Magnetic Flux Quantization of the Landau Problem
NASA Astrophysics Data System (ADS)
Wang, Jianhua; Li, Kang; Long, Shuming; Yuan, Yi
2014-08-01
Landau problem has a very important application in modern physics, in which two-dimensional electron gas system and quantum Hall effect are outstanding. In this paper, first we review the solution of the Pauli equation, then using the single electron wave function, we calculate moving area expectations of the ideal 2-dimensional electron gas system and the per unit area's degeneracy of the electron gas system. As a result, how to calculate the magnetic flux of the electron gas system is given. It shows that the magnetic flux of 2-dimensional electron gas system in magnetic field is quantized, and magnetic flux quantization results from the quantization of the moving area expectations of electron gas system.
Flux insertion, entanglement, and quantized responses
NASA Astrophysics Data System (ADS)
Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
2014-10-01
There has been much discussion about which aspects of the entanglement spectrum are in fact robust properties of a bulk phase. By making use of a trick for constructing the ground state of a system on a ring given the ground state on an infinite chain, we show why the entanglement spectrum combined with the quantum numbers of the Schmidt states encodes a variety of robust topological observables. We introduce a method that allows us to characterize phases by measuring quantized responses, such as the Hall conductance, using data contained in the entanglement spectrum. As concrete examples, we show how the Berry phase allows us to map out the phase diagram of a spin-1 model and calculate the Hall conductivity of a quantum Hall system.
Theory of the Knight Shift and Flux Quantization in Superconductors
DOE R&D Accomplishments Database
Cooper, L. N.; Lee, H. J.; Schwartz, B. B.; Silvert, W.
1962-05-01
Consequences of a generalization of the theory of superconductivity that yields a finite Knight shift are presented. In this theory, by introducing an electron-electron interaction that is not spatially invariant, the pairing of electrons with varying total momentum is made possible. An expression for Xs (the spin susceptibility in the superconducting state) is derived. In general Xs is smaller than Xn, but is not necessarily zero. The precise magnitude of Xs will vary from sample to sample and will depend on the nonuniformity of the samples. There should be no marked size dependence and no marked dependence on the strength of the magnetic field; this is in accord with observation. The basic superconducting properties are retained, but there are modifications in the various electromagnetic and thermal properties since the electrons paired are not time sequences of this generalized theory on flux quantization arguments are presented.(auth)
Bäcklund flux quantization in a model of electrodiffusion based on Painlevé II
NASA Astrophysics Data System (ADS)
Bracken, A. J.; Bass, L.; Rogers, C.
2012-03-01
A previously established model of steady one-dimensional two-ion electrodiffusion across a liquid junction is reconsidered. It involves three coupled first-order nonlinear ordinary differential equations and has the second-order Painlevé II equation at its core. Solutions are now grouped by Bäcklund transformations into infinite sequences, partially labelled by two Bäcklund invariants. Each sequence is characterized by evenly-spaced quantized fluxes of the two ionic species, and hence evenly-spaced quantization of the electric current density. Finite subsequences of exact solutions are identified, with positive ionic concentrations and quantized fluxes, starting from a solution with zero electric field found by Planck, and suggesting an interpretation as a ground state plus excited states of the system. Positivity of ionic concentrations is established whenever Planck’s charge-neutral boundary conditions apply. Exact solutions are obtained for the electric field and ionic concentrations in well-stirred reservoirs outside each face of the junction, enabling the formulation of more realistic boundary conditions. In an approximate form, these lead to radiation boundary conditions for Painlevé II. Illustrative numerical solutions are presented, and the problem of establishing compatibility of boundary conditions with the structure of flux-quantizing sequences is discussed.
Control and readout of current-induced magnetic flux quantization in a superconducting transformer
NASA Astrophysics Data System (ADS)
Kerner, C.; Hackens, B.; Golubović, D. S.; Poli, S.; Faniel, S.; Magnus, W.; Schoenmaker, W.; Bayot, V.; Maes, H.
2009-02-01
We demonstrate a simple and robust method for inducing and detecting changes of magnetic flux quantization in the absence of an externally applied magnetic field. In our device, an isolated ring is interconnected with two access loops via permalloy cores, forming a superconducting transformer. By applying and tuning a direct current at the first access loop, the number of flux quanta trapped in the isolated ring is modified without the aid of an external field. The flux state of the isolated ring is simply detected by recording the evolution of the critical current of the second access loop.
RSFQ: Ultrafast Logic Based on Magnetic Flux Quantization
NASA Astrophysics Data System (ADS)
Likharev, Konstantin
2000-03-01
I will review the progress and prospects of Rapid Single-Flux-Quantum (RSFQ) logic family, the newest generation of ultrafast superconductor digital circuits. Elementary cells of this family, based on overdamped Josephson junctions, store and process digital bits in the form of single quanta of magnetic flux, while intercell signaling is provided by picosecond pulses transferred along superconductor microstrip lines, with a speed approaching speed of light. RSFQ integrated circuits may provide the highest speed available in superconductor digital electronics: simple devices like digital frequency dividers have been demonstrated to operate at frequencies up to 770 GHz. Simultaneously, power consumption of RSFQ devices is extremely low (at helium temperatures, about 10-18 Joule per bit), allowing very compact chip packaging, and hence dramatic cuts in the interchip communication latency. Finally, the technology of fabrication of the niobium-based RSFQ circuits is considerably simpler than the standard silicon CMOS process. As a result of the recent work at Stony Brook, HYPRES and elsewhere, relatively complex RSFQ circuits (with thousands of Josephson junctions), including notably the world's fastest analog-to-digital and digital-to-analog converters and digital autocorrelators, have been designed, fabricated, and successfully tested. The main problem with the practical introduction of RSFQ circuits is the necessity of their deep refrigeration. Helium-range closed-cycle refrigerators are still costly and bulky, while HTS RSFQ circuits run into fabrication yield and layout problems. However, for several important applications (including A/D and D/A conversion, digital SQUIDs, RF voltage standards and calibrators, digital correlators, and possibly high-performance computing), the unparalleled performance of LTS RSFQ devices may overweigh the inconvenience of their helium cooling. I will describe the recent advances in these directions, with a special emphasis on the
Flux quantization in rings for Hubbard (attractive and repulsive) and t - J -like Hamiltonians
Ferretti, A. ); Kulik, I.O. ); Lami, A. )
1992-03-01
The ground-state energy of rings with 10 or 16 sites and 2 or 4 fermions (holes or electrons) is computed as a function of the flux {Phi} created by a vector potential constant along the ring (Aharonov-Bohm setup) for three different model Hamiltonians: the attractive ({ital U}{lt}0) and repulsive ({ital U}{gt}0) Hubbard and a {ital t}-{ital J}-like Hamiltonian. In all cases the flux is found to be quantized in units {ital hc}/2{ital e}, showing that the charge carriers are pairs. The possible role of phonon fluctuations in discriminating among the different models is also investigated.
Sensitivity of ultracold atoms to quantized flux in a superconducting ring.
Weiss, P; Knufinke, M; Bernon, S; Bothner, D; Sárkány, L; Zimmermann, C; Kleiner, R; Koelle, D; Fortágh, J; Hattermann, H
2015-03-20
We report on the magnetic trapping of an ultracold ensemble of (87)Rb atoms close to a superconducting ring prepared in different states of quantized magnetic flux. The niobium ring of 10 μm radius is prepared in a flux state n Φ(0), where Φ(0)=h/2e is the flux quantum and n varying between ±6. An atomic cloud of 250 nK temperature is positioned with a harmonic magnetic trapping potential at ∼18 μm distance below the ring. The inhomogeneous magnetic field of the supercurrent in the ring contributes to the magnetic trapping potential of the cloud. The induced deformation of the magnetic trap impacts the shape of the cloud, the number of trapped atoms, as well as the center-of-mass oscillation frequency of Bose-Einstein condensates. When the field applied during cooldown of the chip is varied, the change of these properties shows discrete steps that quantitatively match flux quantization. PMID:25839266
Low-power high-resolution superconducting flux-quantizing A/D converter for IR array readout
NASA Astrophysics Data System (ADS)
Rylov, Sergey V.; Robertazzi, R. P.
1994-06-01
We have developed a new architecture for a superconducting high-resolution analog-to-digital converter (ADC) which is highly beneficial for IR array readout applications due to its high sensitivity, wide dynamic range and sub-mW power consumption. This ADC is based on the principles of magnetic flux quantization, direct differential coding and decimation filtering. The digital part of the ADC employs elements of the Rapid Single Flux Quantum logic family which are capable of clock frequencies in excess of 100 GHz. We discuss the limits of ADC performance and present an analysis of the power consumption in these ADCs. We also report experimental verification of several key components of this architecture in Niobium technology (operating at 4.2 K), particularly the implementation of a synchronizer unit (necessary for the generation of the differential digital code) as well as a dual-counter synchronous ADC.
A high accuracy all-angle gyroscope readout using quantized flux
NASA Technical Reports Server (NTRS)
Anderson, J. T.; Everitt, C. W. F.
1977-01-01
Means are described to use SQUID magnetometer flux counting and the London moment of a spherical superconducting gyroscope to read out the gyroscope spin axis direction to an accuracy of at least 23 bits per quadrant. The system is discussed in analogy to optical fringe counting as applied to distance measurement. Several methods of applying both analog and digital SQUID magnetometers to the readout problem are given, as well as limitations on each. Described are two methods of increasing the flux available for measurement: magnetizing the gyroscope with a trapped field, and optimizing readout circuit inductances. Finally, the same principle on which the gyroscope readout is based is applied to a description of a high accuracy, flux counting, digital angle encoder.
NASA Astrophysics Data System (ADS)
Faizal, Mir
2013-12-01
In this Letter we will analyze the creation of the multiverse. We will first calculate the wave function for the multiverse using third quantization. Then we will fourth-quantize this theory. We will show that there is no single vacuum state for this theory. Thus, we can end up with a multiverse, even after starting from a vacuum state. This will be used as a possible explanation for the creation of the multiverse. We also analyze the effect of interactions in this fourth-quantized theory.
NASA Technical Reports Server (NTRS)
Gray, Robert M.
1989-01-01
During the past ten years Vector Quantization (VQ) has developed from a theoretical possibility promised by Shannon's source coding theorems into a powerful and competitive technique for speech and image coding and compression at medium to low bit rates. In this survey, the basic ideas behind the design of vector quantizers are sketched and some comments made on the state-of-the-art and current research efforts.
Seligman, Thomas H.; Prosen, Tomaz
2010-12-23
The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a non-orthogonal basis, the latter requires the introduction of a dual set of spaces. In both cases an operator algebra closely resembling the canonical one is developed and used to define the dual sets of bases. We here concentrated on the bosonic case where the unboundedness of the operators requires the definitions of dual spaces to support the pair of bases. Some applications, mainly to non-equilibrium steady states, will be mentioned.
Lagrange structure and quantization
NASA Astrophysics Data System (ADS)
Kazinski, Peter O.; Lyakhovich, Simon L.; Sharapov, Alexey A.
2005-07-01
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d+1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.
Weak associativity and deformation quantization
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
2016-09-01
Non-commutativity and non-associativity are quite natural in string theory. For open strings it appears due to the presence of non-vanishing background two-form in the world volume of Dirichlet brane, while in closed string theory the flux compactifications with non-vanishing three-form also lead to non-geometric backgrounds. In this paper, working in the framework of deformation quantization, we study the violation of associativity imposing the condition that the associator of three elements should vanish whenever each two of them are equal. The corresponding star products are called alternative and satisfy important for physical applications properties like the Moufang identities, alternative identities, Artin's theorem, etc. The condition of alternativity is invariant under the gauge transformations, just like it happens in the associative case. The price to pay is the restriction on the non-associative algebra which can be represented by the alternative star product, it should satisfy the Malcev identity. The example of nontrivial Malcev algebra is the algebra of imaginary octonions. For this case we construct an explicit expression of the non-associative and alternative star product. We also discuss the quantization of Malcev-Poisson algebras of general form, study its properties and provide the lower order expression for the alternative star product. To conclude we define the integration on the algebra of the alternative star products and show that the integrated associator vanishes.
Quantization Effects on Complex Networks.
Wang, Ying; Wang, Lin; Yang, Wen; Wang, Xiaofan
2016-01-01
Weights of edges in many complex networks we constructed are quantized values of the real weights. To what extent does the quantization affect the properties of a network? In this work, quantization effects on network properties are investigated based on the spectrum of the corresponding Laplacian. In contrast to the intuition that larger quantization level always implies a better approximation of the quantized network to the original one, we find a ubiquitous periodic jumping phenomenon with peak-value decreasing in a power-law relationship in all the real-world weighted networks that we investigated. We supply theoretical analysis on the critical quantization level and the power laws. PMID:27226049
Quantization Effects on Complex Networks
NASA Astrophysics Data System (ADS)
Wang, Ying; Wang, Lin; Yang, Wen; Wang, Xiaofan
2016-05-01
Weights of edges in many complex networks we constructed are quantized values of the real weights. To what extent does the quantization affect the properties of a network? In this work, quantization effects on network properties are investigated based on the spectrum of the corresponding Laplacian. In contrast to the intuition that larger quantization level always implies a better approximation of the quantized network to the original one, we find a ubiquitous periodic jumping phenomenon with peak-value decreasing in a power-law relationship in all the real-world weighted networks that we investigated. We supply theoretical analysis on the critical quantization level and the power laws.
Quantization Effects on Complex Networks
Wang, Ying; Wang, Lin; Yang, Wen; Wang, Xiaofan
2016-01-01
Weights of edges in many complex networks we constructed are quantized values of the real weights. To what extent does the quantization affect the properties of a network? In this work, quantization effects on network properties are investigated based on the spectrum of the corresponding Laplacian. In contrast to the intuition that larger quantization level always implies a better approximation of the quantized network to the original one, we find a ubiquitous periodic jumping phenomenon with peak-value decreasing in a power-law relationship in all the real-world weighted networks that we investigated. We supply theoretical analysis on the critical quantization level and the power laws. PMID:27226049
NASA Astrophysics Data System (ADS)
Fröhlich, J.; Knowles, A.; Pizzo, A.
2007-03-01
Within the framework of the theory of interacting classical and quantum gases, it is shown that the atomistic constitution of gases can be understood as a consequence of (second) quantization of a continuum theory of gases. In this paper, this is explained in some detail for the theory of non-relativistic interacting Bose gases, which can be viewed as the second quantization of a continuum theory whose dynamics is given by the Hartree equation. Conversely, the Hartree equation emerges from the theory of Bose gases in the mean-field limit. It is shown that, for such systems, the time evolution of 'observables' commutes with their Wick quantization, up to quantum corrections that tend to zero in the mean-field limit. This is an Egorov-type theorem.
NASA Astrophysics Data System (ADS)
He, Xiao-Gang; Ma, Bo-Qiang
We show that black holes can be quantized in an intuitive and elegant way with results in agreement with conventional knowledge of black holes by using Bohr's idea of quantizing the motion of an electron inside the atom in quantum mechanics. We find that properties of black holes can also be derived from an ansatz of quantized entropy Δ S = 4π k Δ R/{{-{λ }}}, which was suggested in a previous work to unify the black hole entropy formula and Verlinde's conjecture to explain gravity as an entropic force. Such an Ansatz also explains gravity as an entropic force from quantum effect. This suggests a way to unify gravity with quantum theory. Several interesting and surprising results of black holes are given from which we predict the existence of primordial black holes ranging from Planck scale both in size and energy to big ones in size but with low energy behaviors.
On Quantizable Odd Lie Bialgebras
NASA Astrophysics Data System (ADS)
Khoroshkin, Anton; Merkulov, Sergei; Willwacher, Thomas
2016-09-01
Motivated by the obstruction to the deformation quantization of Poisson structures in infinite dimensions, we introduce the notion of a quantizable odd Lie bialgebra. The main result of the paper is a construction of the highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so-called quantizable Poisson structures.
ERIC Educational Resources Information Center
DeBuvitz, William
2014-01-01
I am a volunteer reader at the Princeton unit of "Learning Ally" (formerly "Recording for the Blind & Dyslexic") and I recently discovered that high school students are introduced to the concept of quantization well before they take chemistry and physics. For the past few months I have been reading onto computer files a…
Uniform quantized electron gas.
Høye, Johan S; Lomba, Enrique
2016-10-19
In this work we study the correlation energy of the quantized electron gas of uniform density at temperature T = 0. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the partition function of quantized systems. With this representation the quantum mechanical problem can be interpreted as, and is equivalent to, a classical polymer problem in four dimensions where the fourth dimension is imaginary time. Thus methods, results, and properties obtained in the statistical mechanics of classical fluids can be utilized. From this viewpoint we recover the well known RPA (random phase approximation). Then to improve it we modify the RPA by requiring the corresponding correlation function to be such that electrons with equal spins can not be on the same position. Numerical evaluations are compared with well known results of a standard parameterization of Monte Carlo correlation energies. PMID:27546166
Quantization of Constrained Systems
NASA Astrophysics Data System (ADS)
Klauder, John R.
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of coherent-state, phase-space path integration, and show that all such cases may be treated, within the original classical phase space, by using suitable path-integral measures for the Lagrange multipliers which ensure that the quantum system satisfies the appropr iate quantum constraint conditions. Unlike conventional methods, our procedures involve no delta-functionals of the classical constraints, no need for dynamical gauge fixing of first-class constraints nor any average thereover, no need to eliminate second-class constraints, no potentially ambiguous determinants, as well as no need to add auxiliary dynamical variables expanding the phase space beyond its original classical formulation, including no ghosts. Bes ides several pedagogical examples, we also study: (i) the quantization procedure for reparameterization invariant models, (ii) systems for which the original set of Lagrange multipliers are elevated to the status of dynamical variables and used to define an extended dynamical system which is completed with the addition of suitable conjugates and new sets of constraints and their associated Lagrange multipliers, (iii) special examples of alternative but equivalent formulations of given first-class constraint s, as well as (iv) a comparison of both regular and irregular constraints.
Coherent state quantization of quaternions
Muraleetharan, B. E-mail: santhar@gmail.com; Thirulogasanthar, K. E-mail: santhar@gmail.com
2015-08-15
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols, and related quantities are analyzed. Quaternionic version of the harmonic oscillator and Weyl-Heisenberg algebra are also obtained.
Coherent state quantization of quaternions
NASA Astrophysics Data System (ADS)
Muraleetharan, B.; Thirulogasanthar, K.
2015-08-01
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols, and related quantities are analyzed. Quaternionic version of the harmonic oscillator and Weyl-Heisenberg algebra are also obtained.
Divergence-based vector quantization.
Villmann, Thomas; Haase, Sven
2011-05-01
Supervised and unsupervised vector quantization methods for classification and clustering traditionally use dissimilarities, frequently taken as Euclidean distances. In this article, we investigate the applicability of divergences instead, focusing on online learning. We deduce the mathematical fundamentals for its utilization in gradient-based online vector quantization algorithms. It bears on the generalized derivatives of the divergences known as Fréchet derivatives in functional analysis, which reduces in finite-dimensional problems to partial derivatives in a natural way. We demonstrate the application of this methodology for widely applied supervised and unsupervised online vector quantization schemes, including self-organizing maps, neural gas, and learning vector quantization. Additionally, principles for hyperparameter optimization and relevance learning for parameterized divergences in the case of supervised vector quantization are given to achieve improved classification accuracy. PMID:21299418
Tse, Wang-Kong; MacDonald, A H
2012-12-01
We investigate the Casimir effect between two-dimensional electron systems driven to the quantum Hall regime by a strong perpendicular magnetic field. In the large-separation (d) limit where retardation effects are essential, we find (i) that the Casimir force is quantized in units of 3ħcα(2)/8π(2)d(4) and (ii) that the force is repulsive for mirrors with the same type of carrier and attractive for mirrors with opposite types of carrier. The sign of the Casimir force is therefore electrically tunable in ambipolar materials such as graphene. The Casimir force is suppressed when one mirror is a charge-neutral graphene system in a filling factor ν=0 quantum Hall state. PMID:23368242
First quantized electrodynamics
Bennett, A.F.
2014-06-15
The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation of electrons entangled in space or time. The parametrized formalism leads directly and without further conjecture to the Bethe–Salpeter equation for bound states. The formalism also yields the Uehling shift of the hydrogenic spectrum, the anomalous magnetic moment of the electron to leading order in the fine structure constant, the Lamb shift and the axial anomaly of QED. -- Highlights: •First-quantized electrodynamics of the parametrized Dirac equation is developed. •Unrestricted entanglement in time is made explicit. •Bethe and Salpeter’s equation for relativistic bound states is derived without further conjecture. •One-loop scattering corrections and the axial anomaly are derived using a partial summation. •Wide utility of semi-classical Quantum Electrodynamics is argued.
Quantized beam shifts in graphene
de Melo Kort-Kamp, Wilton Junior; Sinitsyn, Nikolai; Dalvit, Diego Alejandro Roberto
2015-10-08
We predict the existence of quantized Imbert-Fedorov, Goos-Hanchen, and photonic spin Hall shifts for light beams impinging on a graphene-on-substrate system in an external magnetic field. In the quantum Hall regime the Imbert-Fedorov and photonic spin Hall shifts are quantized in integer multiples of the fine structure constant α, while the Goos-Hanchen ones in multiples of α^{2}. We investigate the influence on these shifts of magnetic field, temperature, and material dispersion and dissipation. An experimental demonstration of quantized beam shifts could be achieved at terahertz frequencies for moderate values of the magnetic field.
VLSI Processor For Vector Quantization
NASA Technical Reports Server (NTRS)
Tawel, Raoul
1995-01-01
Pixel intensities in each kernel compared simultaneously with all code vectors. Prototype high-performance, low-power, very-large-scale integrated (VLSI) circuit designed to perform compression of image data by vector-quantization method. Contains relatively simple analog computational cells operating on direct or buffered outputs of photodetectors grouped into blocks in imaging array, yielding vector-quantization code word for each such block in sequence. Scheme exploits parallel-processing nature of vector-quantization architecture, with consequent increase in speed.
QED in Krein Space Quantization
NASA Astrophysics Data System (ADS)
Zarei, A.; Forghan, B.; Takook, M. V.
2011-08-01
In this paper we consider the QED in Krein space quantization. We show that the theory is automatically regularized. The three primitive divergences integrals in usual QED are considered in Krein QED. The photon self energy, electron self energy and vertex function are calculated in this formalism. We show that these quantities are finite. The infrared and ultraviolet divergencies do not appear. We discuss that Krein space quantization is similar to Pauli-Villars regularization, so we have called it the "Krein regularization".
