On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature

The boundary beta-function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta-function, expressing it as the gradient of the boundary entropy s at fixed non-zero temperature. The gradient formula implies that s decreases under renormalization except at critical points (where it stays constant). At a critical point, the number exp(s) is the ``ground-state degeneracy,'' g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature except at critical points, where it is independent of temperature. The boundary thermodynamic energy u then also decreases with temperature. It remains open whether the boundary entropy of a 1-d quantum system is always bounded below. If s is bounded below, then u is also bounded below.Comment: 12 pages, Latex, 1 eps-figure; v2: some expository material added, a slightly more condensed version of the paper is publihed in Phys. Rev. Let

Generalizations of Weighted Trapezoidal Inequality for Monotonic Mappings and Its Applications

In this paper, we establish some generalizations of weighted trapezoid inequality for monotonic mappings, and give several applications for r − moment, the expectation of a continuous random variable and the Beta mapping

A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment

A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range

Hybrid Optoelectronic Correlator Architecture for Shift Invariant Target Recognition

In this paper, we present theoretical details and the underlying architecture of a hybrid optoelectronic correlator that correlates images using Spatial Light Modulators (SLM), detector arrays and Field Programmable Gate Array (FPGA). The proposed architecture bypasses the need for nonlinear materials such as photorefractive polymer films by using detectors instead, and the phase information is yet conserved by the interference of plane waves with the images. However, the output of such a Hybrid Opto-electronic Correlator (HOC) has four terms: two convolution signals and two cross-correlation signals. By implementing a phase stabilization and scanning circuit, the convolution terms can be eliminated, so that the behavior of an HOC becomes essentially identical to that of a conventional holographic correlator (CHC). To achieve the ultimate speed of such a correlator, we also propose an opto-electronic chip which would perform all the electrical processes in a parallel manner. The HOC architecture along with the phase stabilization technique would thus be as good as a CHC, capable of high speed image recognition in a translation invariant manner

Analysis of Mono-, Di- and Oligosaccharides by CE Using a Two-Stage Derivatization Method and LIF Detection.

A sensitive CE with LIF method has been developed for quantitative analysis of small carbohydrates. In this work, 17 carbohydrates including mono-, di- and oligosaccharides were simultaneously derivatized with 4-fluoro 7-nitrobenzo furazane (NBD-F) via a twostep reaction involving reductive amination with ammonia followed by condensation with NBD-F. Under the optimized derivatization conditions all carbo-hydrates were successfully derivatized within 2.5 h and separated within 15 min using borate buffer (90 mmol/L, pH 9.2). For sugar standards LODs were in the range of 49.7 to 243.6 nmol/L. Migration time and peak area reproducibility were better than RSD 0.1 and 3%, respectively. The method was applied to measure sugars in nanoliter volume samples of phloem sap obtained by stylectomy from wheat and to honeydew samples obtained from aphids feeding from wheat and willow

Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. For finding solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N2xN2. When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a fifteen-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels

Fast-Light in a Photorefractive Crystal for Gravitational Wave Detection

We demonstrate superluminal light propagation using two frequency multiplexed pump beams to produce a gain doublet in a photorefractive crystal of Ce:BaTiO3. The two gain lines are obtained by two-wave mixing between a probe field and two individual pump fields. The angular frequencies of the pumps are symmetrically tuned from the frequency of the probe. The frequency difference between the pumps corresponds to the separation of the two gain lines; as it increases, the crystal gradually converts from normal dispersion without detuning to an anomalously dispersive medium. The time advance is measured as 0.28 sec for a pulse propagating through a medium with a 2Hz gain separation, compared to the same pulse propagating through empty space. We also demonstrate directly anomalous dispersion profile using a modfied experimental configuration. Finally, we discuss how anomalous dispersion produced this way in a faster photorefractive crystal (such as SPS: Sn2P2S6) could be employed to enhance the sensitivity-bandwidth product of a LIGO type gravitational wave detector augmented by a White Light Cavity.Comment: 14 pages, 5 figure

Steady, oscillatory, and unsteady subsonic Aerodynamics, production version 1.1 (SOUSSA-P1.1). Volume 2: User/programmer manual

A user/programmer manual for the computer program SOUSSA P 1.1 is presented. The program was designed to provide accurate and efficient evaluation of steady and unsteady loads on aircraft having arbitrary shapes and motions, including structural deformations. These design goals were in part achieved through the incorporation of the data handling capabilities of the SPAR finite element Structural Analysis computer program. As a further result, SOUSSA P possesses an extensive checkpoint/ restart facility. The programmer's portion of this manual includes overlay/subroutine hierarchy, logical flow of control, definition of SOUSSA P 1.1 FORTRAN variables, and definition of SOUSSA P 1.1 subroutines. Purpose of the SOUSSA P 1.1 modules, input data to the program, output of the program, hardware/software requirements, error detection and reporting capabilities, job control statements, a summary of the procedure for running the program and two test cases including input and output and listings are described in the user oriented portion of the manual