Quantization of the damped harmonic oscillator revisited

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. (C) 2011 Elsevier B.V. All rights reserved.

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

Color Segmentation using LVQ-Learning Vector Quantization

This thesis aims to present a color segmentation approach for traffic sign recognition based on LVQ neural networks. The RGB images were converted into HSV color space, and segmented using LVQ depending on the hue and saturation values of each pixel in the HSV color space. LVQ neural network was used to segment red, blue and yellow colors on the road and traffic signs to detect and recognize them. LVQ was effectively applied to 536 sampled images taken from different countries in different conditions with 89% accuracy and the execution time of each image among 31 images was calculated in between 0.726sec to 0.844sec. The method was tested in different environmental conditions and LVQ showed its capacity to reasonably segment color despite remarkable illumination differences. The results showed high robustness.

A two stage vector quantization approach via self-organizing map

In this paper, a two-stage algorithm for vector quantization is proposed based on a self-organizing map (SOM) neural network. First, a conventional self-organizing map is modified to deal with dead codebooks in the learning process and is then used to obtain the codebook distribution structure for a given set of input data. Next, subblocks are classified based on the previous structure distribution with a prior criteria. Then, the conventional LBG algorithm is applied to these sub-blocks for data classification with initial values obtained via the SOM. Finally, extensive simulations illustrate that the proposed two-stage algorithm is very effective.

Identification of concurrent control chart patterns with singular spectrum analysis and learning vector quantization

Identification of unnatural control chart patterns (CCPs) from manufacturing process measurements is a critical task in quality control as these patterns indicate that the manufacturing process is out-of-control. Recently, there have been numerous efforts in developing pattern recognition and classification methods based on artificial neural network to automatically recognize unnatural patterns. Most of them assume that a single type of unnatural pattern exists in process data. Due to this restrictive assumption, severe performance degradations are observed in these methods when unnatural concurrent CCPs present in process data. To address this problem, this paper proposes a novel approach based on singular spectrum analysis (SSA) and learning vector quantization network to identify concurrent CCPs. The main advantage of the proposed method is that it can be applied to the identification of concurrent CCPs in univariate manufacturing processes. Moreover, there are no permutation and scaling ambiguities in the CCPs recovered by the SSA. These desirable features make the proposed algorithm an attractive alternative for the identification of concurrent CCPs. Computer simulations and a real application for aluminium smelting processes confirm the superior performance of proposed algorithm for sets of typical concurrent CCPs.

Robustness enhancement of quantization based audio watermarking method using adaptive safe-band

This paper presents a novel adaptive safe-band for quantization based audio watermarking methods, aiming to improve robustness. Considerable number of audio watermarking methods have been developed using quantization based techniques. These techniques are generally vulnerable to signal processing attacks. For these conventional quantization based techniques, robustness can be marginally improved by choosing larger step sizes at the cost of significant perceptual quality degradation. We first introduce fixed size safe-band between two quantization steps to improve robustness. This safe-band will act as a buffer to withstand certain types of attacks. Then we further improve the robustness by adaptively changing the size of the safe-band based on the audio signal feature used for watermarking. Compared with conventional quantization based method and the fixed size safe-band based method, the proposed adaptive safe-band based quantization method is more robust to attacks. The effectiveness of the proposed technique is demonstrated by simulation results. © 2014 IEEE.

Quantization rules for bound states in quantum wells

An algebraic reformulation of the Bohr-Sommerfeld (BS) quantization rule is suggested and applied to the study of bound states in one-dimensional quantum wells. The energies obtained with the present quantization rule are compared to those obtained with the usual BS and WKB quantization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular physics, the present quantization rule not only yields a good approximation to the exact solution of the Schrodinger equation, but yields more precise energies than those obtained with the usual BS and/or WKB quantization rules. Among the examples considered numerically are the Poeschl-Teller potential and several anharmonic oscillator potentials. which simulate molecular vibrational spectra and the problem of an isolated quantum well structure subject to an external electric field.

Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena

We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this held theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and extreme Reissner-Nordstrom black holes in arbitrary dimensions higher than three.

Quantization of the superstring in Ramond-Ramond backgrounds

Sigma model actions are constructed for the type II superstring compactified to four-and six-dimensional curved backgrounds which can contain non-vanishing Ramond-Ramond fields. These actions are N = 2 worldsheet superconformally invariant and can be covariantly quantized preserving manifest spacetime supersymmetry. They are constructed using a hybrid Version of superstring variables which combines features of the Ramond-Neveu-Schwarz and Green-Schwarz formalisms. For the AdS(2) x S-2 and AdS(3) x S-3 backgrounds, these actions differ from the classical Green-Schwarz actions by a crucial kinetic term for the fermions. Parts of this work have been done in collaborations with M Bershadsky, T Hauer, W Siegel, C Vafa, E Witten, S Zhukov and B Zwiebach.

Reply to comment on 'Quantization rules for bound states in quantum wells'

In this reply to the comment on 'Quantization rules for bound states in quantum wells' we point out some interesting differences between the supersymmetric Wentzel-Kramers-Brillouin (WKB) quantization rule and a matrix generalization of usual WKB (mWKB) and Bohr-Sommerfeld (mBS) quantization rules suggested by us. There are certain advantages in each of the supersymmetric WKB (SWKB), mWKB and mBS quantization rules. Depending on the quantum well, one of these could be more useful than the other and it is premature to claim unconditional superiority of SWKB over mWKB and mBS quantization rules.

Electric charge quantization and the muon anomalous magnetic moment

We investigate some proposals to solve the electric charge quantization puzzle that simultaneously explain the recent measured deviation on the muon anomalous magnetic moment. For this we assess extensions of the electro-weak standard model spanning modifications on the scalar sector only. It is interesting to verify that one can have modest extensions which easily account for the solution for both problems.

First quantized approaches to neutrino oscillations and second quantization

Neutrino oscillations are treated from the point of view of relativistic first quantized theories and compared to second quantized treatments. Within first quantized theories, general oscillation probabilities can be found for Dirac fermions and charged spin 0 bosons. A clear modification in the oscillation formulas can be obtained and its origin is elucidated and confirmed to be inevitable from completeness and causality requirements. The left-handed nature of created and detected neutrinos can also be implemented in the first quantized Dirac theory in the presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. Concerning second quantized approaches, it is shown in a calculation using virtual neutrino propagation that both neutrinos and antineutrinos may also contribute as intermediate particles. The sign of the contributing neutrino energy may have to be chosen explicitly without being automatic in the formalism. At last, a simple second quantized description of the flavor oscillation phenomenon is devised. In this description there is no interference terms between positive and negative components, but it still gives simple normalized oscillation probabilities. A new effect appearing in this context is an inevitable but tiny violation of the initial flavor of neutrinos. The probability loss due to the conversion of left-handed neutrinos to right-handed neutrinos is also presented.

Covariant quantization of the superstring

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincare covariant manner. Quantization can be generalized to curved supergravity backgrounds and the vertex operator for fluctuations around AdS(5) x S-5 is explicitly constructed.

Increase of temperature of an ideal nondegenerate quantum gas in a suddenly expanding box due to energy quantization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)