Visibility of wavelet quantization noise
NASA Technical Reports Server (NTRS)
Watson, A. B.; Yang, G. Y.; Solomon, J. A.; Villasenor, J.
1997-01-01
The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Visibility of Wavelet Quantization Noise
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John; Null, Cynthia H. (Technical Monitor)
1995-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Escobar, W. A.
2013-01-01
The proposed model holds that, at its most fundamental level, visual awareness is quantized. That is to say that visual awareness arises as individual bits of awareness through the action of neural circuits with hundreds to thousands of neurons in at least the human striate cortex. Circuits with specific topologies will reproducibly result in visual awareness that correspond to basic aspects of vision like color, motion, and depth. These quanta of awareness (qualia) are produced by the feedforward sweep that occurs through the geniculocortical pathway but are not integrated into a conscious experience until recurrent processing from centers like V4 or V5 select the appropriate qualia being produced in V1 to create a percept. The model proposed here has the potential to shift the focus of the search for visual awareness to the level of microcircuits and these likely exist across the kingdom Animalia. Thus establishing qualia as the fundamental nature of visual awareness will not only provide a deeper understanding of awareness, but also allow for a more quantitative understanding of the evolution of visual awareness throughout the animal kingdom. PMID:24319436
Periodic roads and quantized wheels
NASA Astrophysics Data System (ADS)
de Campos Valadares, Eduardo
2016-08-01
We propose a simple approach to determine all possible wheels that can roll smoothly without slipping on a periodic roadbed, while maintaining the center of mass at a fixed height. We also address the inverse problem that of obtaining the roadbed profile compatible with a specific wheel and all other related "quantized wheels." The role of symmetry is highlighted, which might preclude the center of mass from remaining at a fixed height. A straightforward consequence of such geometric quantization is that the gravitational potential energy and the moment of inertia are discrete, suggesting a parallelism between macroscopic wheels and nano-systems, such as carbon nanotubes.
Fermionic Quantization of Hopf Solitons
NASA Astrophysics Data System (ADS)
Krusch, S.; Speight, J. M.
2006-06-01
In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss possible quantum ground states up to Hopf charge Q=7.
Deformation quantization of cosmological models
NASA Astrophysics Data System (ADS)
Cordero, Rubén; García-Compeán, Hugo; Turrubiates, Francisco J.
2011-06-01
The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is applied to cosmological models in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in a flat minisuperspace. The de Sitter cosmological model is worked out in detail and the computation of the Wigner functions for the Hartle-Hawking, Vilenkin and Linde wave functions are done numerically. The Wigner function is analytically calculated for the Kantowski-Sachs model in (non)commutative quantum cosmology and for string cosmology with dilaton exponential potential. Finally, baby universes solutions are described in this context and the Wigner function is obtained.
Geometric Quantization and Foliation Reduction
NASA Astrophysics Data System (ADS)
Skerritt, Paul
A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether "quantization commutes with reduction." Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kahler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kahler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds. In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kahler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or "admissible", values of momentum. We first propose a reduction procedure for the prequantum geometric structures that "covers" symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems. We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces. Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees
Deformation of second and third quantization
NASA Astrophysics Data System (ADS)
Faizal, Mir
2015-03-01
In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the second quantized commutator and obtain a deformed version of the Wheeler-DeWitt equation. Then we will further deform the third quantized theory by deforming the third quantized canonical commutation relation. This way we will obtain a deformed version of the third quantized theory for the multiverse.
Quantized beam shifts in graphene
NASA Astrophysics Data System (ADS)
Kort-Kamp, Wilton; Sinitsyn, Nikolai; Dalvit, Diego
We show that the magneto-optical response of a graphene-on-substrate system in the presence of an external magnetic field strongly affects light beam shifts. In the quantum Hall regime, we predict quantized Imbert-Fedorov, Goos-Hänchen, and photonic spin Hall shifts. The Imbert-Fedorov and photonic spin Hall shifts are given in integer multiples of the fine structure constant α, while the Goos-Hänchen ones in discrete multiples of α2. Due to time-reversal symmetry breaking the IF shifts change sign when the direction of the applied magnetic field is reversed, while the other shifts remain unchanged. We investigate the influence on these shifts of magnetic field, temperature, and material dispersion and dissipation. An experimental demonstration of quantized beam shifts could be achieved at terahertz frequencies for moderate values of the magnetic field. We acknowledge the LANL LDRD program for financial support.
Third Quantization and Quantum Universes
NASA Astrophysics Data System (ADS)
Kim, Sang Pyo
2014-01-01
We study the third quantization of the Friedmann-Robertson-Walker cosmology with N-minimal massless fields. The third quantized Hamiltonian for the Wheeler-DeWitt equation in the minisuperspace consists of infinite number of intrinsic time-dependent, decoupled oscillators. The Hamiltonian has a pair of invariant operators for each universe with conserved momenta of the fields that play a role of the annihilation and the creation operators and that construct various quantum states for the universe. The closed universe exhibits an interesting feature of transitions from stable states to tachyonic states depending on the conserved momenta of the fields. In the classical forbidden unstable regime, the quantum states have googolplex growing position and conjugate momentum dispersions, which defy any measurements of the position of the universe.
Quantized Cosmology: A Simple Approach
Weinstein, M
2004-06-03
I discuss the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology and show how, after a simple change of variables, to quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-deWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. To clarify how things work in this formalism I briefly outline the way in which our formalism works for the exactly solvable case of de-Sitter space.
Systolic architectures for vector quantization
NASA Technical Reports Server (NTRS)
Davidson, Grant A.; Cappello, Peter R.; Gersho, Allen
1988-01-01
A family of architectural techniques are proposed which offer efficient computation of weighted Euclidean distance measures for nearest-neighbor codebook searching. The general approach uses a single metric comparator chip in conjunction with a linear array of inner product processor chips. Very high vector-quantization (VQ) throughput can be achieved for many speech and image-processing applications. Several alternative configurations allow reasonable tradeoffs between speed and VLSI chip area required.
Exact quantization conditions for cluster integrable systems
NASA Astrophysics Data System (ADS)
Franco, Sebastián; Hatsuda, Yasuyuki; Mariño, Marcos
2016-06-01
We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi–Yau manifolds. Our conjecture builds upon recent results on the quantization of mirror curves, and generalizes a previous proposal for the quantization of the relativistic Toda lattice. We present explicit tests of our conjecture for the integrable systems associated to the resolved {{{C}}3}/{{{Z}}5} and {{{C}}3}/{{{Z}}6} orbifolds.
Quantized-"Gray-Scale" Electronic Synapses
NASA Technical Reports Server (NTRS)
Lamb, James L.; Daud, Taher; Thakoor, Anilkumar P.
1990-01-01
Proposed array of programmable synaptic connections for electronic neural network applications offers multiple quantized levels of connection strength using only simple, two-terminal, binary microswitch devices. Subgrids in fine grid of programmable resistive connections connected externally in parallel to form coarser synaptic grid. By selection of pattern of connections in each subgrid, connection strength of synaptic node represented by that subgrid set at quantized "gray level". Device structures promise implementations of quantized-"gray-scale" synaptic arrays with very high density.
On abelian group actions and Galois quantizations
NASA Astrophysics Data System (ADS)
Huru, H. L.; Lychagin, V. V.
2013-08-01
Quantizations of actions of finite abelian groups G are explicitly described by elements in the tensor square of the group algebra of G. Over algebraically closed fields of characteristic 0 these are in one to one correspondence with the second cohomology group of the dual of G. With certain adjustments this result is applied to group actions over any field of characteristic 0. In particular we consider the quantizations of Galois extensions, which are quantized by "deforming" the multiplication. For the splitting fields of products of quadratic polynomials this produces quantized Galois extensions that all are Clifford type algebras.
Adaptive image segmentation by quantization
NASA Astrophysics Data System (ADS)
Liu, Hui; Yun, David Y.
1992-12-01
Segmentation of images into textural homogeneous regions is a fundamental problem in an image understanding system. Most region-oriented segmentation approaches suffer from the problem of different thresholds selecting for different images. In this paper an adaptive image segmentation based on vector quantization is presented. It automatically segments images without preset thresholds. The approach contains a feature extraction module and a two-layer hierarchical clustering module, a vector quantizer (VQ) implemented by a competitive learning neural network in the first layer. A near-optimal competitive learning algorithm (NOLA) is employed to train the vector quantizer. NOLA combines the advantages of both Kohonen self- organizing feature map (KSFM) and K-means clustering algorithm. After the VQ is trained, the weights of the network and the number of input vectors clustered by each neuron form a 3- D topological feature map with separable hills aggregated by similar vectors. This overcomes the inability to visualize the geometric properties of data in a high-dimensional space for most other clustering algorithms. The second clustering algorithm operates in the feature map instead of the input set itself. Since the number of units in the feature map is much less than the number of feature vectors in the feature set, it is easy to check all peaks and find the `correct' number of clusters, also a key problem in current clustering techniques. In the experiments, we compare our algorithm with K-means clustering method on a variety of images. The results show that our algorithm achieves better performance.
Vector quantization for volume rendering
NASA Technical Reports Server (NTRS)
Ning, Paul; Hesselink, Lambertus
1992-01-01
Volume rendering techniques typically process volumetric data in raw, uncompressed form. As algorithmic and architectural advances improve rendering speeds, however, larger data sets will be evaluated requiring consideration of data storage and transmission issues. In this paper, we analyze the data compression requirements for volume rendering applications and present a solution based on vector quantization. The proposed system compresses volumetric data and then renders images directly from the new data format. Tests on a fluid flow data set demonstrate that good image quality may be achieved at a compression ratio of 17:1 with only a 5 percent cost in additional rendering time.
Quantized ionic conductance in nanopores.
Zwolak, Michael; Lagerqvist, Johan; Di Ventra, Massimiliano
2009-09-18
Ionic transport in nanopores is a fundamentally and technologically important problem in view of its occurrence in biological processes and its impact on novel DNA sequencing applications. Using molecular dynamics simulations we show that ion transport may exhibit strong nonlinearities as a function of the pore radius reminiscent of the conductance quantization steps as a function of the transverse cross section of quantum point contacts. In the present case, however, conductance steps originate from the break up of the hydration layers that form around ions in aqueous solution. We discuss this phenomenon and the conditions under which it should be experimentally observable. PMID:19792463
Completely quantized collapse and consequences
Pearle, Philip
2005-08-15
Promotion of quantum theory from a theory of measurement to a theory of reality requires an unambiguous specification of the ensemble of realizable states (and each state's probability of realization). Although not yet achieved within the framework of standard quantum theory, it has been achieved within the framework of the continuous spontaneous localization (CSL) wave-function collapse model. In CSL, a classical random field w(x,t) interacts with quantum particles. The state vector corresponding to each w(x,t) is a realizable state. In this paper, I consider a previously presented model, which is predictively equivalent to CSL. In this completely quantized collapse (CQC) model, the classical random field is quantized. It is represented by the operator W(x,t) which satisfies [W(x,t),W(x{sup '},t{sup '})]=0. The ensemble of realizable states is described by a single state vector, the 'ensemble vector'. Each superposed state which comprises the ensemble vector at time t is the direct product of an eigenstate of W(x,t{sup '}), for all x and for 0{<=}t{sup '}{<=}t, and the CSL state corresponding to that eigenvalue. These states never interfere (they satisfy a superselection rule at any time), they only branch, so the ensemble vector may be considered to be, as Schroedinger put it, a 'catalog' of the realizable states. In this context, many different interpretations (e.g., many worlds, environmental decoherence, consistent histories, modal interpretation) may be satisfactorily applied. Using this description, a long-standing problem is resolved, where the energy comes from the particles gain due to the narrowing of their wave packets by the collapse mechanism. It is shown how to define the energy of the random field and its energy of interaction with particles so that total energy is conserved for the ensemble of realizable states. As a by-product, since the random-field energy spectrum is unbounded, its canonical conjugate, a self-adjoint time operator, can be
Quantization of general linear electrodynamics
Rivera, Sergio; Schuller, Frederic P.
2011-03-15
General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength 2-form and induction 2-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory predictive and physically interpretable. Taking into account the higher-order polynomial dispersion relation and associated causal structure of general linear electrodynamics, we carefully develop its Hamiltonian formulation from first principles. Canonical quantization of the resulting constrained system then results in a quantum vacuum which is sensitive to the constitutive tensor of the classical theory. As an application we calculate the Casimir effect in a birefringent linear optical medium.
Quantization of higher spin fields
Wagenaar, J. W.; Rijken, T. A
2009-11-15
In this article we quantize (massive) higher spin (1{<=}j{<=}2) fields by means of Dirac's constrained Hamilton procedure both in the situation were they are totally free and were they are coupled to (an) auxiliary field(s). A full constraint analysis and quantization is presented by determining and discussing all constraints and Lagrange multipliers and by giving all equal times (anti)commutation relations. Also we construct the relevant propagators. In the free case we obtain the well-known propagators and show that they are not covariant, which is also well known. In the coupled case we do obtain covariant propagators (in the spin-3/2 case this requires b=0) and show that they have a smooth massless limit connecting perfectly to the massless case (with auxiliary fields). We notice that in our system of the spin-3/2 and spin-2 case the massive propagators coupled to conserved currents only have a smooth limit to the pure massless spin-propagator, when there are ghosts in the massive case.
Breathers on quantized superfluid vortices.
Salman, Hayder
2013-10-18
We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings. PMID:24182275
Perceptual quantization of chromatic components
NASA Astrophysics Data System (ADS)
Saadane, Abdelhakim; Bedat, Laurent; Barba, Dominique
1998-07-01
In order to achieve a color image coding based on the human visual system features, we have been interested by the design of a perceptually based quantizer. The cardinal directions Ach, Cr1 and Cr2, designed by Krauskopf from habituation experiments and validated in our lab from spatial masking experiments, have been used to characterize color images. The achromatic component, already considered in previous study, will not be considered here. The same methodology has been applied to the two chromatic components to specify the decision thresholds and the reconstruction levels which ensure that the degradations induced will be lower than their visibility thresholds. Two observers have been used for each of the two components. From the values obtained for Cr1 component one should notice that the decision thresholds and reconstruction levels follow a linear law even at higher levels. However, for Cr2 component the values seem following a monotonous increasing function. To determine if these behaviors are frequency dependent, further experiments have been conducted with stimulus frequencies varying from 1cy/deg to 4cy/deg. The measured values show no significant variations. Finally, instead of sinusoidal stimuli, filtered textures have been used to take into account the spatio-frequential combination. The same laws (linear for Cr1 and monotonous increasing for Cr2) have been observed even if a variation in the quantization intervals is reported.
Breathers on Quantized Superfluid Vortices
NASA Astrophysics Data System (ADS)
Salman, Hayder
2013-10-01
We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings.
Weighted Bergman Kernels and Quantization}
NASA Astrophysics Data System (ADS)
Engliš, Miroslav
Let Ω be a bounded pseudoconvex domain in CN, φ, ψ two positive functions on Ω such that - log ψ, - log φ are plurisubharmonic, and z∈Ω a point at which - log φ is smooth and strictly plurisubharmonic. We show that as k-->∞, the Bergman kernels with respect to the weights φkψ have an asymptotic expansion
Quantization of Electromagnetic Fields in Cavities
NASA Technical Reports Server (NTRS)
Kakazu, Kiyotaka; Oshiro, Kazunori
1996-01-01
A quantization procedure for the electromagnetic field in a rectangular cavity with perfect conductor walls is presented, where a decomposition formula of the field plays an essential role. All vector mode functions are obtained by using the decomposition. After expanding the field in terms of the vector mode functions, we get the quantized electromagnetic Hamiltonian.
Quantization noise in adaptive weighting networks
NASA Astrophysics Data System (ADS)
Davis, R. M.; Sher, P. J.-S.
1984-09-01
Adaptive weighting networks can be implemented using in-phase and quadrature, phase-phase, or phase-amplitude modulators. The statistical properties of the quantization error are derived for each modulator and the quantization noise power produced by the modulators are compared at the output of an adaptive antenna. Other relevant characteristics of the three types of modulators are also discussed.
Covariant Photon Quantization in the SME
NASA Astrophysics Data System (ADS)
Colladay, D.
2014-01-01
The Gupta-Bleuler quantization procedure is applied to the SME photon sector. A direct application of the method to the massless case fails due to an unavoidable incompleteness in the polarization states. A mass term can be included into the photon lagrangian to rescue the quantization procedure and maintain covariance.
Logarithmic Adaptive Quantization Projection for Audio Watermarking
NASA Astrophysics Data System (ADS)
Zhao, Xuemin; Guo, Yuhong; Liu, Jian; Yan, Yonghong; Fu, Qiang
In this paper, a logarithmic adaptive quantization projection (LAQP) algorithm for digital watermarking is proposed. Conventional quantization index modulation uses a fixed quantization step in the watermarking embedding procedure, which leads to poor fidelity. Moreover, the conventional methods are sensitive to value-metric scaling attack. The LAQP method combines the quantization projection scheme with a perceptual model. In comparison to some conventional quantization methods with a perceptual model, the LAQP only needs to calculate the perceptual model in the embedding procedure, avoiding the decoding errors introduced by the difference of the perceptual model used in the embedding and decoding procedure. Experimental results show that the proposed watermarking scheme keeps a better fidelity and is robust against the common signal processing attack. More importantly, the proposed scheme is invariant to value-metric scaling attack.
Quantized conic sections; quantum gravity
Noyes, H.P.
1993-03-15
Starting from free relativistic particles whose position and velocity can only be measured to a precision < {Delta}r{Delta}v > {equivalent_to} {plus_minus} k/2 meter{sup 2}sec{sup {minus}1} , we use the relativistic conservation laws to define the relative motion of the coordinate r = r{sub 1} {minus} r{sub 2} of two particles of mass m{sub 1}, m{sub 2} and relative velocity v = {beta}c = {sub (k{sub 1} + k{sub 2}})/ {sup (k{sub 1} {minus} k{sub 2}}) in terms of conic section equation v{sup 2} = {Gamma} [2/r {plus_minus} 1/a] where ``+`` corresponds to hyperbolic and ``{minus}`` to elliptical trajectories. Equation is quantized by expressing Kepler`s Second Law as conservation of angular niomentum per unit mass in units of k. Principal quantum number is n {equivalent_to} j + {1/2} with``square`` {sub T{sup 2}}/{sup A{sup 2}} = (n {minus}1)nk{sup 2} {equivalent_to} {ell}{sub {circle_dot}}({ell}{sub {circle_dot}} + 1)k{sup 2}. Here {ell}{sub {circle_dot}} = n {minus} 1 is the angular momentumquantum number for circular orbits. In a sense, we obtain ``spin`` from this quantization. Since {Gamma}/a cannot reach c{sup 2} without predicting either circular or asymptotic velocities equal to the limiting velocity for particulate motion, we can also quantize velocities in terms of the principle quantum number by defining {beta}{sub n}/{sup 2} = {sub c{sup 2}}/{sup v{sub n{sup 2}} = {sub n{sup 2}}/1({sub c{sup 2}}a/{Gamma}) = ({sub nN{Gamma}}/1){sup 2}. For the Z{sub 1}e,Z{sub 2}e of the same sign and {alpha} {triple_bond} e{sup 2}/m{sub e}{kappa}c, we find that {Gamma}/c{sup 2}a = Z{sub 1}Z{sub 2}{alpha}. The characteristic Coulomb parameter {eta}(n) {triple_bond} Z{sub 1}Z{sub 2}{alpha}/{beta}{sub n} = Z{sub 1}Z{sub 2}nN{sub {Gamma}} then specifies the penetration factor C{sup 2}({eta}) = 2{pi}{eta}/(e{sup 2{pi}{eta}} {minus} 1}). For unlike charges, with {eta} still taken as positive, C{sup 2}({minus}{eta}) = 2{pi}{eta}/(1 {minus} e{sup {minus}2{pi}{eta}}).
Quantized ionic conductance in nanopores
Zwolak, Michael; Lagerqvist, Johan; Di Ventra, Massimilliano
2009-01-01
Ionic transport in nanopores is a fundamentally and technologically important problem in view of its ubiquitous occurrence in biological processes and its impact on DNA sequencing applications. Using microscopic calculations, we show that ion transport may exhibit strong non-liDearities as a function of the pore radius reminiscent of the conductance quantization steps as a function of the transverse cross section of quantum point contacts. In the present case, however, conductance steps originate from the break up of the hydration layers that form around ions in aqueous solution. Once in the pore, the water molecules form wavelike structures due to multiple scattering at the surface of the pore walls and interference with the radial waves around the ion. We discuss these effects as well as the conditions under which the step-like features in the ionic conductance should be experimentally observable.
The Necessity of Quantizing Gravity
NASA Astrophysics Data System (ADS)
Adelman, Jeremy
2016-03-01
The Eppley Hannah thought experiment is often cited as justification for attempts by theorists to develop a complete, consistent theory of quantum gravity. A modification of the earlier ``Heisenberg microscope'' argument for the necessity of quantized light, the Eppley-Hannah thought experiment purports to show that purely classical gravitational waves would either not conserve energy or else allow for violations of the uncertainty principle. However, several subsequent papers have cast doubt as to the validity of the Eppley-Hannah argument. In this talk, we will show how to resurrect the Eppley-Hannah thought experiment by modifying the original argument in a way that gets around the present criticisms levied against it. With support from the Department of Energy, Grant Number DE-FG02-91ER40674.
Cosmology Quantized in Cosmic Time
Weinstein, M
2004-06-03
This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, to quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-deWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. We discuss the extension of this result to a full quantum mechanical derivation of the anisotropy ({delta} {rho}/{rho}) in the cosmic microwave background radiation, and the possibility that the extra term in the Friedmann equation could have observable consequences. To clarify the general formalism and explicitly show why we choose to weaken the statement of the Wheeler-deWitt equation, we apply the general formalism to de Sitter space. After exactly solving the relevant Heisenberg equations of motion we give a detailed discussion of the subtleties associated with defining physical states and the emergence of the classical theory. This computation provides the striking result that quantum corrections to this long wavelength limit of gravity eliminate the problem of the big crunch. We also show that the same corrections lead to possibly measurable effects on the CMB radiation. For the sake of completeness, we discuss the special case, {lambda} = 0, and its relation to Minkowski space. Finally, we suggest interesting ways in which these techniques can be generalized to cast light on the question of chaotic or eternal inflation. In particular, we suggest one can put an experimental lower bound on the distance to a universe with a scale factor very different from our own, by looking at its effects on our CMB
Quantized vortices around wavefront nodes, 2
NASA Technical Reports Server (NTRS)
Hirschfelder, J. O.; Goebel, C. J.; Bruch, L. W.
