Generating monoenergetic proton beam by using circularly polarlzed laser

The interaction of ultrashort intense circularly polarized laser with ultra thin overdense foil is studied by particle-in-cell simulation and analytic model.It is found that with the balance between pondermotive force and electrostatic force,highly quasi-monoenergetic proton beam can be generated by Phase Stable Acceleration(PSA)process.As in conventional accelerators,ion will be accelerated and bunched up in the longitudinal direction at the same time.     

Density functional study of structural and electronic properties of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>P (2 ≤ <Emphasis Type="Italic">n</Emphasis> ≤ 12) clusters

Low-lying equilibrium geometric structures of Phosphorus-doped aluminum cluster Al _n P (n = 2–12) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee-Yang-Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static polarizabilities are calculated for the ground-state structures within the GGA. It is observed that symmetric structures with the P atom occupying a peripheral position are lowest-energy geometries of Al _n P (n = 2, 4–11), while the P impurities of Al₃P and Al₁₂P prefer to occupy internal sites in the aluminum clusters. Generalized gradient approximation extends bond lengths as compared to the LSDA lengths. The odd-even oscillations in the dissociation energy, the second differences in energy, the HOMO–LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within both GGA and LSDA. The stability analysis based on the energies clearly shows the clusters with an even number of valence electrons are more stable than clusters with odd number of valence electrons.     

On Quantum Phase Transition. II. The Falicov–Kimball Model

The Falicov–Kimball (FK) model⁽¹⁾ involves two types of interacting particles: first the itinerant spinless electrons are quantum particles, secondly the static ions are classical particles. It is striking to see that, despite the simplicity of its hamiltonian, the phase diagram of the FK model is highly sophisticated, moreover it remains in great part conjectural. An antiferromagnetic phase transition was proven for the FK model on a square lattice in the seminal paper of T. Kennedy and E. Lieb.⁽²⁾ This result was extended by Lebowitz and Macris⁽³⁾ to small magnetic field. Then the same result was obtained by using a new method.⁽⁴⁾ The main results of this paper concerns the two dimensional FK model on a square lattice, for which we apply the general results contained in ref. 5. First there exists an effective hamiltonian which is a long range many body Ising model, and which governs the behaviour of the ions. Secondly we compute explicitly the truncated effective hamiltonian up to the fourth order w.r.t. a small parameter (the inverse of the on site energy). Finally we use the classical Pirogov–Sinai theory, to get the hierarchy of the phase diagrams up to the fourth order. More precisely, we show that, when the chemical potential varies, the FK model exhibits, at low temperature, a sequence of phase transitions: first between phases of period two, then of period three, then of period four, and finally of period five. In each case the completeness of the phase diagram is proved. This paper supports the conjecture that the phase diagram of the FK model contains periodic phases outside of a Cantor set.     

On Quantum Phase Transition. I. Spinless Electrons Strongly Correlated with Ions

We study a large class F of models of the quantum statistical mechanics dealing with two types of particles. First the spinless electrons are quantum particles obeying to the Fermi statistics, they can hop. Secondly the ions which cannot move, are classical particles. The Falicov–Kimball (FK) model⁽¹⁾ is a well known model belonging to F, for which the existence of an antiferomagnetic phase transition was proven in the seminal paper of Kennedy and Lieb.⁽²⁾ This result was extended by Lebowitz and Macris.⁽³⁾ A new approach to this problem based on quantum selection of the ground states was proposed in ref. 4. In this paper we extend this approach to show that, under the strong insulating condition, any hamiltonian of the class F admits, at every temperature, an effective hamiltonian, which governs the behaviour of the ions interacting through forces mediated by the electrons. The effective hamiltonians are long range many body Ising hamiltonians, which can be computed by a cluster expansion expressed in term of the quantum fluctuations. Our main result is that we can apply the powerfull results of the classical statistical mechanics to our quantum models. In particular we can use the classical Pirogov–Sinai theory to establish a hierarchy of phase diagrams, we can also study of the behaviour of the quantum inter- faces,⁽²⁹⁾ and so on...     

Accelerating infinite products

Slowly convergent infinite products are considered, where is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the “remainder” of the infinite product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and efficient for some classes of sequences . For complicated sequences it involves the solution of some linear systems, but it is still effective. This revised version was published online in June 2006 with corrections to the Cover Date.     

Fourier acceleration of iterative processes in disordered systems

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.     

Acceleration waves analyzed by a new continuum model of solids incorporating microscopic thermal vibrations

Acceleration waves propagating in isotropic solids at finite temperatures are studied by applying the method of singular surfaces to a new continuum model derived statistical-mechanically from a three-dimensional lattice model. The continuum model explicitly takes into account the microscopic thermal vibrations of the constituent atoms as one of the field variables. The propagation speeds and the ratios of mechanical and thermal amplitudes for both longitudinal and transverse waves are consistently determined. The differential equations that govern the time variation of the amplitudes of the waves are also derived. The analytical results, which are valid over a wide temperature range that includes the melting point, are evaluated numerically for several materials, and their physical implications are discussed. One of the findings to be emphasized is that of the singularities of the characteristic quantities at the melting point.Received: 13 March 2003, Accepted: 20 June 2003PACS: 62.30. + d, 65.40.-bM. Sugiyama: Correspondence to Dedicated to Prof. Ingo Müller on the occasion of his 65th birthday.     

A novel electron scattering apparatus combining a laser photoelectron source and a triply differentially pumped supersonic beam target: characterization and results for the resonance

A novel electron scattering apparatus for high resolution studies of angle-differential elastic and inelastic electron scattering from atoms and molecules in the gas phase is described and its performance characterized. It combines a laser photoelectron source, a triply differentially pumped collimated supersonic beam target (half angle 0.015 rad, background to beam density ratio < 0.01), and several electron multipliers for simultaneous detection of elastically scattered electrons and metastable atoms (or molecules) due to inelastic scattering. In detailed test measurements of the yield for the production of metastable He^*(2³S₁) atoms around its threshold, the dependence of the overall energy width on various experimental parameters has been investigated. So far a resolution down to 7 meV (FWHM) has been obtained. Under such conditions we have investigated the profile of the He^- (1 s 2 s ^{2 2} S _1/2 ) resonance at the scattering angles 22 ^° , 45 ^° , and 90 ^° . From a consistent fit of the measured profiles by resonant scattering theory we determine a new value for the resonance energy ( E _r = 19.365(1) eV) and an accurate resonance width ( Γ = 11.2(5) meV). These results are consistent with the previously recommended values. Received 23 July 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: hotop@physik.uni-kl.de RID="b" ID="b"Permanent address: Department of Physics and Astronomy, Drake University, Des Moines, IA 50311, USA.     

Remarks on the Formulation of the Cosmological Constant/Dark Energy Problems

Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.