Superpositions of the Orbital Angular Momentum for Applications in Quantum Experiments

Two different experimental techniques for preparation and analyzing superpositions of the Gaussian and Laguerre-Gassian modes are presented. This is done exploiting an interferometric method on the one hand and using computer generated holograms on the other hand. It is shown that by shifting the hologram with respect to an incoming Gaussian beam different superpositions of the Gaussian and the Laguerre-Gaussian beam can be produced. An analytical expression between the relative phase and the amplitudes of the modes and the displacement of the hologram is given. The application of such orbital angular momenta superpositions in quantum experiments such as quantum cryptography is discussed.Comment: 18 pages, 4 figures. to appear in Journal of Optics

Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes

Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in longwavelength fluctuations and is a universal function of the macroscopic decay rate

Fermi-liquid effects in the Fulde-Ferrell-Larkin-Ovchinnikov state of two-dimensional d-wave superconductors

We study the effects of Fermi-liquid interactions on quasi-two-dimensional d-wave superconductors in a magnetic field. The phase diagram of the superconducting state, including the periodic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in high magnetic fields, is discussed for different strengths of quasiparticle many-body interactions within Landau's theory of Fermi liquids. Decreasing the Fermi-liquid parameter $F_0^a$ causes the magnetic spin susceptibility to increase, which in turn leads to a reduction of the FFLO phase. It is shown that a negative $F_0^a$ results in a first-order phase transition from the normal to the uniform superconducting state in a finite temperature interval. Finally, we discuss the thermodynamic implications of a first-order phase transition for CeCoIn$_5$.Comment: published version; removed direct comparison with experiment for the upper critical field, as required by the referee

Spatial fluctuations of a surviving particle in the trapping reaction

We consider the trapping reaction, $A+B\to B$, where $A$ and $B$ particles have a diffusive dynamics characterized by diffusion constants $D_A$ and $D_B$. The interaction with $B$ particles can be formally incorporated in an effective dynamics for one $A$ particle as was recently shown by Bray {\it et al}. [Phys. Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space dimension $d=1$, the asymptotic behaviour of the spatial fluctuation, $^{1/2}$, for a surviving $A$ particle in the perturbative regime, $D_A/D_B\ll 1$, for the case of an initially uniform distribution of $B$ particles. We show that, for $t\gg 1$, $^{1/2} \propto t^{\phi}$ with $\phi=1/4$. By contrast, the fluctuations of paths constrained to return to their starting point at time $t$ grow with the larger exponent 1/3. Numerical tests are consistent with these predictions.Comment: 10 pages, 5 figure

Pauli-Limited Superconductivity with Classical Magnetic Fluctuations

We examine the effect of classical magnetic fluctuations on the phase diagram of paramagneticallylimited two-dimensional superconductors under a Zeeman magnetic field. We derive the free energy expansion in powers of the superconducting order parameter and analyze the character of the normalsuperconducting transition. While the transition is of the second order for all temperatures in the absence of magnetic fluctuations, we find that proximity to magnetism drives both the transition into the uniform state and that into the modulated (Fulde-Ferrell-Larkin-Ovchinnikov, FFLO) state to first order at intermediate temperatures. We compute the thermodynamic signatures of the normal-superconducting transition along the upper critical field.Comment: 16 pages, 9 figure

Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation

The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating function to the moments of the local FPTD matrix. This relationship can be physically interpreted in terms of steady-state relaxation, an extension of steady-state flow. Moreover, it is amenable to a statistical error analysis that can be used to significantly increase computational efficiency. The efficiency improvement can be extended to the FPTD itself by modelling it using a Gamma distribution or rational function approximation to its Laplace transform

There is no degree map for 0-cycles on Artin stacks

We show that there is no way to define degrees of 0-cycles on Artin stacks with proper good moduli spaces so that (i) the degree of an ordinary point is non-zero, and (ii) degrees are compatible with closed immersions.Comment: 3 page

Dampak Alokasi Anggaran Pengeluaran Pembangunan terhadap Perekonomian Indonesia: suatu Analisis Simulasi Kebijakan

This study aims (1) to construct Econometric Input-Output Model for Indonesia,which emphasizes the linkage between sectors, and (2) to analyze the impact of budgetallocation policy of development expenditure on Indonesian economy.The model, which construct by combining the advantages of input-output modeland econometric model, is called Model Input-Output Ekonometrika Indonesia. Themodel consists of 112 dynamic simultaneous equations, and it uses secondary data from1980-2000. The equation\u27s parameters are estimated by using the combination of threeestimation methods: (1) Ordinary Least Squares, (2) First Order of Autoregressive, and(3) Second Order of Autoregressive. The model is validated by Gauss-Siedel Methodand it is used for policy simulation analysis of budget development expenditure.The study shows that the impact of budget reallocation of developmentexpenditure on Indonesian economy (final demand, output, income, and sectoralemployment) is better than the budget allocation of development expenditure inRAPBN (National Budgetary Plan) 2002. Plantation sector gave the highestcontribution in supporting the output multiplier and high income. Furthermore, the food,beverages, and tobacco industries gave the highest contribution in creating highemployment multiplier

Effects of Two Energy Scales in Weakly Dimerized Antiferromagnetic Quantum Spin Chains

By means of thermal expansion and specific heat measurements on the high-pressure phase of (VO)$_2$P$_2$O$_7$, the effects of two energy scales of the weakly dimerized antiferromagnetic $S$ = 1/2 Heisenberg chain are explored. The low energy scale, given by the spin gap $\Delta$, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing T-DMRG calculations, shows that this feature originates from changes in the magnetic entropy with respect to $\Delta$, $\partial S^{m}/ \partial \Delta$. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in $\Delta$.Comment: 4 pages, 4 figures now identical with finally published versio