1974-01-01
Quantized vortices can occur around nodal points in wavefunctions. The derivation depends only on the wavefunction being single valued, continuous, and having continuous first derivatives. Since the derivation does not depend upon the dynamical equations, the quantized vortices are expected to occur for many types of waves such as electromagnetic and acoustic. Such vortices have appeared in the calculations of the H + H2 molecular collisions and play a role in the chemical kinetics. In a companion paper, it is shown that quantized vortices occur when optical waves are internally reflected from the face of a prism or particle beams are reflected from potential energy barriers.
Loop quantization of Schwarzschild interior revisited
NASA Astrophysics Data System (ADS)
Singh, Parampreet; Corichi, Alejandro
2016-03-01
Several studies of different inequivalent loop quantizations have shown, that there exists no fully satisfactory quantum theory for the Schwarzschild interior. Existing quantizations fail either on dependence on the fiducial structure or on the lack of the classical limit. Here we put forward a novel viewpoint to construct the quantum theory that overcomes all of the known problems of the existing quantizations. It is shown that the quantum gravitational constraint is well defined past the singularity and that its effective dynamics possesses a bounce into an expanding regime. The classical singularity is avoided, and a semiclassical spacetime satisfying vacuum Einstein's equations is recovered on the ``other side'' of the bounce. We argue that such metric represents the interior region of a white-hole spacetime, but for which the corresponding ``white-hole mass'' differs from the original black hole mass. We compare the differences in physical implications with other quantizations.
Torus quantization of symmetrically excited helium
Mueller, J. ); Burgdoerfer, J. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6377 ); Noid, D. )
1992-02-01
The recent discovery by Richter and Wintgen (J. Phys. B 23, L197 (1990)) that the classical helium atom is not globally ergodic has stimulated renewed interest in its semiclassical quantization. The Einstein-Brillouin-Keller quantization of Kolmogorov-Arnold-Moser tori around stable periodic orbits becomes locally possible in a selected region of phase space. Using a hyperspherical representation we have found a dynamically confining potential allowing for a stable motion near the Wannier ridge. The resulting semiclassical eigenenergies provide a test for full quantum calculations in the limit of very high quantum numbers. The relations to frequently used group-theoretical classifications for doubly excited states and to the periodic-orbit quantization of the chaotic portion of the phase space are discussed. The extrapolation of the semiclassical quantization to low-lying states give remarkably accurate estimates for the energies of all symmetric {ital L}=0 states of helium.
A note on quantizations of Galois extensions
NASA Astrophysics Data System (ADS)
İlhan, Aslı Güçlükan
2014-12-01
In Huru and Lychagin (2013), it is conjectured that the quantizations of splitting fields of products of quadratic polynomials, which are obtained by deforming the multiplication, are Clifford type algebras. In this paper, we prove this conjecture.
Topologies on quantum topoi induced by quantization
Nakayama, Kunji
2013-07-15
In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantum topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.
Towards quantized current arbitrary waveform synthesis
NASA Astrophysics Data System (ADS)
Mirovsky, P.; Fricke, L.; Hohls, F.; Kaestner, B.; Leicht, Ch.; Pierz, K.; Melcher, J.; Schumacher, H. W.
2013-06-01
The generation of ac modulated quantized current waveforms using a semiconductor non-adiabatic single electron pump is demonstrated. In standard operation, the single electron pump generates a quantized output current of I = ef, where e is the charge of the electron and f is the pumping frequency. Suitable frequency modulation of f allows the generation of ac modulated output currents with different characteristics. By sinusoidal and saw tooth like modulation of f accordingly modulated quantized current waveforms with kHz modulation frequencies and peak currents up to 100 pA are obtained. Such ac quantized current sources could find applications ranging from precision ac metrology to on-chip signal generation.
Image indexing based on vector quantization
NASA Astrophysics Data System (ADS)
Grana Romay, Manuel; Rebollo, Israel
2000-10-01
We propose the computation of the color palette of each image in isolation, using Vector Quantization methods. The image features are, then, the color palette and the histogram of the color quantization of the image with this color palette. We propose as a measure of similitude the weighted sum of the differences between the color palettes and the corresponding histograms. This approach allows the increase of the database without the recomputation of the image features and without substantial loss of discriminative power.
Quantization of color histograms using GLA
NASA Astrophysics Data System (ADS)
Yang, Christopher C.; Yip, Milo K.
2002-09-01
Color histogram has been used as one of the most important image descriptor in a wide range of content-based image retrieval (CBIR) projects for color image indexing. It captures the global chromatic distribution of an image. Traditionally, there are two major approaches to quantize the color space: (1) quantize each dimension of a color coordinate system uniformly to generate a fixed number of bins; and (2) quantize a color coordinate system arbitrarily. The first approach works best on cubical color coordinate systems, such as RGB. For other non-cubical color coordinate system, such as CIELAB and CIELUV, some bins may fall out of the gamut (transformed from the RGB cube) of the color space. As a result, it reduces the effectiveness of the color histogram and hence reduces the retrieval performance. The second approach uses arbitrarily quantization. The volume of the bins is not necessary uniform. As a result, it affects the effectiveness of the histogram significantly. In this paper, we propose to develop the color histogram by tessellating the non-cubical color gamut transformed from RGB cube using a vector quantization (VQ) method, the General Loyld Algorithm (GLA) [6]. Using such approach, the problem of empty bins due to the gamut of the color coordinate system can be avoided. Besides, all bins quantized by GLA will occupy the same volume. It guarantees that uniformity of each quantized bins in the histogram. An experiment has been conducted to evaluate the quantitative performance of our approach. The image collection from UC Berkeley's digital library project is used as the test bed. The indexing effectiveness of a histogram space [3] is used as the measurement of the performance. The experimental result shows that using the GLA quantization approach significantly increase the indexing effectiveness.
Controlling charge quantization with quantum fluctuations.
Jezouin, S; Iftikhar, Z; Anthore, A; Parmentier, F D; Gennser, U; Cavanna, A; Ouerghi, A; Levkivskyi, I P; Idrisov, E; Sukhorukov, E V; Glazman, L I; Pierre, F
2016-08-01
In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal-semiconductor hybrids relevant to topological quantum computing, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices. PMID:27488797
A recursive technique for adaptive vector quantization
NASA Technical Reports Server (NTRS)
Lindsay, Robert A.
1989-01-01
Vector Quantization (VQ) is fast becoming an accepted, if not preferred method for image compression. The VQ performs well when compressing all types of imagery including Video, Electro-Optical (EO), Infrared (IR), Synthetic Aperture Radar (SAR), Multi-Spectral (MS), and digital map data. The only requirement is to change the codebook to switch the compressor from one image sensor to another. There are several approaches for designing codebooks for a vector quantizer. Adaptive Vector Quantization is a procedure that simultaneously designs codebooks as the data is being encoded or quantized. This is done by computing the centroid as a recursive moving average where the centroids move after every vector is encoded. When computing the centroid of a fixed set of vectors the resultant centroid is identical to the previous centroid calculation. This method of centroid calculation can be easily combined with VQ encoding techniques. The defined quantizer changes after every encoded vector by recursively updating the centroid of minimum distance which is the selected by the encoder. Since the quantizer is changing definition or states after every encoded vector, the decoder must now receive updates to the codebook. This is done as side information by multiplexing bits into the compressed source data.
Controlling charge quantization with quantum fluctuations
NASA Astrophysics Data System (ADS)
Jezouin, S.; Iftikhar, Z.; Anthore, A.; Parmentier, F. D.; Gennser, U.; Cavanna, A.; Ouerghi, A.; Levkivskyi, I. P.; Idrisov, E.; Sukhorukov, E. V.; Glazman, L. I.; Pierre, F.
2016-08-01
In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal–semiconductor hybrids relevant to topological quantum computing, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.
Quantization of Prior Probabilities for Collaborative Distributed Hypothesis Testing
NASA Astrophysics Data System (ADS)
Rhim, Joong Bum; Varshney, Lav R.; Goyal, Vivek K.
2012-09-01
This paper studies the quantization of prior probabilities, drawn from an ensemble, for distributed detection and data fusion. Design and performance equivalences between a team of N agents tied by a fixed fusion rule and a more powerful single agent are obtained. Effects of identical quantization and diverse quantization are compared. Consideration of perceived common risk enables agents using diverse quantizers to collaborate in hypothesis testing, and it is proven that the minimum mean Bayes risk error is achieved by diverse quantization. The comparison shows that optimal diverse quantization with K cells per quantizer performs as well as optimal identical quantization with N(K-1)+1 cells per quantizer. Similar results are obtained for maximum Bayes risk error as the distortion criterion.
Quantization of Generally Covariant Systems
NASA Astrophysics Data System (ADS)
Sforza, Daniel M.
2000-12-01
Finite dimensional models that mimic the constraint structure of Einstein's General Relativity are quantized in the framework of BRST and Dirac's canonical formalisms. The first system to be studied is one featuring a constraint quadratic in the momenta (the "super-Hamiltonian") and a set of constraints linear in the momenta (the "supermomentum" constraints). The starting point is to realize that the ghost contributions to the supermomentum constraint operators can be read in terms of the natural volume induced by the constraints in the orbits. This volume plays a fundamental role in the construction of the quadratic sector of the nilpotent BRST charge. It is shown that the quantum theory is invariant under scaling of the super-Hamiltonian. As long as the system has an intrinsic time, this property translates in a contribution of the potential to the kinetic term. In this aspect, the results substantially differ from other works where the scaling invariance is forced by introducing a coupling to the curvature. The contribution of the potential, far from being unnatural, is beautifully justified in the light of the Jacobi's principle. Then, it is shown that the obtained results can be extended to systems with extrinsic time. In this case, if the metric has a conformal temporal Killing vector and the potential exhibits a suitable behavior with respect to it, the role played by the potential in the case of intrinsic time is now played by the norm of the Killing vector. Finally, the results for the previous cases are extended to a system featuring two super-Hamiltonian constraints. This step is extremely important due to the fact that General Relativity features an infinite number of such constraints satisfying a non trivial algebra among themselves.
Image coding with uniform and piecewise-uniform vector quantizers.
Jeong, D G; Gibson, J D
1995-01-01
New lattice vector quantizer design procedures for nonuniform sources that yield excellent performance while retaining the structure required for fast quantization are described. Analytical methods for truncating and scaling lattices to be used in vector quantization are given, and an analytical technique for piecewise-linear multidimensional companding is presented. The uniform and piecewise-uniform lattice vector quantizers are then used to quantize the discrete cosine transform coefficients of images, and their objective and subjective performance and complexity are contrasted with other lattice vector quantizers and with LBG training-mode designs. PMID:18289966
Virtual topological insulators with real quantized physics
NASA Astrophysics Data System (ADS)
Prodan, Emil
2015-06-01
A concrete strategy is presented for generating strong topological insulators in d +d' dimensions which have quantized physics in d dimensions. Here, d counts the physical and d' the virtual dimensions. It consists of seeking d -dimensional representations of operator algebras which are usually defined in d +d' dimensions where topological elements display strong topological invariants. The invariants are shown, however, to be fully determined by the physical dimensions, in the sense that their measurement can be done at fixed virtual coordinates. We solve the bulk-boundary correspondence and show that the boundary invariants are also fully determined by the physical coordinates. We analyze the virtual Chern insulator in 1 +1 dimensions realized in Y. E. Kraus et al., Phys. Rev. Lett. 109, 106402 (2012), 10.1103/PhysRevLett.109.106402 and predict quantized forces at the edges. We generate a topological system in (3 +1 ) dimensions, which is predicted to have quantized magnetoelectric response.
Quantization ambiguities in isotropic quantum geometry
NASA Astrophysics Data System (ADS)
Bojowald, Martin
2002-10-01
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner. It is shown that these ambiguities do not affect the fate of the classical singularity, demonstrating that the absence of a singularity in loop quantum cosmology is a robust implication of the general quantization scheme. The calculations also allow conclusions about modified operators in the full theory. In particular, using holonomies in a non-fundamental representation of SU(2) to quantize connection components turns out to lead to significant corrections to classical behaviour at macroscopic volume for large values of the spin of the chosen representation.
Smooth big bounce from affine quantization
NASA Astrophysics Data System (ADS)
Bergeron, Hervé; Dapor, Andrea; Gazeau, Jean Pierre; Małkiewicz, Przemysław
2014-04-01
We examine the possibility of dealing with gravitational singularities on a quantum level through the use of coherent state or wavelet quantization instead of canonical quantization. We consider the Robertson-Walker metric coupled to a perfect fluid. It is the simplest model of a gravitational collapse, and the results obtained here may serve as a useful starting point for more complex investigations in the future. We follow a quantization procedure based on affine coherent states or wavelets built from the unitary irreducible representation of the affine group of the real line with positive dilation. The main issue of our approach is the appearance of a quantum centrifugal potential allowing for regularization of the singularity, essential self-adjointness of the Hamiltonian, and unambiguous quantum dynamical evolution.
Deformation quantization for contact interactions and dissipation
NASA Astrophysics Data System (ADS)
Belchev, Borislav Stefanov
This thesis studies deformation quantization and its application to contact interactions and systems with dissipation. We consider the subtleties related to quantization when contact interactions and boundaries are present. We exploit the idea that discontinuous potentials are idealizations that should be realized as limits of smooth potentials. The Wigner functions are found for the Morse potential and in the proper limit they reduce to the Wigner functions for the infinite wall, for the most general (Robin) boundary conditions. This is possible for a very limited subset of the values of the parameters --- so-called fine tuning is necessary. It explains why Dirichlet boundary conditions are used predominantly. Secondly, we consider deformation quantization in relation to dissipative phenomena. For the damped harmonic oscillator we study a method using a modified noncommutative star product. Within this framework we resolve the non-reality problem with the Wigner function and correct the classical limit.
Experimental realization of quantized anomalous Hall effect
NASA Astrophysics Data System (ADS)
Xue, Qi-Kun
2014-03-01
Anomalous Hall effect was discovered by Edwin Hall in 1880. In this talk, we report the experimental observation of the quantized version of AHE, the quantum anomalous Hall effect (QAHE) in thin films of Cr-doped (Bi,Sb)2Te3 magnetic topological insulator. At zero magnetic field, the gate-tuned anomalous Hall resistance exhibits a quantized value of h /e2 accompanied by a significant drop of the longitudinal resistance. The longitudinal resistance vanishes under a strong magnetic field whereas the Hall resistance remains at the quantized value. The realization of QAHE paves a way for developing low-power-consumption electronics. Implications on observing Majorana fermions and other exotic phenomena in magnetic topological insulators will also be discussed. The work was collaborated with Ke He, Yayu Wang, Xucun Ma, Xi Chen, Li Lv, Dai Xi, Zhong Fang and Shoucheng Zhang.
Single Abrikosov vortices as quantized information bits
NASA Astrophysics Data System (ADS)
Golod, T.; Iovan, A.; Krasnov, V. M.
2015-10-01
Superconducting digital devices can be advantageously used in future supercomputers because they can greatly reduce the dissipation power and increase the speed of operation. Non-volatile quantized states are ideal for the realization of classical Boolean logics. A quantized Abrikosov vortex represents the most compact magnetic object in superconductors, which can be utilized for creation of high-density digital cryoelectronics. In this work we provide a proof of concept for Abrikosov-vortex-based random access memory cell, in which a single vortex is used as an information bit. We demonstrate high-endurance write operation and two different ways of read-out using a spin valve or a Josephson junction. These memory cells are characterized by an infinite magnetoresistance between 0 and 1 states, a short access time, a scalability to nm sizes and an extremely low write energy. Non-volatility and perfect reproducibility are inherent for such a device due to the quantized nature of the vortex.
Vector quantization of 3-D point clouds
NASA Astrophysics Data System (ADS)
Sim, Jae-Young; Kim, Chang-Su; Lee, Sang-Uk
2005-10-01
A geometry compression algorithm for 3-D QSplat data using vector quantization (VQ) is proposed in this work. The positions of child spheres are transformed to the local coordinate system, which is determined by the parent children relationship. The coordinate transform makes child positions more compactly distributed in 3-D space, facilitating effective quantization. Moreover, we develop a constrained encoding method for sphere radii, which guarantees hole-free surface rendering at the decoder side. Simulation results show that the proposed algorithm provides a faithful rendering quality even at low bitrates.
Constraints on operator ordering from third quantization
NASA Astrophysics Data System (ADS)
Ohkuwa, Yoshiaki; Faizal, Mir; Ezawa, Yasuo
2016-02-01
In this paper, we analyse the Wheeler-DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.
Minimal representations, geometric quantization, and unitarity.
Brylinski, R; Kostant, B
1994-01-01
In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simply-connected real Lie group Go such that the maximal compact subgroup of Go has finite center and Go admits some minimal representation. We obtain algebraic and analytic results about pio. We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then "quantize" these results to obtain the corresponding representations. We assume (Lie Go)C is simple. PMID:11607478
Kang, Yuhong; Ruan, Hang; Claus, Richard O; Heremans, Jean; Orlowski, Marius
2016-12-01
Quantized conductance is observed at zero magnetic field and room temperature in metal-insulator-metal structures with graphene submicron-sized nanoplatelets embedded in a 3-hexylthiophene (P3HT) polymer layer. In devices with medium concentration of graphene platelets, integer multiples of G o = 2e (2)/h (=12.91 kΩ(-1)), and in some devices partially quantized including a series of with (n/7) × G o, steps are observed. Such an organic memory device exhibits reliable memory operation with an on/off ratio of more than 10. We attribute the quantized conductance to the existence of a 1-D electron waveguide along the conductive path. The partial quantized conductance results likely from imperfect transmission coefficient due to impedance mismatch of the first waveguide modes. PMID:27044308
NASA Astrophysics Data System (ADS)
Kang, Yuhong; Ruan, Hang; Claus, Richard O.; Heremans, Jean; Orlowski, Marius
2016-04-01
Quantized conductance is observed at zero magnetic field and room temperature in metal-insulator-metal structures with graphene submicron-sized nanoplatelets embedded in a 3-hexylthiophene (P3HT) polymer layer. In devices with medium concentration of graphene platelets, integer multiples of G o = 2 e 2/ h (=12.91 kΩ-1), and in some devices partially quantized including a series of with ( n/7) × G o, steps are observed. Such an organic memory device exhibits reliable memory operation with an on/off ratio of more than 10. We attribute the quantized conductance to the existence of a 1-D electron waveguide along the conductive path. The partial quantized conductance results likely from imperfect transmission coefficient due to impedance mismatch of the first waveguide modes.
Hysteresis in a quantized superfluid 'atomtronic' circuit.
Eckel, Stephen; Lee, Jeffrey G; Jendrzejewski, Fred; Murray, Noel; Clark, Charles W; Lobb, Christopher J; Phillips, William D; Edwards, Mark; Campbell, Gretchen K
2014-02-13
Atomtronics is an emerging interdisciplinary field that seeks to develop new functional methods by creating devices and circuits where ultracold atoms, often superfluids, have a role analogous to that of electrons in electronics. Hysteresis is widely used in electronic circuits-it is routinely observed in superconducting circuits and is essential in radio-frequency superconducting quantum interference devices. Furthermore, it is as fundamental to superfluidity (and superconductivity) as quantized persistent currents, critical velocity and Josephson effects. Nevertheless, despite multiple theoretical predictions, hysteresis has not been previously observed in any superfluid, atomic-gas Bose-Einstein condensate. Here we directly detect hysteresis between quantized circulation states in an atomtronic circuit formed from a ring of superfluid Bose-Einstein condensate obstructed by a rotating weak link (a region of low atomic density). This contrasts with previous experiments on superfluid liquid helium where hysteresis was observed directly in systems in which the quantization of flow could not be observed, and indirectly in systems that showed quantized flow. Our techniques allow us to tune the size of the hysteresis loop and to consider the fundamental excitations that accompany hysteresis. The results suggest that the relevant excitations involved in hysteresis are vortices, and indicate that dissipation has an important role in the dynamics. Controlled hysteresis in atomtronic circuits may prove to be a crucial feature for the development of practical devices, just as it has in electronic circuits such as memories, digital noise filters (for example Schmitt triggers) and magnetometers (for example superconducting quantum interference devices). PMID:24522597
Combining Vector Quantization and Histogram Equalization.
ERIC Educational Resources Information Center
Cosman, Pamela C.; And Others
1992-01-01
Discussion of contrast enhancement techniques focuses on the use of histogram equalization with a data compression technique, i.e., tree-structured vector quantization. The enhancement technique of intensity windowing is described, and the use of enhancement techniques for medical images is explained, including adaptive histogram equalization.…
Visual data mining for quantized spatial data
NASA Technical Reports Server (NTRS)
Braverman, Amy; Kahn, Brian
2004-01-01
In previous papers we've shown how a well known data compression algorithm called Entropy-constrained Vector Quantization ( can be modified to reduce the size and complexity of very large, satellite data sets. In this paper, we descuss how to visualize and understand the content of such reduced data sets.
The Quantization Rule and Maslov Index
NASA Astrophysics Data System (ADS)
Gu, Xiao-Yan
Within extensions of the new quantization rule approach in arbitrary dimensions, the Maslov indices and energy spectra of some exactly solvable potentials are presented. We find that the Maslov index for the harmonic oscillator in three dimensions agrees well with those obtained by other methods.
Image compression using address-vector quantization
NASA Astrophysics Data System (ADS)
Nasrabadi, Nasser M.; Feng, Yushu
1990-12-01
A novel vector quantization scheme, the address-vector quantizer (A-VQ), is proposed which exploits the interblock correlation by encoding a group of blocks together using an address-codebook (AC). The AC is a set of address-codevectors (ACVs), each representing a combination of addresses or indices. Each element of the ACV is an address of an entry in the LBG-codebook, representing a vector-quantized block. The AC consists of an active (addressable) region and an inactive (nonaddressable) region. During encoding the ACVs in the AC are reordered adaptively to bring the most probable ACVs into the active region. When encoding an ACV, the active region is checked, and if such an address combination exists, its index is transmitted to the receiver. Otherwise, the address of each block is transmitted individually. The SNR of the images encoded by the A-VQ method is the same as that of a memoryless vector quantizer, but the bit rate is by a factor of approximately two.
