Mixed valency and phase transitions at the (001) SmS surface

A model for mixed valency and phase transitions at (001) SmS is suggested. Focussing on the electron-lattice coupling as a mechanism potentially responsible for both phenomena, the problem of the semi-infinite crystal is factorized and reduced to the investigation of a low-dimensional effective Hamiltonian matrix. Surface geometry and electronic structure are obtained simultaneously by numerical minimization of the free energy. The possible appearance of mixed valency and of phase transitions confined to the surface region and involving relaxed or reconstructed geometry is demonstrated.     

Feynman formulas and path integrals for some evolution semigroups related to τ-quantization

This note is devoted to Feynman formulas (i.e., representations of semigroups by limits of n-fold iterated integrals as n → ∞) and their connections with phase space Feynman path integrals. Some pseudodifferential operators corresponding to different types of quantization of a quadratic Hamiltonian function are considered. Lagrangian and Hamiltonian Feynman formulas for semigroups generated by these operators are obtained. Further, a construction of Hamiltonian (phase space) Feynman path integrals is introduced. Due to this construction, the Hamiltonian Feynman formulas obtained here and in our previous papers do coincide with Hamiltonian Feynman path integrals. This connects phase space Feynman path integrals with some integrals with respect to probability measures. These connections enable us to make a contribution to the theory of phase space Feynman path integrals, to prove the existence of some of these integrals, and to study their properties by means of stochastic analysis. The Feynman path integrals thus obtained are different for different types of quantization. This makes it possible to distinguish the process of quantization in the language of Feynman path integrals.     

The interacting states (020), (100), and (001) of H216O

A fit of 450 rotational levels of the 3 vibrational states (020), (100), and (001) of H₂¹⁶O has been performed using 57 effective constants. The Fermi-type interaction between (020) and (100) and the Coriolis type interaction between (100) and (001) as well as between (020) and (001) are taken into account. The part of the Hamiltonian which is diagonal in the vibrational quantum numbers is a Watson-type Hamiltonian. Most of the perturbed levels are well reproduced and the general agreement between experimental and calculated levels is satisfactory with 70% of the calculated ones falling within 15 × 10^?3 cm^?1 of the observed ones.     

Real Hamiltonian forms of Hamiltonian systems

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate another nonequivalent (real) ones. A crucial role in this construction is played by the assumed analyticity and the invariance of the Hamiltonian under the involution. We show that if the initial system is Liouville integrable, then its complexification and its real forms will be integrable again and this provides a method of finding new integrable systems starting from known ones. We demonstrate our construction by finding real forms of dynamics for the Toda chain and a family of Calogero-Moser models. For these models we also show that the involution of the complexified phase space induces a Cartan-like involution of their Lax representations.Received: 8 October 2003, Published online: 8 June 2004PACS: 02.30.Ik Integrable systems - 45.20.Jj Lagrangian and Hamiltonian mechanics     

Shape dynamics in 2 + 1 dimensions

Shape Dynamics is a formulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance. In this paper we explicitly construct Shape Dynamics for a torus universe in 2 + 1 dimensions through a linking gauge theory that ensures dynamical equivalence with General Relativity. The Hamiltonian we obtain is formally a reduced phase space Hamiltonian. The construction of the Shape Dynamics Hamiltonian on higher genus surfaces is not explicitly possible, but we give an explicit expansion of the Shape Dynamics Hamiltonian for large CMC volume. The fact that all local constraints are linear in momenta allows us to quantize these explicitly under a certain assumption on the kinematic Hilbert space, and the quantization problem for Shape Dynamics turns out to be equivalent to reduced phase space quantization. We consider the large CMC-volume asymptotics of conformal transformations of the wave function. We then discuss the similarity of Shape Dynamics on the 2-torus with the explicitly constructible strong gravity Shape Dynamics Hamiltonian in higher dimensions.     

光纤光栅的温度增敏实验

用热膨胀系数较大的聚合物材料对光纤光栅进行封装处理,极大地提高了光纤光栅的温度灵敏度。我们将光纤光栅封装于两种不同的聚合物材料中,其温度灵敏度分别提高6倍和23倍之多。这是迄今有文献报道的最大的光纤光栅温度灵敏度。     

(001)和(111)取向的张应变量子阱光学特性的比较

以(001)和(111)价带Lutinger-Kohn哈密顿量为基础,讨论了这两种取向的量子阱的能带结构、态密度(DOS)、跃迁矩阵元和增益特性。由于材料结构的各向异性,(111)取向的量子阱在平行生长面内有较小的重空穴有效质量,无应变和压应变激光器可以很好地利用这一点。而(001)取向的量子阱虽有较小的平面内轻空穴有效质量,但并不比(111)量子阱的小多少;加上(001)量子阱的价带耦合效应强,使其DOS比(111)量子阱的大,在相同载流子注入下,张应变(111)量子阱的增益系数比相应(001)量子阱的要高。所以张应变(111)量子阱激光器仍然比相应的(001)量子阱激光器性能要好。可以认为匹配和压应变的(111)激光器优异的性能不仅来自小的面内有效质量,也来自于弱的价带耦合效应。     

