Generation of Micro Mechanical Devices Using Stereo Lithography

A high resolution machining setup for creating three-dimensional precision components from a UV-curable photo-resin has been developed. By using frequency-converted diode-pumped solid state lasers, functional micro-mechanical devices are directly fabricated in a successive layer-bylayer fashion. Within this paper, the direct generation of micro assemblies having moving components without further assembly of parts will be presented. The micro system design is based on user-defined 3D-CAD data and will completively be built up within the fabrication cycle. By using specially developed μSL materials with suitable properties for micromechanical parts, the development from Rapid Prototyping towards Rapid Production of small series is intended.Mechanical Engineerin

Stochastic Matrix Product States

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the hand of the asymmetric exclusion process

Conical: an extended module for computing a numerically satisfactory pair of solutions of the differential equation for conical functions

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine for computing the function ${{\rm R}}^{m}_{-\frac{1}{2}+i\tau}(x)$, a real-valued numerically satisfactory companion of the function ${\rm P}^m_{-\tfrac12+i\tau}(x)$ for $x>1$. In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided.Comment: To appear in Computer Physics Communication

Quantum Metropolis Sampling

The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is believed to be intractable for classical computers. Such a machine would have a wide range of applications in the simulation of many-body quantum physics, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. Here, we demonstrate how to implement a quantum version of the Metropolis algorithm on a quantum computer. This algorithm permits to sample directly from the eigenstates of the Hamiltonian and thus evades the sign problem present in classical simulations. A small scale implementation of this algorithm can already be achieved with today's technologyComment: revised versio

Resonantly enhanced pair production in a simple diatomic model

A new mechanism for the production of electron-positron pairs from the interaction of a laser field and a fully stripped diatomic molecule in the tunneling regime is presented. When the laser field is turned off, the Dirac operator has resonances in both the positive and the negative energy continua while bound states are in the mass gap. When this system is immersed in a strong laser field, the resonances move in the complex energy plane: the negative energy resonances are pushed to higher energies while the bound states are Stark shifted. It is argued here that there is a pair production enhancement at the crossing of resonances by looking at a simple 1-D model: the nuclei are modeled simply by Dirac delta potential wells while the laser field is assumed to be static and of finite spatial extent. The average rate for the number of electron-positron pairs produced is evaluated and the results are compared to the single nucleus and to the free cases. It is shown that positrons are produced by the Resonantly Enhanced Pair Production (REPP) mechanism, which is analogous to the resonantly enhanced ionization of molecular physics. This phenomenon could be used to increase the number of pairs produced at low field strength, allowing the study of the Dirac vacuum.Comment: 11 pages, 4 figure

Fermions on one or fewer Kinks

We find the full spectrum of fermion bound states on a Z_2 kink. In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we find some of the low lying bound states explicitly.Comment: 7 pages, 4 figure

Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders

We consider the problem of computing satisfactory pairs of solutions of the differential equation for Legendre functions of non-negative integer order $\mu$ and degree $-\frac12+i\tau$, where $\tau$ is a non-negative real parameter. Solutions of this equation are the conical functions ${\rm{P}}^{\mu}_{-\frac12+i\tau}(x)$ and ${Q}^{\mu}_{-\frac12+i\tau}(x)$, $x>-1$. An algorithm for computing a numerically satisfactory pair of solutions is already available when $-1<x<1$ (see \cite{gil:2009:con}, \cite{gil:2012:cpc}).In this paper, we present a stable computational scheme for a real valued numerically satisfactory companion of the function ${\rm{P}}^{\mu}_{-\frac12+i\tau}(x)$ for $x>1$, the function $\Re\left\{e^{-i\pi \mu} {{Q}}^{\mu}_{-\frac{1}{2}+i\tau}(x) \right\}$. The proposed algorithm allows the computation of the function on a large parameter domain without requiring the use of extended precision arithmetic.Comment: To be published in Numerical Algoritm

Computation of the coefficients appearing in the uniform asymptotic expansions of integrals

The coefficients that appear in uniform asymptotic expansions for integrals are typically very complicated. In the existing literature the majority of the work only give the first two coefficients. In a limited number of papers where more coefficients are given the evaluation of the coefficients near the coalescence points is normally highly numerically unstable. In this paper, we illustrate how well-known Cauchy type integral representations can be used to compute the coefficients in a very stable and efficient manner. We discuss the cases: (i) two coalescing saddles, (ii) two saddles coalesce with two branch points, (iii) a saddle point near an endpoint of the interval of integration. As a special case of (ii) we give a new uniform asymptotic expansion for Jacobi polynomials $P_n^{(\alpha,\beta)}(z)$ in terms of Laguerre polynomials $L_n^{(\alpha)}(x)$ as $n\to\infty$ that holds uniformly for $z$ near $1$. Several numerical illustrations are included.Comment: 18 page

Crossover between ballistic and diffusive transport: The Quantum Exclusion Process

We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a hierarchy of decoupled equations for the correlation functions emerges. In the special case of incoherent, nearest-neighbour hopping the equation for the two-point functions is solved explicitly. The Green's function for the particle density is obtained analytically and a timescale is identified where a crossover from ballistic to diffusive behaviour takes place. The result can be interpreted as a competition between the two types of conduction channels where diffusion dominates on large timescales.Comment: 20 pages, 5 figure