Bolometric Device Based on Fluxoid Quantization
NASA Technical Reports Server (NTRS)
Bonetti, Joseph A.; Kenyon, Matthew E.; Leduc, Henry G.; Day, Peter K.
2010-01-01
The temperature dependence of fluxoid quantization in a superconducting loop. The sensitivity of the device is expected to surpass that of other superconducting- based bolometric devices, such as superconducting transition-edge sensors and superconducting nanowire devices. Just as important, the proposed device has advantages in sample fabrication.
Scalar-vector quantization of medical images.
Mohsenian, N; Shahri, H; Nasrabadi, N M
1996-01-01
A new coding scheme based on the scalar-vector quantizer (SVQ) is developed for compression of medical images. The SVQ is a fixed rate encoder and its rate-distortion performance is close to that of optimal entropy-constrained scalar quantizers (ECSQs) for memoryless sources. The use of a fixed-rate quantizer is expected to eliminate some of the complexity of using variable-length scalar quantizers. When transmission of images over noisy channels is considered, our coding scheme does not suffer from error propagation that is typical of coding schemes using variable-length codes. For a set of magnetic resonance (MR) images, coding results obtained from SVQ and ECSQ at low bit rates are indistinguishable. Furthermore, our encoded images are perceptually indistinguishable from the original when displayed on a monitor. This makes our SVQ-based coder an attractive compression scheme for picture archiving and communication systems (PACS). PACS are currently under study for use in an all-digital radiology environment in hospitals, where reliable transmission, storage, and high fidelity reconstruction of images are desired. PMID:18285124
Multiverse in the Third Quantized Formalism
NASA Astrophysics Data System (ADS)
Mir, Faizal
2014-11-01
In this paper we will analyze the third quantization of gravity in path integral formalism. We will use the time-dependent version of Wheeler—DeWitt equation to analyze the multiverse in this formalism. We will propose a mechanism for baryogenesis to occur in the multiverse, without violating the baryon number conservation.
Quantization of Two Classical Models by Means of the BRST Quantization Method
NASA Astrophysics Data System (ADS)
Bracken, Paul
2008-12-01
An elementary gauge-non-invariant model and the bosonized form of the chiral Schwinger model are introduced as classical theories. The constraint structure is then investigated. It is shown that by introducing a new field, these models can be made gauge-invariant. The BRST form of quantization is reviewed and applied to each of these models in turn such that gauge-invariance is not broken. Some consequences of this form of quantization are discussed.
Video data compression using artificial neural network differential vector quantization
NASA Technical Reports Server (NTRS)
Krishnamurthy, Ashok K.; Bibyk, Steven B.; Ahalt, Stanley C.
1991-01-01
An artificial neural network vector quantizer is developed for use in data compression applications such as Digital Video. Differential Vector Quantization is used to preserve edge features, and a new adaptive algorithm, known as Frequency-Sensitive Competitive Learning, is used to develop the vector quantizer codebook. To develop real time performance, a custom Very Large Scale Integration Application Specific Integrated Circuit (VLSI ASIC) is being developed to realize the associative memory functions needed in the vector quantization algorithm. By using vector quantization, the need for Huffman coding can be eliminated, resulting in superior performance against channel bit errors than methods that use variable length codes.
Quantization of polarization states through scattering mechanisms
NASA Astrophysics Data System (ADS)
Stratis, Glafkos
This dissertation investigates, in a comprehensive and unified effort, three major areas: (a) The quantization of polarization states through various scattering mechanisms and frequencies. (b) Scattering multispectra mechanisms, mainly diffraction and reflection combined with the split of polarization states, introduce polarization dynamics, creates new opportunities and applications in communication systems, detection algorithms and various other applications. (c) Combine the Finite-Difference Time-Domain (FDTD) and Geometrical Optics (GO) resulting in realistic monostatic-bistatic UWB (Ultra Wide Band) polarimetric capabilities for both high frequency and low frequency applications under a single computation engine, where current methods Physical Optics (PO) and GO are only capable for high frequency Radar Cross Section (RCS) applications; these methods are based on separate computational engines. The quantization of polarization states is a result of various scattering mechanisms, when Electromagnetic waves of various frequencies, are incident on various scatterers. We generate and introduce for the first time the concept of quantization matrix revealing the unique characteristics of scatterers. This is a similar and very close concept related to the quantization of energy states in quantum mechanics. The split of polarization states causes the coherency/incoherency of depolarization through the various scattering mechanisms and frequencies. It is shown (in chapter 3) that by increasing the number of frequencies, the quantization matrix size increases as well, allowing better and higher resolution. The edge diffraction was chosen as one of the scattering mechanisms showing strong polarization filtering effects. Furthermore the filtering of polarization through edges combined with reflections, links with polarization dynamics in NLOS (non line of sight) applications. In addition, the fact that wedge scattering is more sensitive to polarization versus reflections
Exact quantization of a superparticle in AdS{sub 5}xS{sup 5}
Horigane, Tetsuo; Kazama, Yoichi
2010-02-15
As a step toward deeper understanding of the AdS/CFT correspondence, exact quantization of a Brink-Schwarz superparticle in the AdS{sub 5}xS{sup 5} background with Ramond-Ramond flux is performed from the first principle in the phase space formulation. It includes the construction of the quantum Noether charges for the psu(2,2|4) superconformal symmetry and by solving the superconformal primary conditions we obtain the complete physical spectrum of the system with the explicit wave functions. The spectrum agrees precisely with the supergravity results, including all the Kaluza-Klein excitations. Our method and the result are expected to shed light on the eventual quantization of a superstring in this important background.
Spin foam model from canonical quantization
Alexandrov, Sergei
2008-01-15
We suggest a modification of the Barrett-Crane spin foam model of four-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrett-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bivectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of the Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barrett-Crane model.
Eigenvalue spacings for quantized cat maps
NASA Astrophysics Data System (ADS)
Gamburd, Alex; Lafferty, John; Rockmore, Dan
2003-03-01
According to one of the basic conjectures in quantum chaos, the eigenvalues of a quantized chaotic Hamiltonian behave like the spectrum of the typical member of the appropriate ensemble of random matrices. We study one of the simplest examples of this phenomenon in the context of ergodic actions of groups generated by several linear toral automorphisms - 'cat maps'. Our numerical experiments indicate that for 'generic' choices of cat maps, the unfolded consecutive spacing distribution in the irreducible components of the Nth quantization (given by the N-dimensional Weil representation) approaches the GOE/GSE law of random matrix theory. For certain special 'arithmetic' transformations, related to the Ramanujan graphs of Lubotzky, Phillips and Sarnak, the experiments indicate that the unfolded consecutive spacing distribution follows Poisson statistics; we provide a sharp estimate in that direction.
Vector Quantization Algorithm Based on Associative Memories
NASA Astrophysics Data System (ADS)
Guzmán, Enrique; Pogrebnyak, Oleksiy; Yáñez, Cornelio; Manrique, Pablo
This paper presents a vector quantization algorithm for image compression based on extended associative memories. The proposed algorithm is divided in two stages. First, an associative network is generated applying the learning phase of the extended associative memories between a codebook generated by the LBG algorithm and a training set. This associative network is named EAM-codebook and represents a new codebook which is used in the next stage. The EAM-codebook establishes a relation between training set and the LBG codebook. Second, the vector quantization process is performed by means of the recalling stage of EAM using as associative memory the EAM-codebook. This process generates a set of the class indices to which each input vector belongs. With respect to the LBG algorithm, the main advantages offered by the proposed algorithm is high processing speed and low demand of resources (system memory); results of image compression and quality are presented.
Loop quantization of the Schwarzschild black hole.
Gambini, Rodolfo; Pullin, Jorge
2013-05-24
We quantize spherically symmetric vacuum gravity without gauge fixing the diffeomorphism constraint. Through a rescaling, we make the algebra of Hamiltonian constraints Abelian, and therefore the constraint algebra is a true Lie algebra. This allows the completion of the Dirac quantization procedure using loop quantum gravity techniques. We can construct explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. New observables living in the bulk appear at the quantum level (analogous to spin in quantum mechanics) that are not present at the classical level and are associated with the discrete nature of the spin network states of loop quantum gravity. The resulting quantum space-times resolve the singularity present in the classical theory inside black holes. PMID:23745855
Segmentation and texture representation with vector quantizers
NASA Astrophysics Data System (ADS)
Yuan, Li; Barba, Joseph
1990-11-01
An algorithm for segmentation of cell images and the extraction of texture textons based on vector quantization is presented. Initially a few low dimensional code vectors are employed in a standard vector quantization algorithm to generate a coarse code book a procedure which is equivalent to histogram sharpening. Representative gray level value from each coarse code vector are used to construct a larger fine code book. Coding the original image with the fine code book produces a less distorted image and facilitates cell and nuclear extraction. Texture textons are extracted by application of the same algorithm to the cell area using a larger number of initial code vectors and fine code book. Applications of the algorithm to cytological specimen are presented.
Second quantization in bit-string physics
NASA Technical Reports Server (NTRS)
Noyes, H. Pierre
1993-01-01
Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.
Adiabatic Quantization of Andreev Quantum Billiard Levels
NASA Astrophysics Data System (ADS)
Silvestrov, P. G.; Goorden, M. C.; Beenakker, C. W.
2003-03-01
We identify the time T between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent λ), coupled to a superconductor by an N-mode constriction. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods Tn, which in turn generate a ladder of excited states ɛnm=(m+1/2)πℏ/Tn. The largest quantized period is the Ehrenfest time T0=λ-1ln(N. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension W/(N), much below the width W of the constriction.
Positronium in basis light-front quantization
NASA Astrophysics Data System (ADS)
Zhao, Xingbo; Wiecki, Paul; Li, Yang; Maris, Pieter; Vary, James
2014-09-01
Basis light-front quantization (BLFQ) has been recently developed as a first-principles nonperturbative approach for quantum field theory. Adopting the light-front quantization and Hamiltonian formalism, it solves for the mass eigenstates of quantum field theory as the eigenvalue problem of the associated light-front Hamiltonian. In this work we apply BLFQ to the positronium system in QED and solve for its eigenspectrum in the Fock space with the lowest two Fock sectors included. We explicitly demonstrate our nonperturbative renormalization procedure, in which we infer the various needed renormalization factors through solving a series of parallel single electron problems. We then compare our numerical results for the mass spectrum to the expected Bohr spectrum from nonrelativistic quantum mechanics. Basis light-front quantization (BLFQ) has been recently developed as a first-principles nonperturbative approach for quantum field theory. Adopting the light-front quantization and Hamiltonian formalism, it solves for the mass eigenstates of quantum field theory as the eigenvalue problem of the associated light-front Hamiltonian. In this work we apply BLFQ to the positronium system in QED and solve for its eigenspectrum in the Fock space with the lowest two Fock sectors included. We explicitly demonstrate our nonperturbative renormalization procedure, in which we infer the various needed renormalization factors through solving a series of parallel single electron problems. We then compare our numerical results for the mass spectrum to the expected Bohr spectrum from nonrelativistic quantum mechanics. Supported by DOE (under Grants DESC0008485 SciDAC/NUCLEI, DE-FG02-87ER40371) and NSF (under Grant 0904782).
Quantization: Towards a comparison between methods
NASA Astrophysics Data System (ADS)
Tuynman, G. M.
1987-12-01
In this paper it is shown that the procedure of geometric quantiztion applied to Kähler manifolds gives the following result: the Hilbert space H consists, roughly speaking, of holomorphic functions on the phase space M and to each classical observable f (i.e., a real function on M) is associated an operator f on H as follows: first multiply by f+ 1/4 ℏΔdRf (ΔdR being the Laplace-de Rham operator on the Kähler manifold M) and then take the holomorphic part [see G. M. Tuynman, J. Math. Phys. 27, 573 (1987)]. This result is correct on compact Kähler manifolds and correct modulo a boundary term ∫Mdα on noncompact Kähler manifolds. In this way these results can be compared with the quantization procedure of Berezin [Math. USSR Izv. 8, 1109 (1974); 9, 341 (1975); Commun. Math. Phys. 40, 153 (1975)], which is strongly related to quantization by *-products [e.g., see C. Moreno and P. Ortega-Navarro; Amn. Inst. H. Poincaré Sec. A: 38, 215 (1983); Lett. Math. Phys. 7, 181 (1983); C. Moreno, Lett. Math. Phys. 11, 361 (1986); 12, 217 (1986)]. It is shown that on irreducible Hermitian spaces [see S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic, Orlando, FL, 1978] the contravariant symbols (in the sense of Berezin) of the operators f as above are given by the functions f+ 1/4 ℏΔdRf. The difference with the quantization result of Berezin is discussed and a change in the geometric quantization scheme is proposed.
Getzler symbol calculus and deformation quantization
NASA Astrophysics Data System (ADS)
Mesa, Camilo
2013-11-01
In this paper we give a construction of Fedosov quantization incorporating the odd variables and an analogous formula to Getzler's pseudodifferential calculus composition formula is obtained. A Fedosov type connection is constructed on the bundle of Weyl tensor Clifford algebras over the cotangent bundle of a Riemannian manifold. The quantum algebra associated with this connection is used to define a deformation of the exterior algebra of Riemannian manifolds.
Exact quantization of a paraxial electromagnetic field
Aiello, A.; Woerdman, J. P.
2005-12-15
A nonperturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. This theoretical formalism yields a seamless transition between the paraxial- and the Maxwell-equation solutions. This obviates the need to introduce either ad hoc or perturbatively defined field operators. Moreover, our (exact) formalism remains valid beyond the quasimonochromatic paraxial limit.
Loop quantization of vacuum Bianchi I cosmology
Martin-Benito, M.; Mena Marugan, G. A.; Pawlowski, T.
2008-09-15
We analyze the loop quantization of the family of vacuum Bianchi I spacetimes, a gravitational system of which classical solutions describe homogeneous anisotropic cosmologies. We rigorously construct the operator that represents the Hamiltonian constraint, showing that the states of zero volume completely decouple from the rest of quantum states. This fact ensures that the classical cosmological singularity is resolved in the quantum theory. In addition, this allows us to adopt an equivalent quantum description in terms of a well-defined densitized Hamiltonian constraint. This latter constraint can be regarded in a certain sense as a difference evolution equation in an internal time provided by one of the triad components, which is polymerically quantized. Generically, this evolution equation is a relation between the projection of the quantum states in three different sections of constant internal time. Nevertheless, around the initial singularity the equation involves only the two closest sections with the same orientation of the triad. This has a double effect: on the one hand, physical states are determined just by the data on one section, on the other hand, the evolution defined in this way never crosses the singularity, without the need of any special boundary condition. Finally, we determine the inner product and the physical Hilbert space employing group averaging techniques, and we specify a complete algebra of Dirac observables. This completes the quantization program.
Conductance Quantization in Resistive Random Access Memory.
Li, Yang; Long, Shibing; Liu, Yang; Hu, Chen; Teng, Jiao; Liu, Qi; Lv, Hangbing; Suñé, Jordi; Liu, Ming
2015-12-01
The intrinsic scaling-down ability, simple metal-insulator-metal (MIM) sandwich structure, excellent performances, and complementary metal-oxide-semiconductor (CMOS) technology-compatible fabrication processes make resistive random access memory (RRAM) one of the most promising candidates for the next-generation memory. The RRAM device also exhibits rich electrical, thermal, magnetic, and optical effects, in close correlation with the abundant resistive switching (RS) materials, metal-oxide interface, and multiple RS mechanisms including the formation/rupture of nanoscale to atomic-sized conductive filament (CF) incorporated in RS layer. Conductance quantization effect has been observed in the atomic-sized CF in RRAM, which provides a good opportunity to deeply investigate the RS mechanism in mesoscopic dimension. In this review paper, the operating principles of RRAM are introduced first, followed by the summarization of the basic conductance quantization phenomenon in RRAM and the related RS mechanisms, device structures, and material system. Then, we discuss the theory and modeling of quantum transport in RRAM. Finally, we present the opportunities and challenges in quantized RRAM devices and our views on the future prospects. PMID:26501832
Single Abrikosov vortices as quantized information bits
Golod, T.; Iovan, A.; Krasnov, V. M.
2015-01-01
Superconducting digital devices can be advantageously used in future supercomputers because they can greatly reduce the dissipation power and increase the speed of operation. Non-volatile quantized states are ideal for the realization of classical Boolean logics. A quantized Abrikosov vortex represents the most compact magnetic object in superconductors, which can be utilized for creation of high-density digital cryoelectronics. In this work we provide a proof of concept for Abrikosov-vortex-based random access memory cell, in which a single vortex is used as an information bit. We demonstrate high-endurance write operation and two different ways of read-out using a spin valve or a Josephson junction. These memory cells are characterized by an infinite magnetoresistance between 0 and 1 states, a short access time, a scalability to nm sizes and an extremely low write energy. Non-volatility and perfect reproducibility are inherent for such a device due to the quantized nature of the vortex. PMID:26456592
Conductance Quantization in Resistive Random Access Memory
NASA Astrophysics Data System (ADS)
Li, Yang; Long, Shibing; Liu, Yang; Hu, Chen; Teng, Jiao; Liu, Qi; Lv, Hangbing; Suñé, Jordi; Liu, Ming
2015-10-01
The intrinsic scaling-down ability, simple metal-insulator-metal (MIM) sandwich structure, excellent performances, and complementary metal-oxide-semiconductor (CMOS) technology-compatible fabrication processes make resistive random access memory (RRAM) one of the most promising candidates for the next-generation memory. The RRAM device also exhibits rich electrical, thermal, magnetic, and optical effects, in close correlation with the abundant resistive switching (RS) materials, metal-oxide interface, and multiple RS mechanisms including the formation/rupture of nanoscale to atomic-sized conductive filament (CF) incorporated in RS layer. Conductance quantization effect has been observed in the atomic-sized CF in RRAM, which provides a good opportunity to deeply investigate the RS mechanism in mesoscopic dimension. In this review paper, the operating principles of RRAM are introduced first, followed by the summarization of the basic conductance quantization phenomenon in RRAM and the related RS mechanisms, device structures, and material system. Then, we discuss the theory and modeling of quantum transport in RRAM. Finally, we present the opportunities and challenges in quantized RRAM devices and our views on the future prospects.
Light-Front Quantization of Gauge Theories
Brodskey, Stanley
2002-12-01
Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.
NASA Astrophysics Data System (ADS)
Zhang, Zhong-Shuai; Xiao, Shi-Fa; Xun, Da-Mao; Liu, Quan-Hui
2015-01-01
For a non-relativistic particle that freely moves on a curved surface, the fundamental commutation relations between positions and momenta are insufficient to uniquely determine the operator form of the momenta. With introduction of more commutation relations between positions and Hamiltonian and those between momenta and Hamiltonian, our recent sequential studies imply that the Cartesian system of coordinates is physically preferable, consistent with Dirac' observation. In present paper, we study quantization problem of the motion constrained on the two-dimensional sphere and develop a discriminant that can be used to show how the quantization within the intrinsic geometry is improper. Two kinds of parameterization of the spherical surface are explicitly invoked to investigate the quantization problem within the intrinsic geometry.
A visual detection model for DCT coefficient quantization
NASA Technical Reports Server (NTRS)
Ahumada, Albert J., Jr.; Peterson, Heidi A.
1993-01-01
The discrete cosine transform (DCT) is widely used in image compression, and is part of the JPEG and MPEG compression standards. The degree of compression, and the amount of distortion in the decompressed image are determined by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. Our approach is to set the quantization level for each coefficient so that the quantization error is at the threshold of visibility. Here we combine results from our previous work to form our current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color.
Quantized Nambu-Poisson manifolds and n-Lie algebras
NASA Astrophysics Data System (ADS)
DeBellis, Joshua; Sämann, Christian; Szabo, Richard J.
2010-12-01
We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of {{R}}^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.
Quantized Nambu-Poisson manifolds and n-Lie algebras
DeBellis, Joshua; Saemann, Christian; Szabo, Richard J.
2010-12-15
We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of R{sup n} by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.
NASA Astrophysics Data System (ADS)
Koide, T.; Kodama, T.
2015-09-01
The stochastic variational method (SVM) is the generalization of the variational approach to systems described by stochastic variables. In this paper, we investigate the applicability of SVM as an alternative field-quantization scheme, by considering the complex Klein-Gordon equation. There, the Euler-Lagrangian equation for the stochastic field variables leads to the functional Schrödinger equation, which can be interpreted as the Euler (ideal fluid) equation in the functional space. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, e.g., in the definition of Noether charges.
Canonical quantization of the kink model beyond the static solution
Kapustnikov, A.A.; Pashnev, A.; Pichugin, A.
1997-02-01
A new approach to the quantization of the relativistic kink model around the solitonic solution is developed on the grounds of the collective coordinates method. The corresponding effective action is proved to be the action of the nonminimal d=1+1 point particle with curvature. It is shown that upon canonical quantization this action yields the spectrum of the kink solution obtained first with the help of WKB quantization. {copyright} {ital 1997} {ital The American Physical Society}
The decoding method based on wavelet image En vector quantization
NASA Astrophysics Data System (ADS)
Liu, Chun-yang; Li, Hui; Wang, Tao
2013-12-01
With the rapidly progress of internet technology, large scale integrated circuit and computer technology, digital image processing technology has been greatly developed. Vector quantization technique plays a very important role in digital image compression. It has the advantages other than scalar quantization, which possesses the characteristics of higher compression ratio, simple algorithm of image decoding. Vector quantization, therefore, has been widely used in many practical fields. This paper will combine the wavelet analysis method and vector quantization En encoder efficiently, make a testing in standard image. The experiment result in PSNR will have a great improvement compared with the LBG algorithm.
Homotopy of rational maps and the quantization of Skyrmions
NASA Astrophysics Data System (ADS)
Krusch, Steffen
2003-04-01
The Skyrme model is a classical field theory which models the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein-Rubinstein constraints into account. The aim of this paper is to show how to calculate these FR constraints directly from the rational map ansatz using basic homotopy theory. We then apply this construction in order to quantize the Skyrme model in the simplest approximation, the zero mode quantization. This is carried out for up to 22 nucleons and the results are compared to experiment.