Microscopic view of a two-dimensional lattice-Gas ising system within the grand canonical ensemble

A reversible 2D critical transition is observed on the GaAs(001) surface and modeled as a lattice-gas Ising system. Without depositing any material, 2D GaAs islands spontaneously form. The order parameter, four critical exponents, and coupling energies are measured from scanning tunneling microscope images of the microscopic domain structure and correlation functions as a function of temperature and pressure. Unprecedented insight into the domain structure of a 2D Ising system through the critical point and a complete Hamiltonian for modeling the GaAs(001) surface are presented.     

Surface excitations in magnetic systems with a singlet ground state

We have investigated surface excitations in a system wherein the ionic ground state is a magnetic singlet. The pseudospin formalism is employed to account for the crystal-field and exchange interactions between the ions in a Heisenberg ferromagnet with the singlet-triplet crystal-field-only level scheme. The Hamiltonian was studied in the molecular field approximation to find the possible ground states. Surface excitations for the simple cubic structure were investigated for the (001) surface in the random phase approximation. Analytic expressions have been obtained for the thermodynamic Green functions. For a fully magnetized molecular field ground state, there are in general two bulk bands, the spin-wave and the excitonic. Surface modes were found to exist below the spin-wave band, above the excitonic band and between the bands. The dispersion curves can exist only over one or two limited regions of the two-dimensional wave-vector parallel to the crystal surface.     

Two nonlinear Dicke models

We consider two simple classes of nonlinear extensions of the Dicke model in order to understand how sensitive the presence of the phase transition is to the structural form of the model Hamiltonian. In both classes, second order phase transitions can occur for sufficiently large values of the coupling constant λ. Gap equations are derived for both classes of nonlinear extensions. Second order phase transitions cannot occur in these classes of models unless the model Hamiltonian contains a bilinear interaction term of the form originally proposed by Dicke.     

Theory of an Fm3m→I4/m structural phase transition in an Rb2KScF6 crystal

An Rb₂KScF₆ crystal having an elpasolite structure undergoes a sequence of Fm3m→I4/m→P12₁/n1 structural phase transitions where the transition to the tetragonal phase is associated with “rotation” of the ScF₆ octahedron. An effective Hamiltonian is constructed to describe the Fm3m→I4/m transition using the approximation of a local mode for which we selected a “soft mode” whose eigenvector corresponds to the rotation of the octahedron. The effective Hamiltonian also includes the relationship between the local mode and the homogeneous elastic strains. The parameters of the effective Hamiltonian were determined using the generalized Gordon-Kim model of an ionic crystal which allows for the deformability and polarizability of the ions. The thermodynamic properties of a system with this model Hamiltonian were investigated using the Monte Carlo method. The calculated phase transition temperature of 250 K is almost the same as the experimental value (252 K). The tetragonal phase remains stable as far as T=0 K and a second transition (to the monoclinic phase) cannot be obtained using this effective Hamiltonian. This suggests that if the transition to the tetragonal phase is mainly associated with “rotations” of the octahedrons, in order to describe the phase transition to the monoclinic phase the effective Hamiltonian must allow for additional degrees of freedom mainly associated with the motion of rubidium ions.     

Interface magnetic effects in vanadium overlayers on manganese substrate

The magnetic structure of V/Mn systems is investigated at T=0 K using real-space tight-binding approach. The magnetism is described in the Hartree-Fock approximation (HFA) of the Hubbard Hamiltonian and the density of states is calculated within the recursion technique. The semiempirical tight-binding (TB) method is used to investigate the magnetism of the systems, where the Hamiltonian is constructed using the Slater-Koster (SK) parameters. It is found that the hybridization of V with Mn d-bands and the neighboring effects play decisive roles in determining the magnetic structure of V-Mn systems. It is found that the magnetic moments of V and Mn in the (111) orientation are greater than those of (001) orientation for one and two V overlayers due to the local environment.     

Non-linear diffusion in Hamiltonian systems exhibiting chaotic motion

The exact evolution equation for the angle averaged phase space density in action-angle space is derived from the Liouville equation using projection operator techniques. This equation involves a correlation function of the initial value of the phase space density with the angle dependent part of the Hamiltonian and a correlation function of the angle dependent part of the Hamiltonian and a correlation function of the angle dependent part of the Hamiltonian with itself. Each of these correlation functions develops in time with angle projected dynamics. We show their relation to the correlation functions which develop in time with usual Hamiltonian dynamics. These correlation functions are then studied in the standard model of Chirikov, and we conclude that they behave as $\text{e}{}^{\mathrm{-\sigma t}}\text{cos}\text{(Ωt + φ)}$ in regions of irregular motion. We conjecture that angle averaged correlation functions behave this way in general, and we give an argument based on the mixing property of the Hamiltonian system. Our argument goes beyond the usual mixing, so we regard it as a quasi-mixing hypothesis. Under this hypothesis the equation for the angle averaged phase space density becomes a diffusion equation which incorporates much of the non-linear dynamics of Hamiltonian systems exhibiting chaotic motion.     

