Quantum particle trajectories and geometric phase

Particle trajectories are defined as integrable dx _μ dp ^μ=0 paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalize in (x, p) projection, the phase associated with the trajectories related to the geometric (Berry) phase and the classical mechanics action. Properties at high energies of the states evolving on particle trajectories are discussed.     

The influence of Bose-Einstein correlations on intermittency inp\bar p collisions at\sqrt s = 630 GeV

The influence of Bose-Einstein correlations on the rise of factorial moments is small in the 1-dimensional phase space given by the pseudorapidity η, where the 2-body correlation function is dominated by unlike-sign particle correlations. Contraily, the influence is dominant in the higher dimensional phase space. This is shown by using correlation integrals. They exhibit clear power law dependences on the four-momentum transferQ ² for all orders investigated (i=2–5). When searching for the origin of this behaviour, we found that the Bose-Einstein ratio itself shows a steep rise forQ ²→0, compatible with a power law.     

Modeling and computation of two phase geometric biomembranes using surface finite elements

Biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions. The modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces. This leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints. In this paper we propose a new computational tool for computing equilibria based on an L² relaxation flow for the total energy in which the line energy is approximated by a surface Ginzburg–Landau phase field functional. The relaxation dynamics couple a nonlinear fourth order geometric evolution equation of Willmore flow type for the membrane with a surface Allen–Cahn equation describing the lateral decomposition. A novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface, the mean curvature vector and the surface phase field function. The resulting variational formulation uses H¹ spaces, and we employ triangulated surfaces and H¹ conforming quadratic surface finite elements for approximating solutions. Together with a semi-implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only. Numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells, discocytes and starfishes with lateral phase separation.     

Non-cyclic geometric phase of nuclear quadrupole resonance signals of powdered samples

The non-cyclic geometric phase of ¹⁴N and ³⁵Cl NQR signals induced by the character of trajectory of nuclear magnetization motion upon pulse r.f. excitation of powdered samples is studied. Analytical expressions for the geometric phases of NQR signals of the nuclei of spins I=1 and 3/2 upon nuclear magnetization rotation induced by means of r.f. pulses with frequency detuned from the resonance and for any impulse duration for a separate crystallite are obtained. It is shown that the geometric phase recorded for the signal from a powdered sample at Δω=0 can be different from zero and can oscillate upon changes in duration of the r.f. excitation pulse. An alternative variant of the nutation experiment aimed at obtaining the asymmetry parameter η from locations of frequency singularities in the nutation phase spectrum for nuclei of spin I=3/2 in powder substances is proposed.     

On the state of superdense configurations

During gravitational compression of superdense astronomical objects the rest mass of the component particles of the object is a variable quantity and is determined along with the other parameters of the system from the condition of equilibrium. The theory of such systems should begin from the symmetry of the formE ²-p ₁ ² -p ₂ ² -p ₃ ² -m²= 0,p ₅=m, c=?=1. For this reason the dimension of the phase space should be enlarged from six to seven. In this paper the fundamental thermodynamic quantities of an equilibrium system in a seven-dimensional phase space are defined, and several examples of their application are considered for the equation of state of a degenerate Fermi gas in a seven-dimensional phase space. It is shown as a separate question in the statistical theory of multiple creation of particles, that the fluctuations of the thermodynamic quantities in such a system are large ΔA/A ～ 1, and gravitational condensation in an expanding Friedman universe is discussed.     

Geometric phase in Bohmian mechanics

Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2π. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.     