Coarse quantization with the fast digital shearlet transform
NASA Astrophysics Data System (ADS)
Bodmann, Bernhard G.; Kutyniok, Gitta; Zhuang, Xiaosheng
2011-09-01
The fast digital shearlet transform (FDST) was recently introduced as a means to analyze natural images efficiently, owing to the fact that those are typically governed by cartoon-like structures. In this paper, we introduce and discuss a first-order hybrid sigma-delta quantization algorithm for coarsely quantizing the shearlet coefficients generated by the FDST. Radial oversampling in the frequency domain together with our choice for the quantization helps suppress the reconstruction error in a similar way as first-order sigma-delta quantization for finite frames. We provide a theoretical bound for the reconstruction error and confirm numerically that the error is in accordance with this theoretical decay.
Semiclassical quantization of nonadiabatic systems with hopping periodic orbits.
Fujii, Mikiya; Yamashita, Koichi
2015-02-21
We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a nonadiabatic form. The quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics. PMID:25701999
Semiclassical quantization of nonadiabatic systems with hopping periodic orbits
Fujii, Mikiya Yamashita, Koichi
2015-02-21
We present a semiclassical quantization condition, i.e., quantum–classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller’s trace formula to a nonadiabatic form. The quantum–classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics.
Topological Quantization in Units of the Fine Structure Constant
Maciejko, Joseph; Qi, Xiao-Liang; Drew, H.Dennis; Zhang, Shou-Cheng; /Stanford U., Phys. Dept. /Stanford U., Materials Sci. Dept. /SLAC
2011-11-11
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant {alpha} = e{sup 2}/{h_bar}c. In this Letter, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other.
Quantization effects in radiation spectroscopy based on digital pulse processing
Jordanov, V. T.; Jordanova, K. V.
2011-07-01
Radiation spectra represent inherently quantization data in the form of stacked channels of equal width. The spectrum is an experimental measurement of the discrete probability density function (PDF) of the detector pulse heights. The quantization granularity of the spectra depends on the total number of channels covering the full range of pulse heights. In analog pulse processing the total number of channels is equal to the total digital values produced by a spectroscopy analog-to-digital converter (ADC). In digital pulse processing each detector pulse is sampled and quantized by a fast ADC producing certain number of quantized numerical values. These digital values are linearly processed to obtain a digital quantity representing the peak of the digitally shaped pulse. Using digital pulse processing it is possible to acquire a spectrum with the total number of channels greater than the number of ADC values. Noise and sample averaging are important in the transformation of ADC quantized data into spectral quantized data. Analysis of this transformation is performed using an area sampling model of quantization. Spectrum differential nonlinearity (DNL) is shown to be related to the quantization at low noise levels and small number of averaged samples. Theoretical analysis and experimental measurements are used to obtain the condition to minimize the DNL due to quantization. (authors)
Separable quantizations of Stäckel systems
NASA Astrophysics Data System (ADS)
Błaszak, Maciej; Marciniak, Krzysztof; Domański, Ziemowit
2016-08-01
In this article we prove that many Hamiltonian systems that cannot be separably quantized in the classical approach of Robertson and Eisenhart can be separably quantized if we extend the class of admissible quantizations through a suitable choice of Riemann space adapted to the Poisson geometry of the system. Actually, in this article we prove that for every quadratic in momenta Stäckel system (defined on 2 n dimensional Poisson manifold) for which Stäckel matrix consists of monomials in position coordinates there exist infinitely many quantizations-parametrized by n arbitrary functions-that turn this system into a quantum separable Stäckel system.
Observation of quantized conductance in neutral matter
NASA Astrophysics Data System (ADS)
Krinner, Sebastian; Stadler, David; Husmann, Dominik; Brantut, Jean-Philippe; Esslinger, Tilman
2015-01-01
In transport experiments, the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps, with a size determined solely by Planck's constant h. Observations of quantized steps in electrical conductance have provided important insights into the physics of mesoscopic systems and have allowed the development of quantum electronic devices. Even though quantized conductance should not rely on the presence of electric charges, it has never been observed for neutral, massive particles. In its most fundamental form, it requires a quantum-degenerate Fermi gas, a ballistic and adiabatic transport channel, and a constriction with dimensions comparable to the Fermi wavelength. Here we report the observation of quantized conductance in the transport of neutral atoms driven by a chemical potential bias. The atoms are in an ultraballistic regime, where their mean free path exceeds not only the size of the transport channel, but also the size of the entire system, including the atom reservoirs. We use high-resolution lithography to shape light potentials that realize either a quantum point contact or a quantum wire for atoms. These constrictions are imprinted on a quasi-two-dimensional ballistic channel connecting the reservoirs. By varying either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaux in the atom conductance. The conductance in the first plateau is found to be equal to the universal conductance quantum, 1/h. We use Landauer's formula to model our results and find good agreement for low gate potentials, with all parameters determined a priori. Our experiment lets us investigate quantum conductors with wide control not only over the channel geometry, but also over the reservoir properties, such as interaction strength, size and thermalization rate.
Błaszak, Maciej Domański, Ziemowit
2013-12-15
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. -- Highlights: •An invariant quantization procedure of classical mechanics on the phase space over flat configuration space is presented. •The passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. •Explicit form of position and momentum operators and their appropriate ordering in curvilinear coordinates is shown. •The invariant form of Hamiltonian operators quadratic and cubic in momenta is derived. •The extension of presented formalism onto non-flat case and related ambiguities of the quantization process are discussed.
Quantization of lumped elements electrical circuits revisited
NASA Astrophysics Data System (ADS)
Lalumiere, Kevin; Najafi-Yazdi, Alireza
In 1995, the ``Les Houches'' seminar of Michel Devoret introduced a method to quantize lumped elements electrical circuits. This method has since been formalized using the matricial formalism, in particular by G. Burkard. Starting from these seminal contributions, we present a new algorithm to quantify electrical circuits. This algorithm unites the features of Devoret's and Burkad's approaches. We minimize the set of assumptions made so that the method can treat directly most electrical circuits. This includes circuits with resistances, mutual inductances, voltage and current sources. We conclude with a discussion about the choice of the basis in which the Hamiltonian operator should be written, an issue which is often overlooked.
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Quantum mechanics, gravity and modified quantization relations.
Calmet, Xavier
2015-08-01
In this paper, we investigate a possible energy scale dependence of the quantization rules and, in particular, from a phenomenological point of view, an energy scale dependence of an effective [Formula: see text] (reduced Planck's constant). We set a bound on the deviation of the value of [Formula: see text] at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation has taken place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about 10(16) GeV. PMID:26124253
Quantized gauged massless Rarita-Schwinger fields
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2015-10-01
We study the quantization of a minimally gauged massless Rarita-Schwinger field, by both the Dirac bracket and functional integral methods. The Dirac bracket approach in the covariant radiation gauge leads to an anticommutator that has a nonsingular limit as gauge fields approach zero, is manifestly positive semidefinite, and is Lorentz invariant. The constraints also have the form needed to apply the Faddeev-Popov method for deriving a functional integral, using the same constrained Hamiltonian and inverse constraint matrix that appear in the Dirac bracket approach.
The pointwise product in Weyl quantization
NASA Astrophysics Data System (ADS)
Dubin, D. A.; Hennings, M. A.
2004-07-01
We study the odot-product of Bracken [1], which is the Weyl quantized version of the pointwise product of functions in phase space. We prove that it is not compatible with the algebras of finite rank and Hilbert-Schmidt operators. By solving the linearization problem for the special Hermite functions, we are able to express the odot-product in terms of the component operators, mediated by the linearization coefficients. This is applied to finite rank operators and their matrices, and operators whose symbols are radial and angular distributions.
Brief Review on Black Hole Loop Quantization
NASA Astrophysics Data System (ADS)
Olmedo, Javier
2016-06-01
Here, we present a review about the quantization of spherically-symmetric spacetimes adopting loop quantum gravity techniques. Several models that have been studied so far share similar properties: the resolution of the classical singularity and some of them an intrinsic discretization of the geometry. We also explain the extension to Reissner---Nordstr\\"om black holes. Besides, we review how quantum test fields on these quantum geometries allow us to study phenomena, like the Casimir effect or Hawking radiation. Finally, we briefly describe a recent proposal that incorporates spherically-symmetric matter, discussing its relevance for the understanding of black hole evolution.
Quantization of soluble classical constrained systems
Belhadi, Z.; Menas, F.; Bérard, A.; Mohrbach, H.
2014-12-15
The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the determination of the classical brackets which does neither require Dirac’s formalism nor the symplectic method of Faddeev and Jackiw. This approach is based on the computation of the brackets between the constants of integration of the exact solutions of the equations of motion. From them all brackets of the dynamical variables of the system can be deduced in a straightforward way.
Path integral quantization of generalized quantum electrodynamics
Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2011-02-15
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green's functions and a discussion about the obtained results are presented.
A visual detection model for DCT coefficient quantization
NASA Technical Reports Server (NTRS)
Ahumada, Albert J., Jr.; Watson, Andrew B.
1994-01-01
The discrete cosine transform (DCT) is widely used in image compression and is part of the JPEG and MPEG compression standards. The degree of compression and the amount of distortion in the decompressed image are controlled by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. One approach is to set the quantization level for each coefficient so that the quantization error is near the threshold of visibility. Results from previous work are combined to form the current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color. A model-based method of optimizing the quantization matrix for an individual image was developed. The model described above provides visual thresholds for each DCT frequency. These thresholds are adjusted within each block for visual light adaptation and contrast masking. For given quantization matrix, the DCT quantization errors are scaled by the adjusted thresholds to yield perceptual errors. These errors are pooled nonlinearly over the image to yield total perceptual error. With this model one may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix.
Bohmian quantization of the big rip
Pinto-Neto, Nelson; Pantoja, Diego Moraes
2009-10-15
It is shown in this paper that minisuperspace quantization of homogeneous and isotropic geometries with phantom scalar fields, when examined in the light of the Bohm-de Broglie interpretation of quantum mechanics, does not eliminate, in general, the classical big rip singularity present in the classical model. For some values of the Hamilton-Jacobi separation constant present in a class of quantum state solutions of the Wheeler-De Witt equation, the big rip can be either completely eliminated or may still constitute a future attractor for all expanding solutions. This is contrary to the conclusion presented in [M. P. Dabrowski, C. Kiefer, and B. Sandhofer, Phys. Rev. D 74, 044022 (2006).], using a different interpretation of the wave function, where the big rip singularity is completely eliminated ('smoothed out') through quantization, independently of such a separation constant and for all members of the above mentioned class of solutions. This is an example of the very peculiar situation where different interpretations of the same quantum state of a system are predicting different physical facts, instead of just giving different descriptions of the same observable facts: in fact, there is nothing more observable than the fate of the whole Universe.
Loop quantization of the Schwarzschild interior revisited
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Singh, Parampreet
2016-03-01
The loop quantization of the Schwarzschild interior region, as described by a homogeneous anisotropic Kantowski-Sachs model, is re-examined. As several studies of different—inequivalent—loop quantizations have shown, to date there exists no fully satisfactory quantum theory for this model. This fact poses challenges to the validity of some scenarios to address the black hole information problem. Here we put forward a novel viewpoint to construct the quantum theory that builds from some of the models available in the literature. The final picture is a quantum theory that is both independent of any auxiliary structure and possesses a correct low curvature limit. It represents a subtle but non-trivial modification of the original prescription given by Ashtekar and Bojowald. It is shown that the quantum gravitational constraint is well defined past the singularity and that its effective dynamics possesses a bounce into an expanding regime. The classical singularity is avoided, and a semiclassical spacetime satisfying vacuum Einstein’s equations is recovered on the ‘other side’ of the bounce. We argue that such a metric represents the interior region of a white-hole spacetime, but for which the corresponding ‘white hole mass’ differs from the original black hole mass. Furthermore, we find that the value of the white hole mass is proportional to the third power of the starting black hole mass.
Light-cone quantization of quantum chromodynamics
Brodsky, S.J. ); Pauli, H.C. )
1991-06-01
We discuss the light-cone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The light-cone Fock state expansion of wavefunctions at fixed light cone time provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of light-cone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavy-quark contributions to structure functions. A general nonperturbative method for numerically solving quantum field theories, discretized light-cone quantization,'' is outlined and applied to several gauge theories, including QCD in one space and one time dimension, and quantum electrodynamics in physical space-time at large coupling strength. The DLCQ method is invariant under the large class of light-cone Lorentz transformations, and it can be formulated such at ultraviolet regularization is independent of the momentum space discretization. Both the bound-state spectrum and the corresponding relativistic light-cone wavefunctions can be obtained by matrix diagonalization and related techniques. We also discuss the construction of the light-cone Fock basis, the structure of the light-cone vacuum, and outline the renormalization techniques required for solving gauge theories within the light-cone Hamiltonian formalism.
Bohmian quantization of the big rip
NASA Astrophysics Data System (ADS)
Pinto-Neto, Nelson; Pantoja, Diego Moraes
2009-10-01
It is shown in this paper that minisuperspace quantization of homogeneous and isotropic geometries with phantom scalar fields, when examined in the light of the Bohm-de Broglie interpretation of quantum mechanics, does not eliminate, in general, the classical big rip singularity present in the classical model. For some values of the Hamilton-Jacobi separation constant present in a class of quantum state solutions of the Wheeler-De Witt equation, the big rip can be either completely eliminated or may still constitute a future attractor for all expanding solutions. This is contrary to the conclusion presented in [M. P. Dabrowski, C. Kiefer, and B. Sandhofer, Phys. Rev. DPRVDAQ1550-7998 74, 044022 (2006).10.1103/PhysRevD.74.044022], using a different interpretation of the wave function, where the big rip singularity is completely eliminated (“smoothed out”) through quantization, independently of such a separation constant and for all members of the above mentioned class of solutions. This is an example of the very peculiar situation where different interpretations of the same quantum state of a system are predicting different physical facts, instead of just giving different descriptions of the same observable facts: in fact, there is nothing more observable than the fate of the whole Universe.
Image Compression on a VLSI Neural-Based Vector Quantizer.
ERIC Educational Resources Information Center
Chen, Oscal T.-C.; And Others
1992-01-01
Describes a modified frequency-sensitive self-organization (FSO) algorithm for image data compression and the associated VLSI architecture. Topics discussed include vector quantization; VLSI neural processor architecture; detailed circuit implementation; and a neural network vector quantization prototype chip. Examples of images using the FSO…
Exciton condensation in microcavities under three-dimensional quantization conditions
Kochereshko, V. P. Platonov, A. V.; Savvidis, P.; Kavokin, A. V.; Bleuse, J.; Mariette, H.
2013-11-15
The dependence of the spectra of the polarized photoluminescence of excitons in microcavities under conditions of three-dimensional quantization on the optical-excitation intensity is investigated. The cascade relaxation of polaritons between quantized states of a polariton Bose condensate is observed.
Fast color quantization using weighted sort-means clustering.
Celebi, M Emre
2009-11-01
Color quantization is an important operation with numerous applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. However, despite its popularity as a general purpose clustering algorithm, K-means has not received much respect in the color quantization literature because of its high computational requirements and sensitivity to initialization. In this paper, a fast color quantization method based on K-means is presented. The method involves several modifications to the conventional (batch) K-means algorithm, including data reduction, sample weighting, and the use of the triangle inequality to speed up the nearest-neighbor search. Experiments on a diverse set of images demonstrate that, with the proposed modifications, K-means becomes very competitive with state-of-the-art color quantization methods in terms of both effectiveness and efficiency. PMID:19884945
First, Second Quantization and Q-Deformed Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2015-06-01
Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed.
Weighted MinMax Algorithm for Color Image Quantization
NASA Technical Reports Server (NTRS)
Reitan, Paula J.
1999-01-01
The maximum intercluster distance and the maximum quantization error that are minimized by the MinMax algorithm are shown to be inappropriate error measures for color image quantization. A fast and effective (improves image quality) method for generalizing activity weighting to any histogram-based color quantization algorithm is presented. A new non-hierarchical color quantization technique called weighted MinMax that is a hybrid between the MinMax and Linde-Buzo-Gray (LBG) algorithms is also described. The weighted MinMax algorithm incorporates activity weighting and seeks to minimize WRMSE, whereby obtaining high quality quantized images with significantly less visual distortion than the MinMax algorithm.
Nonclassical vibrational states in a quantized trap
NASA Astrophysics Data System (ADS)
Zeng, Heping; Lin, Fucheng
1993-09-01
The quantized center-of-mass (c.m.) motions of a single two-level atom or ion confined into a one-dimensional harmonic potential and interacting with a single-mode classical traveling-wave laser field are examined. We demonstrate that trap quantum states with remarkable nonclassical properties such as quadrature and amplitude-squared squeezing and sub-Poissonian statistics can be generated in this simple trap model when the c.m. motion is initially in certain coherent trap states. Our analyses also indicate that there exist some time regions where the production of nonclassical vibrational states is possible even if squeezing or sub-Poissonian statistics do not appear.
Kerr Black Hole Entropy and its Quantization
NASA Astrophysics Data System (ADS)
Jiang, Ji-Jian; Li, Chuan-An; Cheng, Xie-Feng
2016-08-01
By constructing the four-dimensional phase space based on the observable physical quantity of Kerr black hole and gauge transformation, the Kerr black hole entropy in the phase space was obtained. Then considering the corresponding mechanical quantities as operators and making the operators quantized, entropy spectrum of Kerr black hole was obtained. Our results show that the Kerr black hole has the entropy spectrum with equal intervals, which is in agreement with the idea of Bekenstein. In the limit of large event horizon, the area of the adjacent event horizon of the black hole have equal intervals. The results are in consistent with the results based on the loop quantum gravity theory by Dreyer et al.
Quantized spin waves in antiferromagnetic Heisenberg chains.
Wieser, R; Vedmedenko, E Y; Wiesendanger, R
2008-10-24
The quantized stationary spin wave modes in one-dimensional antiferromagnetic spin chains with easy axis on-site anisotropy have been studied by means of Landau-Lifshitz-Gilbert spin dynamics. We demonstrate that the confined antiferromagnetic chains show a unique behavior having no equivalent, neither in ferromagnetism nor in acoustics. The discrete energy dispersion is split into two interpenetrating n and n' levels caused by the existence of two sublattices. The oscillations of individual sublattices as well as the standing wave pattern strongly depend on the boundary conditions. Particularly, acoustical and optical antiferromagnetic spin waves in chains with boundaries fixed (pinned) on different sublattices can be found, while an asymmetry of oscillations appears if the two pinned ends belong to the same sublattice. PMID:18999780
Optimized regulator for the quantized anharmonic oscillator
NASA Astrophysics Data System (ADS)
Kovacs, J.; Nagy, S.; Sailer, K.
2015-04-01
The energy gap between the first excited state and the ground state is calculated for the quantized anharmonic oscillator in the framework of the functional renormalization group method. The compactly supported smooth regulator is used which includes various types of regulators as limiting cases. It was found that the value of the energy gap depends on the regulator parameters. We argue that the optimization based on the disappearance of the false, broken symmetric phase of the model leads to the Litim's regulator. The least sensitivity on the regulator parameters leads, however, to an IR regulator being somewhat different of the Litim's one, but it can be described as a perturbatively improved, or generalized Litim's regulator and provides analytic evolution equations, too.
DCT quantization matrices visually optimized for individual images
NASA Technical Reports Server (NTRS)
Watson, Andrew B.
1993-01-01
This presentation describes how a vision model incorporating contrast sensitivity, contrast masking, and light adaptation is used to design visually optimal quantization matrices for Discrete Cosine Transform image compression. The Discrete Cosine Transform (DCT) underlies several image compression standards (JPEG, MPEG, H.261). The DCT is applied to 8x8 pixel blocks, and the resulting coefficients are quantized by division and rounding. The 8x8 'quantization matrix' of divisors determines the visual quality of the reconstructed image; the design of this matrix is left to the user. Since each DCT coefficient corresponds to a particular spatial frequency in a particular image region, each quantization error consists of a local increment or decrement in a particular frequency. After adjustments for contrast sensitivity, local light adaptation, and local contrast masking, this coefficient error can be converted to a just-noticeable-difference (jnd). The jnd's for different frequencies and image blocks can be pooled to yield a global perceptual error metric. With this metric, we can compute for each image the quantization matrix that minimizes the bit-rate for a given perceptual error, or perceptual error for a given bit-rate. Implementation of this system demonstrates its advantages over existing techniques. A unique feature of this scheme is that the quantization matrix is optimized for each individual image. This is compatible with the JPEG standard, which requires transmission of the quantization matrix.
HVS-motivated quantization schemes in wavelet image compression
NASA Astrophysics Data System (ADS)
Topiwala, Pankaj N.
1996-11-01
Wavelet still image compression has recently been a focus of intense research, and appears to be maturing as a subject. Considerable coding gains over older DCT-based methods have been achieved, while the computational complexity has been made very competitive. We report here on a high performance wavelet still image compression algorithm optimized for both mean-squared error (MSE) and human visual system (HVS) characteristics. We present the problem of optimal quantization from a Lagrange multiplier point of view, and derive novel solutions. Ideally, all three components of a typical image compression system: transform, quantization, and entropy coding, should be optimized simultaneously. However, the highly nonlinear nature of quantization and encoding complicates the formulation of the total cost function. In this report, we consider optimizing the filter, and then the quantizer, separately, holding the other two components fixed. While optimal bit allocation has been treated in the literature, we specifically address the issue of setting the quantization stepsizes, which in practice is quite different. In this paper, we select a short high- performance filter, develop an efficient scalar MSE- quantizer, and four HVS-motivated quantizers which add some value visually without incurring any MSE losses. A combination of run-length and empirically optimized Huffman coding is fixed in this study.
Quaternionic quantization principle in general relativity and supergravity
NASA Astrophysics Data System (ADS)
Kober, Martin
2016-01-01
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space-time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to 𝒩 = 1 supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.
Quantization table design revisited for image/video coding.