Phase transition-induced superstructures of β-Sn films with atomic-scale thickness

The ultrathin β-Sn(001) films have attracted tremendous attention owing to its topological superconductivity(TSC),which hosts Majorana bound state(MBSs) for quantum computation.Recently,β-Sn(001) thin films have been successfully fabricated via phase transition engineering.However,the understanding of structural phase transition of β-Sn(001)thin films is still elusive.Here,we report the direct growth of ultrathin β-Sn(001) films epitaxially on the highly oriented pyrolytic graphite(HOPG) substrate and the characterization of intricate structural-transition-induced superstructures.The morphology was obtained by using atomic force microscopy(AFM) and low-temperature scanning tunneling microscopy(STM),indicating a structure-related bilayer-by-bilayer growth mode.The ultrathin β-Sn film was made of multiple domains with various superstructures.Both high-symmetric and distorted superstructures were observed in the atomic-resolution STM images of these domains.The formation mechanism of these superstructures was further discussed based on the structural phase transition of β to α-Sn at the atomic-scale thickness.Our work not only brings a deep understanding of the structural phase transition of Sn film at the two-dimensional limit,but also paves a way to investigate their structure-sensitive topological properties.     

Symmetries and regular behavior of Hamiltonian systems

The behavior of the phase trajectories of the Hamilton equations is commonly classified as regular and chaotic. Regularity is usually related to the condition for complete integrability, i.e., a Hamiltonian system with n degrees of freedom has n independent integrals in involution. If at the same time the simultaneous integral manifolds are compact, the solutions of the Hamilton equations are quasiperiodic. In particular, the entropy of the Hamiltonian phase flow of a completely integrable system is zero. It is found that there is a broader class of Hamiltonian systems that do not show signs of chaotic behavior. These are systems that allow n commuting "Lagrangian" vector fields, i.e., the symplectic 2-form on each pair of such fields is zero. They include, in particular, Hamiltonian systems with multivalued integrals. (c) 1996 American Institute of Physics.     

双阱结构含时量子输运的微扰论及输运方程

利用Lewis-Riesenfeld不变量理论和与不变量有关的幺正变换方法研究了双阱结构含时量子 输运的微扰论.获得了双阱内含时薛定谔方程的精确解的完备集，在此基础上，把双阱与左 右热库的相互作用作为微挠，获得了双阱结构一阶近似下的输运方程，并在绝热近似下提供 了一种用于研究量子输运过程中几何相因子(Berry相因子)的方法. 关键词： 含时量子输运 输运方程 不变量 几何相因子     

Oscillatory curie temperature of two-dimensional ferromagnets

The effective exchange interactions of magnetic overlayers Fe/Cu(001) and Co/Cu(001) covered by a Cu-cap layer of varying thickness were calculated in real space from first principles. The effective two-dimensional Heisenberg Hamiltonian was constructed and used to estimate magnon dispersion laws, spin-wave stiffness constants, and overlayer Curie temperatures within the mean-field and random-phase approximations. Overlayer Curie temperature oscillates as a function of the cap-layer thickness in a qualitative agreement with a recent experiment.     

On the solution of the number-projected Hartree-Fock-Bogolyubov equations

The numerical solution of the recently formulated number-projected Hartree-Fock-Bogolyubov (HFB) equations is studied in an exactly solvable cranked-deformed shell-model Hamiltonian. It is found that the solution of these number-projected equations involves similar numerical effort as that of bare HFB. We consider that this is significant progress in the mean-field studies of quantum many-body systems. The results of the projected calculations are shown to be in almost complete agreement with the exact solutions of the model Hamiltonian. The phase transition obtained in the HFB theory as a function of the rotational frequency is shown to be smeared out with the projection.     

The effect of band Jahn-Teller distortion on the magnetoresistivity of manganites: a model study

We present a model study of magnetoresistance through the interplay of magnetisation, structural distortion and external magnetic field for the manganite systems. The manganite system is described by the Hamiltonian which consists of the s-d type double exchange interaction, Heisenberg spin-spin interaction among the core electrons, and the static and dynamic band Jahn-Teller (JT) interaction in the e(g) band. The relaxation time of the e(g) electron is found from the imaginary part of the Green's function using the total Hamiltonian consisting of the interactions due to the electron and phonon. The calculated resistivity exhibits a peak in the pure JT distorted insulating phase separating the low temperature metallic ferromagnetic phase and the high temperature paramagnetic phase. The resistivity is suppressed with the increase of the external magnetic field. The e(g) electron band splitting and its effect on magnetoresistivity is reported here.