On the dimension of deterministic and random Cantor-like sets,symbolic dynamics,and the Eckmann-Ruelle Conjecture

In this paper we unify and extend many of the known results on the dimension of deterministic and random Cantor-like sets in ? ⁿ , and apply these results to study some problems in dynamical systems. In particular, we verify the Eckmann-Ruelle Conjecture for equilibrium measures for Hölder continuous conformal expanding maps and conformal Axiom A^# (topologically hyperbolic) homeomorphims. We also construct a Hölder continuous Axiom A^# homeomorphism of positive topological entropy for which the unique measure of maximal entropy is ergodic and has different upper and lower pointwise dimensions almost everywhere. this example shows that the non-conformal Hölder continuous version of the Eckmann-Ruelle Conjecture is false. The Cantor-like sets we consider are defined by geometric constructions of different types. The vast majority of geometric constructions studied in the literature are generated by a finite collection ofp maps which are either contractions or similarities and are modeled by the full shift onp symbols (or at most a subshift of finite type). In this paper we consider much more general classes of geometric constructions: the placement of the basic sets at each step of the construction can be arbitrary, and they need not be disjoint. Moreover, our constructions are modeled by arbitrary symbolic dynamical systems. The importance of this is to reveal the close and nontrivial relations between the statistical mechanics (and especially the absence of phase transitions) of the symbolic dynamical system underlying the geometric construction and the dimension of its limit set. This has not been previously observed since no phase transitions can occur for subshifts of finite type. We also consider nonstationary constructions, random constructions (determined by an arbitrary ergodic stationary distribution), and combinations of the above.     

Representations of spacetime diffeomorphisms. I. Canonical parametrized field theories

The super-Hamiltonian and supermomentum in canonical geometrodynamics or in a parametried field theory on a given Riemannian background have Poisson brackets which obey the Dirac relations. By smearing the supermomentum with vector fields V^→∈ L Diff Σ on the space manifold Σ, the Lie algebra L Diff Σ of the spatial diffeomorphism group Diff Σ can be mapped antihomomorphically into the Poisson bracket algebra on the phase space of the system. The explicit dependence of the Poisson brackets between two super-Hamiltonians on canonical coordinates (spatial metrics in geometrodynamics and embedding variables in parametrized theories) is usually regarded as an indication that the Dirac relations cannot be connected with a representation of the complete Lie algebra L Diff M of spacetime diffeomorphisms.We show how this difficulty may be overcome and construct a homomorphic mapping of spacetime vector fields V ∈ L Diff M into the Poisson bracket algebra on the phase space of the system. In the present paper, I, we explain how the technique works in the case of a parametrized field theory and in the following paper, II, we generalize it to canonical geometrodynamics. In a parametrized theory, the phase space of the system is the ordinary phase space of the field augmented by the embedding variables X: Σ →Mand their conjugate momenta. The dynamical variable H(V) which represents V ∈ L Diff M generates a deformation of the embedding along the flow lines of V accompanied by the correct dynamical evolution of the field data and preserves the constraints in the extended phase space of the system. We also establish the relation between the representations of Diff Σ and DiffM.     

Holomorphic curves from matrices

Membranes holomorphically embedded in flat non-compact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static solutions to the matrix theory equations of motion, and which can be interpreted as the matrix theory representation of the holomorphically embedded membrane. The problem of finding such matrix representations can be phrased as a problem in geometric quantization, where ϵ ∝ l_P³/R plays the role of the Planck constant and parametrizes families of solutions. The concept of Bergman projection is used as a basic tool, and a local expansion for the action of the projection in inverse powers of curvature is derived. This expansion is then used to compute the required matrices perturbatively in ϵ. The first two terms in the expansion correspond to the standard geometric quantization result and to the result obtained using the metaplectic correction to geometric quantization.     

The geometric SO(3) × D model

The geometric SO(3) × D model is formulated as a computationally viable submodel of the algebraic sp(3, R) model containing the Sp (1, R) model of Arickx et al. as a submodel. It is basically a scheme for constructing a space of states (like the space of Slater determinants) which can be employed either directly, for constrained variational quantal dynamics of the Hartree-Fock, RPA and TDHF type, or to construct a shell-model basis for the diagonalization of a microscopic hamiltonian. The results of HF calculations, restricted to SO(3) × D surfaces, are reported for the nuclei ⁴He, ⁸Be, ¹⁶O and ²⁰Ne.     