Yang, En-Hui; Sun, Chang; Meng, Jin
2014-11-01
Quantization table design is revisited for image/video coding where soft decision quantization (SDQ) is considered. Unlike conventional approaches, where quantization table design is bundled with a specific encoding method, we assume optimal SDQ encoding and design a quantization table for the purpose of reconstruction. Under this assumption, we model transform coefficients across different frequencies as independently distributed random sources and apply the Shannon lower bound to approximate the rate distortion function of each source. We then show that a quantization table can be optimized in a way that the resulting distortion complies with certain behavior. Guided by this new design principle, we propose an efficient statistical-model-based algorithm using the Laplacian model to design quantization tables for DCT-based image coding. When applied to standard JPEG encoding, it provides more than 1.5-dB performance gain in PSNR, with almost no extra burden on complexity. Compared with the state-of-the-art JPEG quantization table optimizer, the proposed algorithm offers an average 0.5-dB gain in PSNR with computational complexity reduced by a factor of more than 2000 when SDQ is OFF, and a 0.2-dB performance gain or more with 85% of the complexity reduced when SDQ is ON. Significant compression performance improvement is also seen when the algorithm is applied to other image coding systems proposed in the literature. PMID:25248184
Modified 8×8 quantization table and Huffman encoding steganography
NASA Astrophysics Data System (ADS)
Guo, Yongning; Sun, Shuliang
2014-10-01
A new secure steganography, which is based on Huffman encoding and modified quantized discrete cosine transform (DCT) coefficients, is provided in this paper. Firstly, the cover image is segmented into 8×8 blocks and modified DCT transformation is applied on each block. Huffman encoding is applied to code the secret image before embedding. DCT coefficients are quantized by modified quantization table. Inverse DCT(IDCT) is conducted on each block. All the blocks are combined together and the steg image is finally achieved. The experiment shows that the proposed method is better than DCT and Mahender Singh's in PSNR and Capacity.
Direct observation of Kelvin waves excited by quantized vortex reconnection.
Fonda, Enrico; Meichle, David P; Ouellette, Nicholas T; Hormoz, Sahand; Lathrop, Daniel P
2014-03-25
Quantized vortices are key features of quantum fluids such as superfluid helium and Bose-Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid (4)He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system. PMID:24704878
Direct observation of Kelvin waves excited by quantized vortex reconnection
Fonda, Enrico; Meichle, David P.; Ouellette, Nicholas T.; Hormoz, Sahand; Lathrop, Daniel P.
2014-01-01
Quantized vortices are key features of quantum fluids such as superfluid helium and Bose–Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid 4He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system. PMID:24704878
NASA Astrophysics Data System (ADS)
Kayahan, Huseyin; Ceylan, Ömer; Yazici, Melik; Gurbuz, Yasar
2014-06-01
This paper presents a digital ROIC for staring type arrays with extending counting method to realize very low quantization noise while achieving a very high charge handling capacity. Current state of the art has shown that digital readouts with pulse frequency method can achieve charge handling capacities higher than 3Ge- with quantization noise higher than 1000e-. Even if the integration capacitance is reduced, it cannot be lower than 1-3 fF due to the parasitic capacitance of the comparator. For achieving a very low quantization noise of 161 electrons in a power efficient way, a new method based on measuring the time to measure the remaining charge on the integration capacitor is proposed. With this approach SNR of low flux pixels are significantly increased while large flux pixels can store electrons as high as 2.33Ge-. A prototype array of 32×32 pixels with 30μm pitch is implemented in 90nm CMOS process technology for verification. Measurement results are given for complete readout.
Wigner quantization of some one-dimensional Hamiltonians
Regniers, G.; Van der Jeugt, J.
2010-12-15
Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown. Among those we have the ubiquitous relation with Lie superalgebras and their representations. In this paper, we study two one-dimensional Hamiltonians for which the Wigner quantization is related with the orthosymplectic Lie superalgebra osp(1|2). One of them, the Hamiltonian H=xp, is popular due to its connection with the Riemann zeros, discovered by Berry and Keating on the one hand and Connes on the other. The Hamiltonian of the free particle, H{sub f}=p{sup 2}/2, is the second Hamiltonian we will examine. Wigner quantization introduces an extra representation parameter for both of these Hamiltonians. Canonical quantization is recovered by restricting to a specific representation of the Lie superalgebra osp(1|2).
Simulation of bit-quantization influence on SAR-images
NASA Astrophysics Data System (ADS)
Wolframm, A. P.; Pike, T. K.
The first European Remote Sensing satellite ERS-1 has two imaging modes, the conventional Synthetic Aperture Radar (SAR) mode and the wave mode. Two quantization schemes, 2-bit and 4-bit, have been proposed for the analogue-to-digital conversion of the video signal of the ERS-1 wave mode. This paper analyzes the influence of these two quantization schemes on ocean-wave spectra. The SAR-images were obtained through simulation using a static oceanwave radar model and a comprehensive software SAR-system simulation model (SARSIM) on the DFVLR computing system. The results indicate that spectra produced by the 4-bit quantization are not significantly degraded from the optimum, but that the 2-bit quantization requires some gain adjustment for optimal spectral reproduction. The conclusions are supported by images and spectral plots covering the various options simulated.
A physically motivated quantization of the electromagnetic field
NASA Astrophysics Data System (ADS)
Bennett, Robert; Barlow, Thomas M.; Beige, Almut
2016-01-01
The notion that the electromagnetic field is quantized is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantization of this field are usually mathematically motivated and begin by introducing a vector potential, followed by the imposition of a gauge that allows the manipulation of the solutions of Maxwell’s equations into a form that is amenable for the machinery of canonical quantization. By contrast, here we quantize the electromagnetic field in a less mathematically and more physically motivated way. Starting from a direct description of what one sees in experiments, we show that the usual expressions of the electric and magnetic field observables follow from Heisenberg’s equation of motion. In our treatment, there is no need to invoke the vector potential in a specific gauge and we avoid the commonly used notion of a fictitious cavity that applies boundary conditions to the field.
Minimum uncertainty and squeezing in diffusion processes and stochastic quantization
NASA Technical Reports Server (NTRS)
Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe
1994-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
Path integral quantization of the relativistic Hopfield model
NASA Astrophysics Data System (ADS)
Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.
2016-03-01
The path-integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path-integral formalism. In particular, we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time-ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.
Quantum Hamilton Mechanics and the Theory of Quantization Conditions
NASA Astrophysics Data System (ADS)
Bracken, Paul
A formulation of quantum mechanics in terms of complex canonical variables is presented. It is seen that these variables are governed by Hamilton's equations. It is shown that the action variables need to be quantized. By formulating a quantum Hamilton equation for the momentum variable, the energies for two different systems are determined. Quantum canonical transformation theory is introduced and the geometrical significance of a set of generalized quantization conditions which are obtained is discussed.
Klauder's quantization in the Almost-Kaehler case
Maraner, P.; Onofri, E. ); Tecchiolli, G.P. )
1992-05-20
In this paper the authors prove that a regularized projection operator on the physical subspace H{sub phys} {contained in} L{sub 2} ({omega}) can be defined for a symplectic manifold {omega} = T*M equipped with an Almost-Kaehler structure, provided that a suitable counterterm is added to Klauder's definition. The present result extends Klauder's quantization to the case in which geometric quantization requires a real polarization.
Visual optimization of DCT quantization matrices for individual images
NASA Technical Reports Server (NTRS)
Watson, Andrew B.
1993-01-01
Many image compression standards (JPEG, MPEG, H.261) are based on the Discrete Cosine Transform (DCT). However, these standards do not specify the actual DCT quantization matrix. We have previously provided mathematical formulae to compute a perceptually lossless quantization matrix. Here I show how to compute a matrix that is optimized for a particular image. The method treats each DCT coefficient as an approximation to the local response of a visual 'channel'. For a given quantization matrix, the DCT quantization errors are adjusted by contrast sensitivity, light adaptation, and contrast masking, and are pooled non-linearly over the blocks of the image. This yields an 8x8 'perceptual error matrix'. A second non-linear pooling over the perceptual error matrix yields total perceptual error. With this model we may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix.
Quantized vortices in interacting gauge theories
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Ohberg, Patrik
2015-05-01
We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle vector potential corresponds to a constant synthetic magnetic field. We find a new type of current non-linearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate on the physical conditions that make the nucleation of a quantized vortex in the system energetically favourable with respect to the non rotating solution. Two different physical interpretations can be given to this new non linearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. We analyze the physical conditions that make a single vortex state energetically favourable. In the Thomas-Fermi limit, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating depends on the density of the cloud. The authors acknowledge support from CM-DTC and EPSRC.
Light-cone quantization and hadron structure
Brodsky, S.J.
1996-04-01
Quantum chromodynamics provides a fundamental description of hadronic and nuclear structure and dynamics in terms of elementary quark and gluon degrees of freedom. In practice, the direct application of QCD to reactions involving the structure of hadrons is extremely complex because of the interplay of nonperturbative effects such as color confinement and multi-quark coherence. In this talk, the author will discuss light-cone quantization and the light-cone Fock expansion as a tractable and consistent representation of relativistic many-body systems and bound states in quantum field theory. The Fock state representation in QCD includes all quantum fluctuations of the hadron wavefunction, including fax off-shell configurations such as intrinsic strangeness and charm and, in the case of nuclei, hidden color. The Fock state components of the hadron with small transverse size, which dominate hard exclusive reactions, have small color dipole moments and thus diminished hadronic interactions. Thus QCD predicts minimal absorptive corrections, i.e., color transparency for quasi-elastic exclusive reactions in nuclear targets at large momentum transfer. In other applications, such as the calculation of the axial, magnetic, and quadrupole moments of light nuclei, the QCD relativistic Fock state description provides new insights which go well beyond the usual assumptions of traditional hadronic and nuclear physics.
Observation of quantized conductance in neutral matter
NASA Astrophysics Data System (ADS)
Husmann, Dominik; Krinner, Sebastian; Lebrat, Martin; Grenier, Charles; Nakajima, Shuta; Häusler, Samuel; Brantut, Jean-Philippe; Esslinger, Tilman
2015-05-01
In transport experiments, the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps, with a size determined solely by Planck's constant h. Here we report the observation of quantized conductance in the transport of neutral atoms driven by a chemical potential bias. We use high-resolution lithography to shape light potentials that realize either a quantum point contact or a quantum wire for atoms. These constrictions are imprinted on a quasi-two-dimensional ballistic channel connecting the reservoirs. By varying either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaux in the atom conductance. The conductance in the first plateau is found to be equal to the universal conductance quantum, 1/h. We use Landauer's formula to model our results and find good agreement for low gate potentials, with all parameters determined a priori. We eventually explore the behavior of a strongly interacting Fermi gas in the same configuration, and the consequences of the emergence of superfluidity.
Quantized vortices in interacting gauge theories
NASA Astrophysics Data System (ADS)
Butera, Salvatore; Valiente, Manuel; Öhberg, Patrik
2016-01-01
We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle zeroth-order vector potential corresponds to a constant synthetic magnetic field. We find a new exotic type of current nonlinearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate the rotational properties of this system in the Thomas-Fermi limit, focusing in particular on the physical conditions that make the existence of a quantized vortex in the system energetically favourable with respect to the non-rotating solution. We point out that two different physical interpretations can be given to this new nonlinearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. Looking at the problem from both of these viewpoints, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating states depends on the density of the cloud.
The Hopfield model revisited: covariance and quantization
NASA Astrophysics Data System (ADS)
Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.
2016-01-01
There are several possible applications of quantum electrodynamics in dielectric media which require a quantum description for the electromagnetic field interacting with matter fields. The associated quantum models can refer to macroscopic electromagnetic fields or, alternatively, to mesoscopic fields (polarization fields) describing an effective interaction between electromagnetic field and matter fields. We adopt the latter approach, and focus on the Hopfield model for the electromagnetic field in a dielectric dispersive medium in a framework in which space-time dependent mesoscopic parameters occur, like susceptibility, matter resonance frequency, and also coupling between electromagnetic field and polarization field. Our most direct goal is to describe in a phenomenological way a space-time varying dielectric perturbation induced by means of the Kerr effect in nonlinear dielectric media. This extension of the model is implemented by means of a Lorentz-invariant Lagrangian which, for constant microscopic parameters, and in the rest frame, coincides with the standard one. Moreover, we deduce a covariant scalar product and provide a canonical quantization scheme which takes into account the constraints implicit in the model. Examples of viable applications are indicated.
Dynamics of Quantized Vortices Before Reconnection
NASA Astrophysics Data System (ADS)
Andryushchenko, V. A.; Kondaurova, L. P.; Nemirovskii, S. K.
2016-04-01
The main goal of this paper is to investigate numerically the dynamics of quantized vortex loops, just before the reconnection at finite temperature, when mutual friction essentially changes the evolution of lines. Modeling is performed on the base of vortex filament method using the full Biot-Savart equation. It was discovered that the initial position of vortices and the temperature strongly affect the dependence on time of the minimum distance δ (t) between tips of two vortex loops. In particular, in some cases, the shrinking and collapse of vortex loops due to mutual friction occur earlier than the reconnection, thereby canceling the latter. However, this relationship takes a universal square-root form δ ( t) =√{( κ/2π ) ( t_{*}-t) } at distances smaller than the distances, satisfying the Schwarz reconnection criterion, when the nonlocal contribution to the Biot-Savart equation becomes about equal to the local contribution. In the "universal" stage, the nearest parts of vortices form a pyramid-like structure with angles which neither depend on the initial configuration nor on temperature.
Binned progressive quantization for compressive sensing.
Wang, Liangjun; Wu, Xiaolin; Shi, Guangming
2012-06-01
Compressive sensing (CS) has been recently and enthusiastically promoted as a joint sampling and compression approach. The advantages of CS over conventional signal compression techniques are architectural: the CS encoder is made signal independent and computationally inexpensive by shifting the bulk of system complexity to the decoder. While these properties of CS allow signal acquisition and communication in some severely resource-deprived conditions that render conventional sampling and coding impossible, they are accompanied by rather disappointing rate-distortion performance. In this paper, we propose a novel coding technique that rectifies, to a certain extent, the problem of poor compression performance of CS and, at the same time, maintains the simplicity and universality of the current CS encoder design. The main innovation is a scheme of progressive fixed-rate scalar quantization with binning that enables the CS decoder to exploit hidden correlations between CS measurements, which was overlooked in the existing literature. Experimental results are presented to demonstrate the efficacy of the new CS coding technique. Encouragingly, on some test images, the new CS technique matches or even slightly outperforms JPEG. PMID:22374362
Interactions between unidirectional quantized vortex rings
NASA Astrophysics Data System (ADS)
Zhu, T.; Evans, M. L.; Brown, R. A.; Walmsley, P. M.; Golov, A. I.
2016-08-01
We have used the vortex filament method to numerically investigate the interactions between pairs of quantized vortex rings that are initially traveling in the same direction but with their axes offset by a variable impact parameter. The interaction of two circular rings of comparable radii produces outcomes that can be categorized into four regimes, dependent only on the impact parameter; the two rings can either miss each other on the inside or outside or reconnect leading to final states consisting of either one or two deformed rings. The fraction of energy that went into ring deformations and the transverse component of velocity of the rings are analyzed for each regime. We find that rings of very similar radius only reconnect for a very narrow range of the impact parameter, much smaller than would be expected from the geometrical cross-section alone. In contrast, when the radii of the rings are very different, the range of impact parameters producing a reconnection is close to the geometrical value. A second type of interaction considered is the collision of circular rings with a highly deformed ring. This type of interaction appears to be a productive mechanism for creating small vortex rings. The simulations are discussed in the context of experiments on colliding vortex rings and quantum turbulence in superfluid helium in the zero-temperature limit.
Canonical quantization of Galilean covariant field theories
NASA Astrophysics Data System (ADS)
Santos, E. S.; de Montigny, M.; Khanna, F. C.
2005-11-01
The Galilean-invariant field theories are quantized by using the canonical method and the five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schrödinger field follows from a reduction of the Klein-Gordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting term λΦ4. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the Lévy-Leblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and cross-sections are calculated for the Coulomb interaction, the electron-electron and the electron-positron scattering. These examples show that the so-called 'non-relativistic' approximations, obtained in low-velocity limits, must be treated with great care to be Galilei-invariant. The non-relativistic Proca field is discussed briefly.
Thickness quantization in a reorientation transition
NASA Astrophysics Data System (ADS)
Venus, David; He, Gengming; Winch, Harrison; Belanger, Randy
The reorientation transition of an ultrathin film from perpendicular to in-plane magnetization is driven by a competition between shape and surface anisotropy. It is accompanied by a ''stripe'' domain structure that evolves as the reorientation progresses. Often, an n layer film has stable perpendicular magnetization and an n+1 layer film has stable in-plane magnetization. If the domain walls are not pinned, the long-range stripe domain pattern averages over this structure so that the transition occurs at a non-integer layer thickness. We report in situ experimental measurements of the magnetic susceptibility (via MOKE) of the reorientation transition in Fe/2 ML Ni/W(110) films as a function of thickness as they are deposited at room temperature. In addition to a peak at the reorientation transition, we observe a strong precursor due to thickness quantization in atomic layers. This peak is described quantitatively by the response of small islands of thickness 3 layers with in-plane anisotropy in a sea of 2 layers Fe with perpendicular anisotropy. The fitted parameters give an estimate of the island size at which the response disappears. This size corresponds to a domain wall thickness, so that the islands become locally in-plane, demonstrating the self-consistency of the model.
Hierarchically clustered adaptive quantization CMAC and its learning convergence.
Teddy, S D; Lai, E M K; Quek, C
2007-11-01
The cerebellar model articulation controller (CMAC) neural network (NN) is a well-established computational model of the human cerebellum. Nevertheless, there are two major drawbacks associated with the uniform quantization scheme of the CMAC network. They are the following: (1) a constant output resolution associated with the entire input space and (2) the generalization-accuracy dilemma. Moreover, the size of the CMAC network is an exponential function of the number of inputs. Depending on the characteristics of the training data, only a small percentage of the entire set of CMAC memory cells is utilized. Therefore, the efficient utilization of the CMAC memory is a crucial issue. One approach is to quantize the input space nonuniformly. For existing nonuniformly quantized CMAC systems, there is a tradeoff between memory efficiency and computational complexity. Inspired by the underlying organizational mechanism of the human brain, this paper presents a novel CMAC architecture named hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC). HCAQ-CMAC employs hierarchical clustering for the nonuniform quantization of the input space to identify significant input segments and subsequently allocating more memory cells to these regions. The stability of the HCAQ-CMAC network is theoretically guaranteed by the proof of its learning convergence. The performance of the proposed network is subsequently benchmarked against the original CMAC network, as well as two other existing CMAC variants on two real-life applications, namely, automated control of car maneuver and modeling of the human blood glucose dynamics. The experimental results have demonstrated that the HCAQ-CMAC network offers an efficient memory allocation scheme and improves the generalization and accuracy of the network output to achieve better or comparable performances with smaller memory usages. Index Terms-Cerebellar model articulation controller (CMAC), hierarchical clustering, hierarchically
Perturbation theory in light-cone quantization
Langnau, A.
1992-01-01
A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.
Momentum space orthogonal polynomial projection quantization
NASA Astrophysics Data System (ADS)
Handy, C. R.; Vrinceanu, D.; Marth, C. B.; Gupta, R.
2016-04-01
The orthogonal polynomial projection quantization (OPPQ) is an algebraic method for solving Schrödinger’s equation by representing the wave function as an expansion {{\\Psi }}(x)={\\displaystyle \\sum }n{{{Ω }}}n{P}n(x)R(x) in terms of polynomials {P}n(x) orthogonal with respect to a suitable reference function R(x), which decays asymptotically not faster than the bound state wave function. The expansion coefficients {{{Ω }}}n are obtained as linear combinations of power moments {μ }{{p}}=\\int {x}p{{\\Psi }}(x) {{d}}x. In turn, the {μ }{{p}}'s are generated by a linear recursion relation derived from Schrödinger’s equation from an initial set of low order moments. It can be readily argued that for square integrable wave functions representing physical states {{lim}}n\\to ∞ {{{Ω }}}n=0. Rapidly converging discrete energies are obtained by setting Ω coefficients to zero at arbitrarily high order. This paper introduces an extention of OPPQ in momentum space by using the representation {{Φ }}(k)={\\displaystyle \\sum }n{{{\\Xi }}}n{Q}n(k)T(k), where Q n (k) are polynomials orthogonal with respect to a suitable reference function T(k). The advantage of this new representation is that it can help solving problems for which there is no coordinate space moment equation. This is because the power moments in momentum space are the Taylor expansion coefficients, which are recursively calculated via Schrödinger’s equation. We show the convergence of this new method for the sextic anharmonic oscillator and an algebraic treatment of Gross-Pitaevskii nonlinear equation.
Quantized Concentration Gradient in Picoliter Scale
NASA Astrophysics Data System (ADS)
Hong, Jong Wook
2010-10-01
Generation of concentration gradient is of paramount importance in the success of reactions for cell biology, molecular biology, biochemistry, drug-discovery, chemotaxis, cell culture, biomaterials synthesis, and tissue engineering. In conventional method of conducting reactions, the concentration gradients is achieved by using pipettes, test tubes, 96-well assay plates, and robotic systems. Conventional methods require milliliter or microliter volumes of samples for typical experiments with multiple and sequential reactions. It is a challenge to carry out experiments with precious samples that have strict limitations with the amount of samples or the price to pay for the amount. In order to overcome this challenge faced by the conventional methods, fluidic devices with micrometer scale channels have been developed. These devices, however, cause restrictions on changing the concentration due to the fixed gradient set based on fixed fluidic channels.ootnotetextJambovane, S.; Duin, E. C.; Kim, S-K.; Hong, J. W., Determination of Kinetic Parameters, KM and kcat, with a Single Experiment on a Chip. textitAnalytical Chemistry, 81, (9), 3239-3245, 2009.^,ootnotetextJambovane, S.; Hong, J. W., Lorenz-like Chatotic System on a Chip In The 14th International Conference on Miniaturized Systems for Chemistry and Life Sciences (MicroTAS), The Netherlands, October, 2010. Here, we present a unique microfluidic system that can generate quantized concentration gradient by using series of droplets generated by a mechanical valve based injection method.ootnotetextJambovane, S.; Rho, H.; Hong, J., Fluidic Circuit based Predictive Model of Microdroplet Generation through Mechanical Cutting. In ASME International Mechanical Engineering Congress & Exposition, Lake Buena Vista, Florida, USA, October, 2009.^,ootnotetextLee, W.; Jambovane, S.; Kim, D.; Hong, J., Predictive Model on Micro Droplet Generation through Mechanical Cutting. Microfluidics and Nanofluidics, 7, (3), 431-438, 2009
Remote Sensing and Quantization of Analog Sensors
NASA Technical Reports Server (NTRS)
Strauss, Karl F.
