阶近似守恒量. 关键词： 两自由度弱非线性耦合系统 近似Lie对称性 近似守恒量     

The reduction of the Laplace equation in certain Riemannian spaces and the resulting Type II hidden symmetries

We prove a general theorem which allows the determination of Lie symmetries of the Laplace equation in a general Riemannian space using the conformal group of the space. Algebraic computing is not necessary. We apply the theorem in the study of the reduction of the Laplace equation in certain classes of Riemannian spaces which admit a gradient Killing vector, a gradient Homothetic vector and a special Conformal Killing vector. In each reduction we identify the source of Type II hidden symmetries. We find that in general the Type II hidden symmetries of the Laplace equation are directly related to the transition of the CKVs from the space where the original equation is defined to the space where the reduced equation resides. In particular we consider the reduction of the Laplace equation (i.e., the wave equation) in the Minkowski space and obtain the results of all previous studies in a straightforward manner. We consider the reduction of Laplace equation in spaces which admit Lie point symmetries generated from a non-gradient HV and a proper CKV and we show that the reduction with these vectors does not produce Type II hidden symmetries. We apply the results to general relativity and consider the reduction of Laplace equation in locally rotational symmetric space times (LRS) and in algebraically special vacuum solutions of Einstein’s equations which admit a homothetic algebra acting simply transitively. In each case we determine the Type II hidden symmetries.     

Quantum communication via controlled holes in the statistical distribution of excitations in a nanoresonator coupled to a Cooper pair box

We propose a scheme to transmit information via the statistical distribution of excitations of a nanomechanical resonator.It employs a controllable coupling between this system and a Cooper pair box.The success probability and the fidelity are calculated and compared with those obtained in an atom-field system in different regimes.Addtionaly,the scheme can also be applied to prepare low excited Fock states.     

Quantum communication via controlled holes in the statistical distribution of excitations in a nanoresonator coupled to a Cooper pair box

We propose a scheme to transmit information via the statistical distribution of excitations of a nanomechanical resonator. It employs a controllable coupling between this system and a Cooper pair box. The success probability and the fidelity are calculated and compared with those obtained in an atom-field system in different regimes. Addtionaly, the scheme can also be applied to prepare low excited Fock states.     

Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation

The coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation is solved. The collimated and diffuse components problems are treated separately. The solution for diffuse radiation is obtained by using a composite discrete ordinates method and includes the development of adaptive directional quadratures to overcome the difficulties usually encountered at the interfaces. The complete radiation numerical model is validated against the predictions obtained by using the Monte Carlo method.     

An orthonormalization method: Theory and application to the j-j coupling of fermions in a single j-shell

An orthonormalization method suitable to deal with an overcomplete and non-orthogonal set of vectors is derived. It is then used to obtain the orthonormal set of states connected with the angular momentum coupling of N fermions in a single j-shell.     

Problem of the Landau Poles in Quantum Field Theory: from N. N. Bogolyubov to the Present Day

Russian Physics Journal - A review of problems associated with the unphysical Landau pole in propagators of quantum particles is given. Approaches to eliminating this pole within the framework of...     

Reprint of : Quantum interference in a Cooper pair splitter: The three sites model

New generation of Cooper pair splitters defined on hybrid nanostructures are devices with high tunable coupling parameters. Transport measurements through these devices revealed clear signatures of interference effects and motivated us to introduce a new model, called the 3-sites model. These devices provide an ideal playground to tune the Cooper pair splitting (CPS) efficiency on demand, and displays a rich variety of physical phenomena. In the present work we analyze theoretically the conductance of the 3-sites model in the linear and non-linear regimes and characterize the most representative features that arise by the interplay of the different model parameters. In the linear regime we find that the local processes typically exhibit Fano-shape resonances, while the CPS contribution exhibits Lorentzian-shapes. Remarkably, we find that under certain conditions, the transport is blocked by the presence of a dark state. In the non-linear regime we established a hierarchy of the model parameters to obtain the conditions for optimal efficiency.     

The halo of the exotic nucleus 11Li: a single Cooper pair

If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron saturated, the nucleus expels most of the wave function of the last neutrons outside to form a halo, which, because of its large size, can have a lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here, we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, a solution which is at the basis of BCS theory of superconductivity. By mimicking this approach using, aside from the bare nucleon-nucleon interaction, the long wavelength vibrations of the nucleus ¹¹Li, the paradigm of halo nuclei, as tailored glues of the least bound neutrons, we are able to obtain a unified and quantitative picture of the observed properties of ¹¹Li. Received: 9 May 2001 / Accepted: 17 November 2001     

Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential

The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and γ⁵${\gamma }^5$ chiral transformations. The cases of pure pseudoscalar and mixed vector–scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions.     