Temperature dependence of the lattice vibrations of triglycine selenate

The polarized Raman spectra below 300 cm^?1 and the far infrared spectra from 400 to 30 cm^?1 of triglycine selenate were measured at various low temperatures. It was found that the Raman doublet at 44 and 38 cm^-1 observed in the paraelectric phase (space group C²_2h) was reduced to a singlet at 38 cm^?1 in the ferroelectric phase (space group C₂²). This spectral anomaly in the paraelectric phase appears to be due to the splitting of the translational mode of glycine I along the crystallographic b axis, the splitting being caused by the tunneling of glycine I across the barrier between the two potential minima which are located symmetrically on either side of the crystallographic ac plane (i.e. at $\text{b =}\text{1}\text{4}$ and $\text{3}\text{4}\text{)}$. New Raman bands which appear below the Curie temperature are also discussed.     

Quantum Image Encryption Based on Iterative Framework of Frequency-Spatial Domain Transforms

A novel quantum image encryption and decryption algorithm based on iteration framework of frequency-spatial domain transforms is proposed. In this paper, the images are represented in the flexible representation for quantum images (FRQI). Previous quantum image encryption algorithms are realized by spatial domain transform to scramble the position information of original images and frequency domain transform to encode the color information of images. But there are some problems such as the periodicity of spatial domain transform, which will make it easy to recover the original images. Hence, we present the iterative framework of frequency-spatial domain transforms. Based on the iterative framework, the novel encryption algorithm uses Fibonacci transform and geometric transform for many times to scramble the position information of the original images and double random-phase encoding to encode the color information of the images. The encryption keys include the iterative time t of the Fibonacci transform, the iterative time l of the geometric transform, the geometric transform matrix G i which is n × n matrix, the classical binary sequences K (\(k_{0}k_{1}{\ldots } k_{2^{2n}-1}\)) and \(D(d_{0}d_{1}{\ldots } d_{2^{2n}-1}\)). Here the key space of Fibonacci transform and geometric transform are both estimated to be 2²⁶. The key space of binary sequences is (2 ^n×n ) × (2 ^n×n ). Then the key space of the entire algorithm is about \(2^{2{n^{2}}+52}\). Since all quantum operations are invertible, the quantum image decryption algorithm is the inverse of the encryption algorithm. The results of numerical simulation and analysis indicate that the proposed algorithm has high security and high sensitivity.     

Strangeness enhancement in sulphur—Nucleus collisions at 200 A GeV/c

The NA35 experiment used several independent methods to determine the strange particle production in p+S and S+A collisions. The different techniques show consistent results. Strangeness conservation in full phase space is used as an additional check of the consistency of the data. On the base of the analysis in full phase space it could be shown that strangeness conservation is fullfilled. The NA35K _S ⁰ in S+S and S+Ag are consistent with the NA44 results forK ⁺ andK ^?. The results of the NA36 collaboration for S+Pb collisions were extrapolated to full phase space. The comparison with the NA35 results shows more than two times lower yields. The ratio of Λ to $\bar \Lambda $ at midrapidity of NA36 is inconsistent with the high baryon density determind by NA35. The strange particle production is compared to the abundance of non strange particles, especially negatively charged pions which are measured in full phase space in the same experiment. A clear enhanced strange hadron production relative to σ^? is observed in S+Ag collisions compared to p+S reactions at the same energy. TheK _S ⁰ multiplicity in full phase space per negative hadron (h ^?) in S+S, S+Ag and Pb+Pb is enhanced by about a factor 1.6 compared to N+N and p+S collisions. The NA36 result for theK _S ⁰ multiplicity perh ^? in S+Pb is below the N+N value.     

The evolution of short distance phase space quanta into hadron jets

A statistical model fore ⁺ e ^? annihilation into hadrons is presented which explains at the same time some short distance phenomena (multiple jet structure, rate of three jet events, scaling) and large distance phenomena (hadron final states, multiplicities). We investigate the change of phase space structure with time under the assumption that the interaction volume expands with velocity of light. At short distancesL?m _π ^?1 elementary quanta in the instantaneous phase space with mass spreadΔm～L ^?1 can be produced. They are unstable and evolve into the jets of hadrons. The time evolution of the system is uniquely determined by sequential application of our principle of equipartition in instantaneous phase space.