2011-01-01
This method enables sensing and quantization of analog strain gauges. By manufacturing a piezoelectric sensor stack in parallel (physical) with a piezoelectric actuator stack, the capacitance of the sensor stack varies in exact proportion to the exertion applied by the actuator stack. This, in turn, varies the output frequency of the local sensor oscillator. The output, F(sub out), is fed to a phase detector, which is driven by a stable reference, F(sub ref). The output of the phase detector is a square waveform, D(sub out), whose duty cycle, t(sub W), varies in exact proportion according to whether F(sub out) is higher or lower than F(sub ref). In this design, should F(sub out) be precisely equal to F(sub ref), then the waveform has an exact 50/50 duty cycle. The waveform, D(sub out), is of generally very low frequency suitable for safe transmission over long distances without corruption. The active portion of the waveform, t(sub W), gates a remotely located counter, which is driven by a stable oscillator (source) of such frequency as to give sufficient digitization of t(sub W) to the resolution required by the application. The advantage to this scheme is that it negates the most-common, present method of sending either very low level signals (viz. direct output from the sensors) across great distances (anything over one-half meter) or the need to transmit widely varying higher frequencies over significant distances thereby eliminating interference [both in terms of beat frequency generation and in-situ EMI (electromagnetic interference)] caused by ineffective shielding. It also results in a significant reduction in shielding mass.
Some effects of quantization on a noiseless phase-locked loop. [sampling phase errors
NASA Technical Reports Server (NTRS)
Greenhall, C. A.
1979-01-01
If the VCO of a phase-locked receiver is to be replaced by a digitally programmed synthesizer, the phase error signal must be sampled and quantized. Effects of quantizing after the loop filter (frequency quantization) or before (phase error quantization) are investigated. Constant Doppler or Doppler rate noiseless inputs are assumed. The main result gives the phase jitter due to frequency quantization for a Doppler-rate input. By itself, however, frequency quantization is impractical because it makes the loop dynamic range too small.
Energy-Constrained Optimal Quantization for Wireless Sensor Networks
NASA Astrophysics Data System (ADS)
Luo, Xiliang; Giannakis, Georgios B.
2007-12-01
As low power, low cost, and longevity of transceivers are major requirements in wireless sensor networks, optimizing their design under energy constraints is of paramount importance. To this end, we develop quantizers under strict energy constraints to effect optimal reconstruction at the fusion center. Propagation, modulation, as well as transmitter and receiver structures are jointly accounted for using a binary symmetric channel model. We first optimize quantization for reconstructing a single sensor's measurement, and deriving the optimal number of quantization levels as well as the optimal energy allocation across bits. The constraints take into account not only the transmission energy but also the energy consumed by the transceiver's circuitry. Furthermore, we consider multiple sensors collaborating to estimate a deterministic parameter in noise. Similarly, optimum energy allocation and optimum number of quantization bits are derived and tested with simulated examples. Finally, we study the effect of channel coding on the reconstruction performance under strict energy constraints and jointly optimize the number of quantization levels as well as the number of channel uses.
Quantized chaotic dynamics and non-commutative KS entropy
Klimek, S.; Lesniewski, A.
1996-06-01
We study the quantization of two examples of classically chaotic dynamics, the Anosov dynamics of {open_quote}{open_quote}cat maps{close_quote}{close_quote} on a two dimensional torus, and the dynamics of baker{close_quote}s maps. Each of these dynamics is implemented as a discrete group of automorphisms of a von Neumann algebra of functions on a quantized torus. We compute the non-commutative generalization of the Kolmogorov-Sinai entropy, namely the Connes-Sto/rmer entropy, of the generator of this group, and find that its value is equal to the classical value. This can be interpreted as a sign of persistence of chaotic behavior in a dynamical system under quantization. Copyright {copyright} 1996 Academic Press, Inc.
Possibility of gravitational quantization under the teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Ming, Kian; Triyanta, Kosasih, J. S.
2016-03-01
Teleparallel gravity (TG) or tele-equivalent general relativity (TEGR) is an alternative gauge theory for gravity. In TG tetrad fields are defined to express gravitational fields and act like gauge potentials in standard gauge theory. The lagrangians for the gravitational field in TG and for the Yang-Mills field in standard gauge theory differ due to different indices that stick on the components of the corresponding fields: two external indices for tetrad field and internal and external indices for the Yang-Mills field. Different types of indices lead to different possible contractions and thus lead to different expression of the lagrangian for the Yang Mills field and for the tetrad field. As TG is a gauge theory it is then natural to quantize gravity in TG by applying the same procedure of quantization as in the standard gauge theory. Here we will discuss on the possibility to quantize gravity, canonically and functionally, under the framework of TG theory.
Locally adaptive vector quantization: Data compression with feature preservation
NASA Technical Reports Server (NTRS)
Cheung, K. M.; Sayano, M.
1992-01-01
A study of a locally adaptive vector quantization (LAVQ) algorithm for data compression is presented. This algorithm provides high-speed one-pass compression and is fully adaptable to any data source and does not require a priori knowledge of the source statistics. Therefore, LAVQ is a universal data compression algorithm. The basic algorithm and several modifications to improve performance are discussed. These modifications are nonlinear quantization, coarse quantization of the codebook, and lossless compression of the output. Performance of LAVQ on various images using irreversible (lossy) coding is comparable to that of the Linde-Buzo-Gray algorithm, but LAVQ has a much higher speed; thus this algorithm has potential for real-time video compression. Unlike most other image compression algorithms, LAVQ preserves fine detail in images. LAVQ's performance as a lossless data compression algorithm is comparable to that of Lempel-Ziv-based algorithms, but LAVQ uses far less memory during the coding process.
Optimal sampling and quantization of synthetic aperture radar signals
NASA Technical Reports Server (NTRS)
Wu, C.
1978-01-01
Some theoretical and experimental results on optimal sampling and quantization of synthetic aperture radar (SAR) signals are presented. It includes a description of a derived theoretical relationship between the pixel signal to noise ratio of processed SAR images and the number of quantization bits per sampled signal, assuming homogeneous extended targets. With this relationship known, a solution may be realized for the problem of optimal allocation of a fixed data bit-volume (for specified surface area and resolution criterion) between the number of samples and the number of bits per sample. The results indicate that to achieve the best possible image quality for a fixed bit rate and a given resolution criterion, one should quantize individual samples coarsely and thereby maximize the number of multiple looks. The theoretical results are then compared with simulation results obtained by processing aircraft SAR data.
Honey Bee Mating Optimization Vector Quantization Scheme in Image Compression
NASA Astrophysics Data System (ADS)
Horng, Ming-Huwi
The vector quantization is a powerful technique in the applications of digital image compression. The traditionally widely used method such as the Linde-Buzo-Gray (LBG) algorithm always generated local optimal codebook. Recently, particle swarm optimization (PSO) is adapted to obtain the near-global optimal codebook of vector quantization. In this paper, we applied a new swarm algorithm, honey bee mating optimization, to construct the codebook of vector quantization. The proposed method is called the honey bee mating optimization based LBG (HBMO-LBG) algorithm. The results were compared with the other two methods that are LBG and PSO-LBG algorithms. Experimental results showed that the proposed HBMO-LBG algorithm is more reliable and the reconstructed images get higher quality than those generated form the other three methods.
Performance of customized DCT quantization tables on scientific data
NASA Technical Reports Server (NTRS)
Ratnakar, Viresh; Livny, Miron
1994-01-01
We show that it is desirable to use data-specific or customized quantization tables for scaling the spatial frequency coefficients obtained using the Discrete Cosine Transform (DCT). DCT is widely used for image and video compression (MP89, PM93) but applications typically use default quantization matrices. Using actual scientific data gathered from divers sources such as spacecrafts and electron-microscopes, we show that the default compression/quality tradeoffs can be significantly improved upon by using customized tables. We also show that significant improvements are possible for the standard test images Lena and Baboon. This work is part of an effort to develop a practical scheme for optimizing quantization matrices for any given image or video stream, under any given quality or compression constraints.
Complex cross correlators with three-level quantization Design tolerances
NASA Astrophysics Data System (ADS)
D'Addario, L. R.; Thompson, A. R.; Schwab, F. R.; Granlund, J.
1984-06-01
It is noted that for cases in which the components behave ideally, digital correlators have been analyzed in considerable detail. Consideration is given here to the effects of the major deviations from ideal behavior that are encountered in practice. Even though attention is restricted to the three-level quantization, the fairly general case of the complex cross correlator is investigated. Among the errors analyzed are quantization threshold errors, quantizer indecision regions, sampler timing skews, quadrature network errors, and numerical errors in algorithms for converting digital measurements to equivalent analog correlations. It is assumed that all the digital operations, including delay, multiplication, summing, and storage, can be implemented without errors. The study is prompted by the requirement for cross-power measurements in Fourier synthesis radio telescopes.
Quantized Space-Time and Black Hole Entropy
NASA Astrophysics Data System (ADS)
Ma, Meng-Sen; Li, Huai-Fan; Zhao, Ren
2014-06-01
On the basis of Snyder’s idea of quantized space-time, we derive a new generalized uncertainty principle and a new modified density of states. Accordingly, we obtain a corrected black hole entropy with a logarithmic correction term by employing the new generalized uncertainty principle. In addition, we recalculate the entropy of spherically symmetric black holes using statistical mechanics. Because of the use of the minimal length in quantized space-time as a natural cutoff, the entanglement entropy we obtained does not have the usual form A/4 but has a coefficient dependent on the minimal length, which shows differences between black hole entropy in quantized space-time and that in continuous space-time.
[An algorithm of a wavelet-based medical image quantization].
Hou, Wensheng; Wu, Xiaoying; Peng, Chenglin
2002-12-01
The compression of medical image is the key to study tele-medicine & PACS. We have studied the statistical distribution of wavelet subimage coefficients and concluded that the distribution of wavelet subimage coefficients is very much similar to that of Laplacian distribution. Based on the statistical properties of image wavelet decomposition, an image quantization algorithm is proposed. In this algorithm, we selected the sample-standard-deviation as the key quantization threshold in every wavelet subimage. The test has proved that, the main advantages of this algorithm are simple computing and the predictability of coefficients in different quantization threshold range. Also, high compression efficiency can be obtained. Therefore, this algorithm can be potentially used in tele-medicine and PACS. PMID:12561372
Quantization of gauge fields, graph polynomials and graph homology
Kreimer, Dirk; Sars, Matthias; Suijlekom, Walter D. van
2013-09-15
We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.
NASA Astrophysics Data System (ADS)
Pedrosa, Inácio A.; Melo, Jilvan L.; Salatiel, Sadoque
2014-11-01
We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system's quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry's phase.
New Exact Quantization Condition for Toric Calabi-Yau Geometries
NASA Astrophysics Data System (ADS)
Wang, Xin; Zhang, Guojun; Huang, Min-xin
2015-09-01
We propose a new exact quantization condition for a class of quantum mechanical systems derived from local toric Calabi-Yau threefolds. Our proposal includes all contributions to the energy spectrum which are nonperturbative in the Planck constant, and is much simpler than the available quantization condition in the literature. We check that our proposal is consistent with previous works and implies nontrivial relations among the topological Gopakumar-Vafa invariants of the toric Calabi-Yau geometries. Together with the recent developments, our proposal opens a new avenue in the long investigations at the interface of geometry, topology and quantum mechanics.
New Exact Quantization Condition for Toric Calabi-Yau Geometries.
Wang, Xin; Zhang, Guojun; Huang, Min-Xin
2015-09-18
We propose a new exact quantization condition for a class of quantum mechanical systems derived from local toric Calabi-Yau threefolds. Our proposal includes all contributions to the energy spectrum which are nonperturbative in the Planck constant, and is much simpler than the available quantization condition in the literature. We check that our proposal is consistent with previous works and implies nontrivial relations among the topological Gopakumar-Vafa invariants of the toric Calabi-Yau geometries. Together with the recent developments, our proposal opens a new avenue in the long investigations at the interface of geometry, topology and quantum mechanics. PMID:26430981
Semiclassical Landau quantization of spin-orbit coupled systems
NASA Astrophysics Data System (ADS)
Li, Tommy; Horovitz, Baruch; Sushkov, Oleg P.
2016-06-01
A semiclassical quantization condition is derived for Landau levels in general spin-orbit coupled systems. This generalizes the Onsager quantization condition via a matrix-valued phase which describes spin dynamics along the classical cyclotron trajectory. We discuss measurement of the matrix phase via magnetic oscillations and electron spin resonance, which may be used to probe the spin structure of the precessing wave function. We compare the resulting semiclassical spectrum with exact results which are obtained for a variety of spin-orbit interactions in two-dimensional systems.
Luminance-model-based DCT quantization for color image compression
NASA Technical Reports Server (NTRS)
Ahumada, Albert J., Jr.; Peterson, Heidi A.
1992-01-01
A model is developed to approximate visibility thresholds for discrete cosine transform (DCT) coefficient quantization error based on the peak-to-peak luminance of the error image. Experimentally measured visibility thresholds for R, G, and B DCT basis functions can be predicted by a simple luminance-based detection model. This model allows DCT coefficient quantization matrices to be designed for display conditions other than those of the experimental measurements: other display luminances, other veiling luminances, and other spatial frequencies (different pixel spacings, viewing distances, and aspect ratios).
Exact quantization conditions for the relativistic Toda lattice
NASA Astrophysics Data System (ADS)
Hatsuda, Yasuyuki; Mariño, Marcos
2016-05-01
Inspired by recent connections between spectral theory and topological string theory, we propose exact quantization conditions for the relativistic Toda lattice of N particles. These conditions involve the Nekrasov-Shatashvili free energy, which resums the perturbative WKB expansion, but they require in addition a non-perturbative contribution, which is related to the perturbative result by an S-duality transformation of the Planck constant. We test the quantization conditions against explicit calculations of the spectrum for N = 3. Our proposal can be generalized to arbitrary toric Calabi-Yau manifolds and might solve the corresponding quantum integrable system of Goncharov and Kenyon.
Effective Field Theory of Fractional Quantized Hall Nematics
Mulligan, Michael; Nayak, Chetan; Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC
2012-06-06
We present a Landau-Ginzburg theory for a fractional quantized Hall nematic state and the transition to it from an isotropic fractional quantum Hall state. This justifies Lifshitz-Chern-Simons theory - which is shown to be its dual - on a more microscopic basis and enables us to compute a ground state wave function in the symmetry-broken phase. In such a state of matter, the Hall resistance remains quantized while the longitudinal DC resistivity due to thermally-excited quasiparticles is anisotropic. We interpret recent experiments at Landau level filling factor {nu} = 7/3 in terms of our theory.
Image Coding By Vector Quantization In A Transformed Domain
NASA Astrophysics Data System (ADS)
Labit, C.; Marescq, J. P...
1986-05-01
Using vector quantization in a transformed domain, TV images are coded. The method exploit spatial redundancies of small 4x4 blocks of pixel : first, a DCT (or Hadamard) trans-form is performed on these blocks. A classification algorithm ranks them into visual and transform properties-based classes. For each class, high energy carrying coefficients are retained and using vector quantization, a codebook is built for the AC remaining part of the transformed blocks. The whole of the codeworks are referenced by an index. Each block is then coded by specifying its DC coefficient and associated index.
Probing quantized Einstein-Rosen waves with massless scalar matter
Fernando Barbero, J. G.; Garay, Inaki; Villasenor, Eduardo J. S.
2006-08-15
The purpose of this paper is to discuss in detail the use of scalar matter coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum gravity in the restricted setting provided by this symmetry reduction of general relativity. We will obtain the relevant Hamiltonian and quantize it with the techniques already used for the purely gravitational case. Finally, we will discuss the use of particlelike modes of the quantized fields to operationally explore some of the features of quantum gravity within this framework. Specifically, we will study two-point functions, the Newton-Wigner propagator, and radial wave functions for one-particle states.
On precanonical quantization of gravity in spin connection variables
Kanatchikov, I. V.
2013-02-21
The basics of precanonical quantization and its relation to the functional Schroedinger picture in QFT are briefly outlined. The approach is then applied to quantization of Einstein's gravity in vielbein and spin connection variables and leads to a quantum dynamics described by the covariant Schroedinger equation for the transition amplitudes on the bundle of spin connection coefficients over space-time, that yields a novel quantum description of space-time geometry. A toy model of precanonical quantum cosmology based on the example of flat FLRW universe is considered.
Experiments to Study Photoemission of Electron Bubbles from Quantized Vortices
Konstantinov, Denis; Hirsch, Matthew; Maris, Humphrey J.
2006-09-07
At sufficiently low temperatures, electron bubbles (negative ions) can become trapped on quantized vortices in superfluid helium. Previously, the escape of electron bubbles from vortices by thermal excitation and through quantum tunneling has been studied. In this paper, we report on an experiment in which light is used to release bubbles from quantized vortices (photoemission). A CO2 laser is used to excite the electron from the 1S to the 1P state, and it is found that each time a photon is absorbed there is a small probability that the bubble containing the electron escapes from the vortex.
Enhanced current quantization in high-frequency electron pumps in a perpendicular magnetic field
Wright, S. J.; Blumenthal, M. D.; Gumbs, Godfrey; Thorn, A. L.; Pepper, M.; Anderson, D.; Jones, G. A. C.; Nicoll, C. A.; Ritchie, D. A.; Janssen, T. J. B. M.; Holmes, S. N.
2008-12-15
We present experimental results of high-frequency quantized charge pumping through a quantum dot formed by the electric field arising from applied voltages in a GaAs/AlGaAs system in the presence of a perpendicular magnetic field B. Clear changes are observed in the quantized current plateaus as a function of applied magnetic field. We report on the robustness in the length of the quantized plateaus and improvements in the quantization as a result of the applied B field.
Separable quantizations of Stäckel systems
NASA Astrophysics Data System (ADS)
Błaszak, Maciej; Marciniak, Krzysztof; Domański, Ziemowit
2016-08-01
In this article we prove that many Hamiltonian systems that cannot be separably quantized in the classical approach of Robertson and Eisenhart can be separably quantized if we extend the class of admissible quantizations through a suitable choice of Riemann space adapted to the Poisson geometry of the system. Actually, in this article we prove that for every quadratic in momenta Stäckel system (defined on 2 n dimensional Poisson manifold) for which Stäckel matrix consists of monomials in position coordinates there exist infinitely many quantizations-parametrized by n arbitrary functions-that turn this system into a quantum separable Stäckel system. In this paper we prove that conjecture for a very large class of Stäckel systems, generated by separation relations of the form (17), where Stäckel matrix consists of monomials in position coordinates. For any Stäckel system from this class we construct a family of metrices for which the minimal quantization leads to quantum separability and commutativity of the quantized constants of motion. We want to stress, however, that we do not deal with spectral theory of the obtained quantum systems, as it requires a separate investigations.The paper is organized as follows. In Section 2 we briefly summarize the results of Robertson-Eisenhart theory of quantum separability. In Section 3 we present some fundamental facts about classical Stäckel systems. Section 4 contains presentation of some results derived from our general theory of quantization of Hamiltonian systems on phase space; especially we demonstrate how to obtain the minimal quantization (4) from our general theory. In Section 5 we relate quantizations of the same Hamiltonian in different metrics g and g ¯ (or in different Hilbert spaces L2(Q ,ωg) and L2(Q ,ωḡ)). Essentially, this construction explains the origin of the quantum correction terms in the classical Hamiltonians introduced in [1] and in [2
Second-quantized molecular time scale generalized Langevin equation theory: Coupled oscillator model
McDowell, H.K.
1986-11-15
A second-quantized, coupled oscillator model is presented which explicitly displays the structure of a second-quantized MTGLE theory. The Adelman ansatz (J. Chem Phys. 75, 5837 (1981)) for a quantum MTGLE response function is shown to generate the correct response function for the model. This result paves the way for the development of a general second-quantized MTGLE theory.
Fast large-scale object retrieval with binary quantization
NASA Astrophysics Data System (ADS)
Zhou, Shifu; Zeng, Dan; Shen, Wei; Zhang, Zhijiang; Tian, Qi
2015-11-01
The objective of large-scale object retrieval systems is to search for images that contain the target object in an image database. Where state-of-the-art approaches rely on global image representations to conduct searches, we consider many boxes per image as candidates to search locally in a picture. In this paper, a feature quantization algorithm called binary quantization is proposed. In binary quantization, a scale-invariant feature transform (SIFT) feature is quantized into a descriptive and discriminative bit-vector, which allows itself to adapt to the classic inverted file structure for box indexing. The inverted file, which stores the bit-vector and box ID where the SIFT feature is located inside, is compact and can be loaded into the main memory for efficient box indexing. We evaluate our approach on available object retrieval datasets. Experimental results demonstrate that the proposed approach is fast and achieves excellent search quality. Therefore, the proposed approach is an improvement over state-of-the-art approaches for object retrieval.
Second quantization techniques in the scattering of nonidentical composite bodies
NASA Technical Reports Server (NTRS)
Norbury, J. W.; Townsend, L. W.; Deutchman, P. A.
1986-01-01
Second quantization techniques for describing elastic and inelastic interactions between nonidentical composite bodies are presented and are applied to nucleus-nucleus collisions involving ground-state and one-particle-one-hole excitations. Evaluations of the resultant collision matrix elements are made through use of Wick's theorem.
Multispectral data compression through transform coding and block quantization
NASA Technical Reports Server (NTRS)
Ready, P. J.; Wintz, P. A.
1972-01-01
Transform coding and block quantization techniques are applied to multispectral aircraft scanner data, and digitized satellite imagery. The multispectral source is defined and an appropriate mathematical model proposed. The Karhunen-Loeve, Fourier, and Hadamard encoders are considered and are compared to the rate distortion function for the equivalent Gaussian source and to the performance of the single sample PCM encoder.
Dynamic contrast-based quantization for lossy wavelet image compression.
Chandler, Damon M; Hemami, Sheila S
2005-04-01
This paper presents a contrast-based quantization strategy for use in lossy wavelet image compression that attempts to preserve visual quality at any bit rate. Based on the results of recent psychophysical experiments using near-threshold and suprathreshold wavelet subband quantization distortions presented against natural-image backgrounds, subbands are quantized such that the distortions in the reconstructed image exhibit root-mean-squared contrasts selected based on image, subband, and display characteristics and on a measure of total visual distortion so as to preserve the visual system's ability to integrate edge structure across scale space. Within a single, unified framework, the proposed contrast-based strategy yields images which are competitive in visual quality with results from current visually lossless approaches at high bit rates and which demonstrate improved visual quality over current visually lossy approaches at low bit rates. This strategy operates in the context of both nonembedded and embedded quantization, the latter of which yields a highly scalable codestream which attempts to maintain visual quality at all bit rates; a specific application of the proposed algorithm to JPEG-2000 is presented. PMID:15825476
Local mesh quantized extrema patterns for image retrieval.