New Concepts from the Evans Unified Field Theory. Part One: The Evolution of Curvature,Oscillatory Universe Without Singularity,Causal Quantum Mechanics,and General Force and Field Equations

No Heading The Evans field equation is solved to give the equations governing the evolution of scalar curvature R and contracted energy-momentum T. These equations show that R and T are always analytical, oscillatory, functions without singularity and apply to all radiated and matter fields from the sub-atomic to the cosmological level. One of the implications is that all radiated and matter fields are both causal and quantized, contrary to the Heisenberg uncertainty principle. The wave equations governing this quantization are deduced from the Evans field equation. Another is that the universe is oscillatory without singularity, contrary to contemporary opinion based on singularity theorems. The Evans field equation is more fundamental than, and leads to, the Einstein field equation as a particular example, and so modifies and generalizes the contemporary Big Bang model. The general force and conservation equations of radiated and matter fields are deduced systematically from the Evans field equation. These include the field equations of electrodynamics, dark matter, and the unified or hybrid field.     

Transmission time of a particle in the reflectionless Sech-squared potential: Quantum clock approach

We investigate the time for a particle to pass through the reflectionless Sech-squared potential. Using the Salecker-Wigner and Peres quantum clock an average transmission time of a Gaussian wave packet representing the particle is explicitly evaluated in terms of average momentum and travel distance. The average transmission time is shown to be shorter than the time of free-particle motion and very close to the classical time for wave packets with well-localized momentum states. Since the clock measures the duration of scattering process the average transmission time can be interpreted as the average dwell time.     

Editor's Note: On the Gravitational Field of a Mass Point According to Einstein's Theory by K. Schwarzschild

We comment on the famous paper by Karl Schwarzschild from 1916, which is reprinted in the present issue.     

The Spinning and Curving of Spacetime: The Electromagnetic and Gravitational Fields in the Evans Field Theory

The unification of the gravitational and electromagnetic fields achieved geometrically in the generally covariant unified field theory of Evans implies that electromagnetism is the spinning of spacetime and gravitation is the curving of spacetime. The homogeneous unified field equation of Evans is a balance of spacetime spin and curvature and governs the influence of electromagnetism on gravitation using the first Bianchi identity of differential geometry. The second Bianchi identity of differential geometry is shown to lead to the conservation law of the Evans unified field, and also to a generalization of the Einstein field equation for the unified field. Rigorous mathematical proofs are given in appendices of the four equations of differential geometry which are the cornerstones of the Evans unified field theory: the first and second Maurer-Cartan structure relations and the first and second Bianchi identities. As an example of the theory, the origin of wavenumber and frequency is traced to elements of the torsion tensor of spinning spacetime.     

Theory of the polarization of highly charged ions in storage rings: Production, preservation, observation and application to the search for a violation of the fundamental symmetries

Theoretical concepts for the production, preservation and control of polarized highly charged ion beams in storage rings are investigated. It is argued that hydrogen-like ions can be polarized efficiently by optical pumping of the Zeeman sublevels of ground state hyperfine levels and that the maximum achievable nuclear polarization exceeds 90%. In order to study the preservation of the polarization during the ion motion through the magnetic system of the ring, the concept of the instantaneous quantization axis is introduced. It is suggested that the employment of “Siberian snakes” may help to preserve the ion beam polarization in the ring. The control of the beam polarization can be achieved by different methods: by measuring the Stokes parameters for the emitted photons or by observing the angular dependence of the transition rates for polarized ions. The important motivation for the production of polarized ion beams is the possibility to observe parity nonconservation effects in the hyperfine-quenched transitions in helium-like highly charged ions, where these effects can reach an unprecedented high value for atomic physics. The possible observation of parity nonconservation effects connected with the nuclear anapole moment is also discussed. A method for the observation of the electric dipole moment of an electron in a storage ring with a polarized highly charged ion beam is proposed. This method allows, in principle, to improve the existing boundaries for the electric dipole moment of an electron. However, the requirements of the corresponding experiment are very stringent.     

Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.