Koteswara Rao, L; Venkata Rao, D; Reddy, L Pratap
2016-01-01
In this paper, we propose a new feature descriptor, named local mesh quantized extrema patterns (LMeQEP) for image indexing and retrieval. The standard local quantized patterns collect the spatial relationship in the form of larger or deeper texture pattern based on the relative variations in the gray values of center pixel and its neighbors. Directional local extrema patterns explore the directional information in 0°, 90°, 45° and 135° for a pixel positioned at the center. A mesh structure is created from a quantized extrema to derive significant textural information. Initially, the directional quantized data from the mesh structure is extracted to form LMeQEP of given image. Then, RGB color histogram is built and integrated with the LMeQEP to enhance the performance of the system. In order to test the impact of proposed method, experimentation is done with bench mark image repositories such as MIT VisTex and Corel-1k. Avg. retrieval rate and avg. retrieval precision are considered as the evaluation metrics to record the performance level. The results from experiments show a considerable improvement when compared to other recent techniques in the image retrieval. PMID:27429886
Consistent quantization of massive chiral electrodynamics in four dimensions
Andrianov, A. ); Bassetto, A.; Soldati, R.
1989-10-09
We discuss the quantization of a four-dimensional model in which a massive Abelian vector field interacts with chiral massless fermions. We show that, by introducing extra scalar fields, a renormalizable unitary {ital S} matrix can be obtained in a suitably defined Hilbert space of physical states.
Semiclassical Quantization of the Electron-Dipole System.
ERIC Educational Resources Information Center
Turner, J. E.
1979-01-01
This paper presents a derivation of the number given by Fermi in 1925, in his semiclassical treatment of the motion of an electron in the field of two stationary positive charges, for Bohr quantization of the electron orbits when the stationary charges are positive, and applies it to an electron moving in the field of a stationary dipole.…
FAST TRACK COMMUNICATION: Quantization over boson operator spaces
NASA Astrophysics Data System (ADS)
Prosen, Tomaž; Seligman, Thomas H.
2010-10-01
The framework of third quantization—canonical quantization in the Liouville space—is developed for open many-body bosonic systems. We show how to diagonalize the quantum Liouvillean for an arbitrary quadratic n-boson Hamiltonian with arbitrary linear Lindblad couplings to the baths and, as an example, explicitly work out a general case of a single boson.
Quantization method for describing the motion of celestial systems
NASA Astrophysics Data System (ADS)
Christianto, Victor; Smarandache, Florentin
2015-11-01
Criticism arises concerning the use of quantization method for describing the motion of celestial systems, arguing that the method is oversimplifying the problem, and cannot explain other phenomena, for instance planetary migration. Using quantization method like Nottale-Schumacher did, one can expect to predict new exoplanets with remarkable result. The ``conventional'' theories explaining planetary migration normally use fluid theory involving diffusion process. Gibson have shown that these migration phenomena could be described via Navier-Stokes approach. Kiehn's argument was based on exact-mapping between Schrodinger equation and Navier-Stokes equations, while our method may be interpreted as an oversimplification of the real planetary migration process which took place sometime in the past, providing useful tool for prediction (e.g. other planetoids, which are likely to be observed in the near future, around 113.8AU and 137.7 AU). Therefore, quantization method could be seen as merely a ``plausible'' theory. We would like to emphasize that the quantization method does not have to be the true description of reality with regards to celestial phenomena. This method could explain some phenomena, while perhaps lacks explanation for other phenomena.
Subband Image Coding Using Entropy-Constrained Residual Vector Quantization.
ERIC Educational Resources Information Center
Kossentini, Faouzi; And Others
1994-01-01
Discusses a flexible, high performance subband coding system. Residual vector quantization is discussed as a basis for coding subbands, and subband decomposition and bit allocation issues are covered. Experimental results showing the quality achievable at low bit rates are presented. (13 references) (KRN)
Quantization of higher abelian gauge theory in generalized differential cohomology
NASA Astrophysics Data System (ADS)
Szabo, R.
We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
Online Adaptive Vector Quantization with Variable Size Codebook Entries.
ERIC Educational Resources Information Center
Constantinescu, Cornel; Storer, James A.
1994-01-01
Presents a new image compression algorithm that employs some of the most successful approaches to adaptive lossless compression to perform adaptive online (single pass) vector quantization with variable size codebook entries. Results of tests of the algorithm's effectiveness on standard test images are given. (12 references) (KRN)
Equivalent Electrical Circuit Representations of AC Quantized Hall Resistance Standards
Cage, M. E.; Jeffery, A.; Matthews, J.
1999-01-01
We use equivalent electrical circuits to analyze the effects of large parasitic impedances existing in all sample probes on four-terminal-pair measurements of the ac quantized Hall resistance RH. The circuit components include the externally measurable parasitic capacitances, inductances, lead resistances, and leakage resistances of ac quantized Hall resistance standards, as well as components that represent the electrical characteristics of the quantum Hall effect device (QHE). Two kinds of electrical circuit connections to the QHE are described and considered: single-series “offset” and quadruple-series. (We eliminated other connections in earlier analyses because they did not provide the desired accuracy with all sample probe leads attached at the device.) Exact, but complicated, algebraic equations are derived for the currents and measured quantized Hall voltages for these two circuits. Only the quadruple-series connection circuit meets our desired goal of measuring RH for both ac and dc currents with a one-standard-deviation uncertainty of 10−8 RH or less during the same cool-down with all leads attached at the device. The single-series “offset” connection circuit meets our other desired goal of also measuring the longitudinal resistance Rx for both ac and dc currents during that same cool-down. We will use these predictions to apply small measurable corrections, and uncertainties of the corrections, to ac measurements of RH in order to realize an intrinsic ac quantized Hall resistance standard of 10−8 RH uncertainty or less.
Quantization and Quantum-Like Phenomena: A Number Amplitude Approach
NASA Astrophysics Data System (ADS)
Robinson, T. R.; Haven, E.
2015-12-01
Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.
An Effective Color Quantization Method Using Octree-Based Self-Organizing Maps
Park, Hyun Jun; Kim, Kwang Baek; Cha, Eui-Young
2016-01-01
Color quantization is an essential technique in color image processing, which has been continuously researched. It is often used, in particular, as preprocessing for many applications. Self-Organizing Map (SOM) color quantization is one of the most effective methods. However, it is inefficient for obtaining accurate results when it performs quantization with too few colors. In this paper, we present a more effective color quantization algorithm that reduces the number of colors to a small number by using octree quantization. This generates more natural results with less difference from the original image. The proposed method is evaluated by comparing it with well-known quantization methods. The experimental results show that the proposed method is more effective than other methods when using a small number of colors to quantize the colors. Also, it takes only 71.73% of the processing time of the conventional SOM method. PMID:26884748
Quantum heat engine: A fully quantized model
NASA Astrophysics Data System (ADS)
Youssef, M.; Mahler, G.; Obada, A.-S. F.
2010-01-01
Motivated by the growing interest in the nanophysics and the field of quantum thermodynamics [J. Gemmer, M. Michel, G. Mahler, Springer, 2005] we study a system consisting of two different 2-level atoms (spins) coupled to a quantum oscillator (resonator field mode), and each spin linked to a heat bath with different temperatures. We find that the energy gradient imposed on the system and the “coherent driving” of the two atoms achieved by the oscillator make this system act as a thermodynamic machine. We analyze the engine dynamics using the recently developed definitions of heat flux and power [E. Boukobza, D.J. Tannor, Phys. Rev. A. 74 (2006) 063823; H. Weimer, M.J. Henrich, F. Rempp, H. Schröder, G. Mahler, Eur. Phys. Lett. 83 (3) (2008) 30008]. The system can work as heat engine (laser) or a heat pump in a non-cyclic continuous mode. We characterize the properties of the resonator field. The concept of work and heat for this machine is discussed.
50 Years of Fluxoid Quantization: 2e or Not 2e
NASA Astrophysics Data System (ADS)
Einzel, Dietrich
2011-06-01
The year 2011 is quite remarkable because it allows us to celebrate not only the centennial of the discovery of superconductivity by Heike Kamerlingh-Onnes (The superconductivity of Mercury, Comm. Phys. Lab. Univ. Leiden, vols. 122, 124, 1911), but also the half-centennial of the discovery of what is referred to as fluxoid quantization in superconductors by Robert Doll and Martin Näbauer (Phys. Rev. Lett. 7:51, 1961; Z. Phys. 169:526, 1962), and, independently, by Bascom S. Deaver Jr. and William Fairbank (Phys. Rev. Lett. 7:43, 1961; Ph.D. Thesis, Stanford University, 1962). The experimental proof of the quantization of magnetic flux (or more accurately fluxoid) in hollow superconducting cylinders actually supports two important theoretical concepts. The form of the fluxoid quantum, on the one hand, which contains twice the elementary charge, allows for the conclusion, that the superconducting ground state can be viewed as a condensate of electron pairs, as predicted by the BCS theory of superconductivity (Bardeen et al. in Phys. Rev. 106:162, 1957; Phys. Rev. 108:1175, 1957). It can be viewed, on the other hand, as a quantum phenomenon seen on macroscopic scales and thus supports the concept of the bosonic macroscopic wave function, here applied to the description of (quasi-bosonic) fermion pair condensates. This review is devoted to a discussion of the physics behind the Doll-Näbauer, Deaver-Fairbank discoveries and is intended to review historically the chain of events which motivated these talented experimentalists and which led to their independent discoveries at quite remote points of the earth.
NASA Technical Reports Server (NTRS)
Chatfield, David C.; Friedman, Ronald S.; Lynch, Gillian C.; Truhlar, Donald G.; Schwenke, David W.
1993-01-01
Accurate quantum mechanical dynamics calculations are reported for the reaction probabilities of O(3P) + H2 yields OH + H with zero total angular momentum on a single potential energy surface. The results show that the reactive flux is gated by quantized transition states up to the highest energy studied, which corresponds to a total energy of 1.90 eV. The quantized transition states are assigned and compared to vibrationally adiabatic barrier maxima; their widths and transmission coefficients are determined; and they are classified as variational, supernumerary of the first kind, and supernumerary of the second kind. Their effects on state-selected and state-to-state reactivity are discussed in detail.
Wavelet/scalar quantization compression standard for fingerprint images
Brislawn, C.M.
1996-06-12
US Federal Bureau of Investigation (FBI) has recently formulated a national standard for digitization and compression of gray-scale fingerprint images. Fingerprints are scanned at a spatial resolution of 500 dots per inch, with 8 bits of gray-scale resolution. The compression algorithm for the resulting digital images is based on adaptive uniform scalar quantization of a discrete wavelet transform subband decomposition (wavelet/scalar quantization method). The FBI standard produces archival-quality images at compression ratios of around 15 to 1 and will allow the current database of paper fingerprint cards to be replaced by digital imagery. The compression standard specifies a class of potential encoders and a universal decoder with sufficient generality to reconstruct compressed images produced by any compliant encoder, allowing flexibility for future improvements in encoder technology. A compliance testing program is also being implemented to ensure high standards of image quality and interchangeability of data between different implementations.
Improved vector quantization scheme for grayscale image compression
NASA Astrophysics Data System (ADS)
Hu, Y.-C.; Chen, W.-L.; Lo, C.-C.; Chuang, J.-C.
2012-06-01
This paper proposes an improved image coding scheme based on vector quantization. It is well known that the image quality of a VQ-compressed image is poor when a small-sized codebook is used. In order to solve this problem, the mean value of the image block is taken as an alternative block encoding rule to improve the image quality in the proposed scheme. To cut down the storage cost of compressed codes, a two-stage lossless coding approach including the linear prediction technique and the Huffman coding technique is employed in the proposed scheme. The results show that the proposed scheme achieves better image qualities than vector quantization while keeping low bit rates.
Size quantization of Dirac fermions in graphene constrictions
NASA Astrophysics Data System (ADS)
Terrés, B.; Chizhova, L. A.; Libisch, F.; Peiro, J.; Jörger, D.; Engels, S.; Girschik, A.; Watanabe, K.; Taniguchi, T.; Rotkin, S. V.; Burgdörfer, J.; Stampfer, C.
2016-05-01
Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ~1.5 × 106 m s-1 in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.
Quantization of Td- and Oh-symmetric Skyrmions
NASA Astrophysics Data System (ADS)
Lau, P. H. C.; Manton, N. S.
2014-06-01
The geometrical construction of rational maps using a cubic grid has led to many new Skyrmion solutions, with baryon numbers up to 108. Energy spectra of some of the new Skyrmions are calculated here by semiclassical quantization. Quantization of the B=20 Td-symmetric Skyrmion, which is one of the newly found Skyrmions, is considered, and this leads to the development of a new approach to solving Finkelstein-Rubinstein constraints. Matrix equations are simplified by introducing a Cartesian version of angular momentum basis states, and the computations are easier. The quantum states of all Td-symmetric Skyrmions, constructed from the cubic grid, are classified into three classes, depending on the contribution of vertex points of the cubic grid to the rational maps. The analysis is extended to the larger symmetry group Oh. Quantum states of Oh-symmetric Skyrmions, constructed from the cubic grid, form a subset of the Td-symmetric quantum states.
Conformal Loop quantization of gravity coupled to the standard model
NASA Astrophysics Data System (ADS)
Pullin, Jorge; Gambini, Rodolfo
2016-03-01
We consider a local conformal invariant coupling of the standard model to gravity free of any dimensional parameter. The theory is formulated in order to have a quantized version that admits a spin network description at the kinematical level like that of loop quantum gravity. The Gauss constraint, the diffeomorphism constraint and the conformal constraint are automatically satisfied and the standard inner product of the spin-network basis still holds. The resulting theory has resemblances with the Bars-Steinhardt-Turok local conformal theory, except it admits a canonical quantization in terms of loops. By considering a gauge fixed version of the theory we show that the Standard model coupled to gravity is recovered and the Higgs boson acquires mass. This in turn induces via the standard mechanism masses for massive bosons, baryons and leptons.
Polymer quantization, stability and higher-order time derivative terms
NASA Astrophysics Data System (ADS)
Cumsille, Patricio; Reyes, Carlos M.; Ossandon, Sebastian; Reyes, Camilo
2016-03-01
The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.
Abductive learning of quantized stochastic processes with probabilistic finite automata.
Chattopadhyay, Ishanu; Lipson, Hod
2013-02-13
We present an unsupervised learning algorithm (GenESeSS) to infer the causal structure of quantized stochastic processes, defined as stochastic dynamical systems evolving over discrete time, and producing quantized observations. Assuming ergodicity and stationarity, GenESeSS infers probabilistic finite state automata models from a sufficiently long observed trace. Our approach is abductive; attempting to infer a simple hypothesis, consistent with observations and modelling framework that essentially fixes the hypothesis class. The probabilistic automata we infer have no initial and terminal states, have no structural restrictions and are shown to be probably approximately correct-learnable. Additionally, we establish rigorous performance guarantees and data requirements, and show that GenESeSS correctly infers long-range dependencies. Modelling and prediction examples on simulated and real data establish relevance to automated inference of causal stochastic structures underlying complex physical phenomena. PMID:23277601
Radiative cooling: lattice quantization and surface emissivity in thin coatings.
Suryawanshi, Chetan N; Lin, Chhiu-Tsu
2009-06-01
Nanodiamond powder (NDP), multiwall carbon nanotube (MWCNT), and carbon black (CB) were dispersed in an acrylate (AC) emulsion to form composite materials. These materials were coated on aluminum panels (alloy 3003) to give thin coatings. The active phonons of the nanomaterials were designed to act as a cooling fan, termed "molecular fan (MF)". The order of lattice quantization, as investigated by Raman spectroscopy, is MWCNT > CB > NDP. The enhanced surface emissivity of the MF coating (as observed by IR imaging) is well-correlated to lattice quantization, resulting in a better cooling performance by the MWCNT-AC composite. MF coatings with different concentrations (0%, 0.4%, 0.7%, and 1%) of MWCNT were prepared. The equilibrium temperature lowering of the coated panel was observed with an increase in the loading of CNTs and was measured as 17 degrees C for 1% loading of MWCNT. This was attributed to an increased density of active phonons in the MF coating. PMID:20355930
Polymer quantization of the Einstein-Rosen wormhole throat
Kunstatter, Gabor; Peltola, Ari; Louko, Jorma
2010-01-15
We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numerical accuracy, the area spectrum obtained from a Schroedinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.
Deformation quantization of the Pais-Uhlenbeck fourth order oscillator
NASA Astrophysics Data System (ADS)
Berra-Montiel, Jasel; Molgado, Alberto; Rojas, Efraín
2015-11-01
We analyze the quantization of the Pais-Uhlenbeck fourth order oscillator within the framework of deformation quantization. Our approach exploits the Noether symmetries of the system by proposing integrals of motion as the variables to obtain a solution to the ⋆-genvalue equation, namely the Wigner function. We also obtain, by means of a quantum canonical transformation the wave function associated to the Schrödinger equation of the system. We show that unitary evolution of the system is guaranteed by means of the quantum canonical transformation and via the properties of the constructed Wigner function, even in the so called equal frequency limit of the model, in agreement with recent results.
Precise quantization of anomalous Hall effect near zero magnetic field
Bestwick, A. J.; Fox, E. J.; Kou, Xufeng; Pan, Lei; Wang, Kang L.; Goldhaber-Gordon, D.
2015-05-04
In this study, we report a nearly ideal quantum anomalous Hall effect in a three-dimensional topological insulator thin film with ferromagnetic doping. Near zero applied magnetic field we measure exact quantization in the Hall resistance to within a part per 10,000 and a longitudinal resistivity under 1 Ω per square, with chiral edge transport explicitly confirmed by nonlocal measurements. Deviations from this behavior are found to be caused by thermally activated carriers, as indicated by an Arrhenius law temperature dependence. Using the deviations as a thermometer, we demonstrate an unexpected magnetocaloric effect and use it to reach near-perfect quantization by cooling the sample below the dilution refrigerator base temperature in a process approximating adiabatic demagnetization refrigeration.
Compression of Ultrasonic NDT Image by Wavelet Based Local Quantization
NASA Astrophysics Data System (ADS)
Cheng, W.; Li, L. Q.; Tsukada, K.; Hanasaki, K.
2004-02-01
Compression on ultrasonic image that is always corrupted by noise will cause `over-smoothness' or much distortion. To solve this problem to meet the need of real time inspection and tele-inspection, a compression method based on Discrete Wavelet Transform (DWT) that can also suppress the noise without losing much flaw-relevant information, is presented in this work. Exploiting the multi-resolution and interscale correlation property of DWT, a simple way named DWCs classification, is introduced first to classify detail wavelet coefficients (DWCs) as dominated by noise, signal or bi-effected. A better denoising can be realized by selective thresholding DWCs. While in `Local quantization', different quantization strategies are applied to the DWCs according to their classification and the local image property. It allocates the bit rate more efficiently to the DWCs thus achieve a higher compression rate. Meanwhile, the decompressed image shows the effects of noise suppressed and flaw characters preserved.
Novel properties of the q-analogue quantized radiation field
NASA Technical Reports Server (NTRS)
Nelson, Charles A.
1993-01-01
The 'classical limit' of the q-analog quantized radiation field is studied paralleling conventional quantum optics analyses. The q-generalizations of the phase operator of Susskind and Glogower and that of Pegg and Barnett are constructed. Both generalizations and their associated number-phase uncertainty relations are manifestly q-independent in the n greater than g number basis. However, in the q-coherent state z greater than q basis, the variance of the generic electric field, (delta(E))(sup 2) is found to be increased by a factor lambda(z) where lambda(z) greater than 1 if q not equal to 1. At large amplitudes, the amplitude itself would be quantized if the available resolution of unity for the q-analog coherent states is accepted in the formulation. These consequences are remarkable versus the conventional q = 1 limit.
Gauge Invariance of Parametrized Systems and Path Integral Quantization
NASA Astrophysics Data System (ADS)
de Cicco, Hernán; Simeone, Claudio
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action functional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called "ideal clock," and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.
Comparing conductance quantization in quantum wires and quantum Hall systems
NASA Astrophysics Data System (ADS)
Alekseev, Anton Yu.; Cheianov, Vadim V.; Fröhlich, Jürg
1996-12-01
We suggest a means to calculate the dc conductance of a one-dimensional electron system described by the Luttinger model. Our approach is based on the ideas of Landauer and Büttiker on transport in ballistic channels and on the methods of current algebra. We analyze in detail the way in which the system can be coupled to external reservoirs. This determines whether the conductance is renormalized or not. We provide a parallel treatment of a quantum wire and a fractional quantum Hall system on a cylinder with two widely separated edges. Although both systems are described by the same effective theory, the physical electrons are identified with different types of excitations, and hence the coupling to external reservoirs is different. As a consequence, the conductance in the wire is quantized in integer units of e2/h per spin orientation whereas the Hall conductance allows for fractional quantization.
Heavy quarkonium in the basis light-front quantization approach
NASA Astrophysics Data System (ADS)
Li, Yang; Vary, James; Maris, Pieter
2015-10-01
I present a study of the charmonium and bottomonium spectra using the basis light-front quantization. We implement a one-gluon exchange interaction in the leading Fock sector following Ref.. We also adopt a phenomenological confining interaction based on the AdS/QCD and light-front holography. The results are compared with the experimental data. Supported by the US DOE Grants DESC0008485 (SciDAC/NUCLEI) and DE-FG02-87ER40371.
Topological invariance of the Hall conductance and quantization
NASA Astrophysics Data System (ADS)
Bracken, Paul
2015-08-01
It is shown that the Kubo equation for the Hall conductance can be expressed as an integral which implies quantization of the Hall conductance. The integral can be interpreted as the first Chern class of a U(1) principal fiber bundle on a two-dimensional torus. This accounts for the conductance given as an integer multiple of e2/h. The formalism can be extended to deduce the fractional conductivity as well.
Hybrid quantization of an inflationary model: The flat case
NASA Astrophysics Data System (ADS)
Fernández-Méndez, Mikel; Mena Marugán, Guillermo A.; Olmedo, Javier
2013-08-01
We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations.
Corrected Hawking Temperature in Snyder's Quantized Space-time
NASA Astrophysics Data System (ADS)
Ma, Meng-Sen; Liu, Fang; Zhao, Ren
2015-06-01
In the quantized space-time of Snyder, generalized uncertainty relation and commutativity are both included. In this paper we analyze the possible form for the corrected Hawking temperature and derive it from the both effects. It is shown that the corrected Hawking temperature has a form similar to the one of noncommutative geometry inspired Schwarzschild black hole, however with an requirement for the noncommutative parameter 𝜃 and the minimal length a.