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H Sazdjian - One of the best experts on this subject based on the ideXlab platform.
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two point gauge invariant quark green s functions with polygonal Phase Factor lines
arXiv: High Energy Physics - Theory, 2014Co-Authors: H SazdjianAbstract:Polygonal lines are used for the paths of the gluon field Phase Factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-Nc limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions.
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structure of the gauge invariant quark green s function in qcd2
Few-body Systems, 2012Co-Authors: H SazdjianAbstract:We study, in two-dimensional QCD and in the large-N c limit, the properties of the gauge invariant quark Green’s function, defined with a path-ordered Phase Factor along a straight line. The analysis is done by means of an exact integrodifferential equation. The Green’s function is found to be infrared finite, with singularities represented by an infinite number of threshold type branch points with a power −3/2, starting at positive mass squared values. Its expression is analytically determined.
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spectral properties of the gauge invariant quark green s function in two dimensional qcd
Physical Review D, 2010Co-Authors: H SazdjianAbstract:The gauge invariant quark Green's function with a path-ordered Phase Factor along a straight line is studied in two-dimensional QCD in the large-N{sub c} limit by means of an exact integrodifferential equation. Its spectral functions are analytically determined. They are infrared finite and lie on the positive real axis of the complex plane of the momentum squared variable, corresponding to momenta in the forward light cone. Their singularities are represented by an infinite number of threshold type branch points with power-law -3/2, starting at positive mass values, characterized by an integer number n and increasing with n. The analytic expression of the Green's function for all momenta is presented. The appearance of strong threshold singularities is suggestive of the fact that quarks could not be observed as asymptotic states.
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spectral properties of the gauge invariant quark green s function in two dimensional qcd
Physical Review D, 2010Co-Authors: H SazdjianAbstract:The gauge invariant quark Green's function with a path-ordered Phase Factor along a straight line is studied in two-dimensional QCD in the large-${N}_{c}$ limit by means of an exact integrodifferential equation. Its spectral functions are analytically determined. They are infrared finite and lie on the positive real axis of the complex plane of the momentum squared variable, corresponding to momenta in the forward light cone. Their singularities are represented by an infinite number of threshold type branch points with power-law $\ensuremath{-}3/2$, starting at positive mass values, characterized by an integer number $n$ and increasing with $n$. The analytic expression of the Green's function for all momenta is presented. The appearance of strong threshold singularities is suggestive of the fact that quarks could not be observed as asymptotic states.
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Integral equation for gauge invariant quark two-point Green's function in QCD
Physical Review D, 2008Co-Authors: H SazdjianAbstract:Gauge invariant quark two-point Green's functions defined with path-ordered gluon field Phase Factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with different numbers of path segments are established. An integral equation is obtained for the Green's function defined with a Phase Factor along a single straight line. The equation implicates an infinite series of two-point Green's functions, having an increasing number of path segments; the related kernels involve Wilson loops with contours corresponding to the skew-polygonal lines of the accompanying Green's function and with functional derivatives along the sides of the contours. The series can be viewed as an expansion in terms of the global number of the functional derivatives of the Wilson loops. The lowest-order kernel, which involves a Wilson loop with two functional derivatives, provides the framework for an approximate resolution of the equation.
Dirk Slock - One of the best experts on this subject based on the ideXlab platform.
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linear precoding for spatial multiplexing mimo systems blind channel estimation aspects
International Conference on Communications, 2002Co-Authors: Abdelkader Medles, Dirk SlockAbstract:For the case of white uncorrelated inputs, most of the blind multichannel identification techniques are not very robust and only allow one to estimate the channel up to a number of ambiguities, especially in the MIMO case. On the other hand, all current standardized communication systems employ some form of known inputs to allow channel estimation. The channel estimation performance in those cases can be optimized by a semiblind approach which exploits both training and blind information. When the inputs are colored and have sufficiently different spectra, the MIMO channel may become blindly identifiable up to one constant Phase Factor per input, and this under looser conditions on the channel. For the case of spatial multiplexing, possible cooperation between the channel inputs allows for more complex MIMO source prefiltering that may allow blind MIMO channel identification up to just one global constant Phase Factor. We introduce semiblind criteria that are motivated by the Gaussian ML approach. They combine a training based weighted least-squares criterion with a blind criterion based on linear prediction. A variety of blind criteria are considered for the various cases of source coloring.
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semiblind channel estimation for mimo spatial multiplexing systems
Vehicular Technology Conference, 2001Co-Authors: Abdelkader Medles, Dirk SlockAbstract:For the case of white uncorrelated inputs, most of the blind multichannel identification techniques are not very robust and only allow to estimate the channel up to a number of ambiguities, especially in the MIMO case. On the other hand, all current standardized communication systems employ some form of known inputs to allow channel estimation. The channel estimation performance in those cases can be optimized by a semiblind approach which exploits both training and blind information. When the inputs are colored and have sufficiently different spectra, the MIMO channel may become blindly identifiable up to one constant Phase Factor per input, and this under looser conditions on the channel. For the case of spatial multiplexing, possible cooperation between the channel inputs allows for more complex MIMO source prefiltering that may allow blind MIMO channel identification up to just one global constant Phase Factor. We introduce semiblind criteria that are motivated by the Gaussian ML approach. They combine a training based weighted least-squares criterion with a blind criterion based on linear prediction. A variety of blind criteria are considered for the various cases of source coloring.
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cramer rao bounds for blind multichannel estimation
Global Communications Conference, 2000Co-Authors: E De Carvalho, J M Cioffi, Dirk SlockAbstract:Certain blind channel estimation techniques allow the identification of the channel up to a scale or Phase Factor. This results in singularity of the Fisher information matrix (FIM). The Cramer-Rao bound, which is the inverse of the FIM, is then not defined. To regularize the estimation problem, one can impose constraints on the parameters. In general, many sets of constraints are possible but are not always relevant. We propose a constrained CRB, the pseudo-inverse of the FIM, which gives, for a minimum number of constraints, the lowest bound on the mean squared estimation error.
Roger G. Newton - One of the best experts on this subject based on the ideXlab platform.
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S matrix as geometric Phase Factor.
Physical Review Letters, 1994Co-Authors: Roger G. NewtonAbstract:We consider the geometric Phase Factor in quantum mechanics for the case of the continuous spectrum, and we find that it is nothing but the [ital S] matrix; for certain specific states the geometric Phase is simply twice the usual Phase shift.
Vladislav Voroninski - One of the best experts on this subject based on the ideXlab platform.
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Phaselift exact and stable signal recovery from magnitude measurements via convex programming
Communications on Pure and Applied Mathematics, 2013Co-Authors: Emmanuel J Candes, Thomas Strohmer, Vladislav VoroninskiAbstract:Suppose we wish to recover a signal \input amssym $\font\abc=cmmib10\def\bi#1{\hbox{\abc#1}} {\bi x} \in {\Bbb C}^n$ from m intensity measurements of the form , ; that is, from data in which Phase information is missing. We prove that if the vectors are sampled independently and uniformly at random on the unit sphere, then the signal x can be recovered exactly (up to a global Phase Factor) by solving a convenient semidefinite program–-a trace-norm minimization problem; this holds with large probability provided that m is on the order of , and without any assumption about the signal whatsoever. This novel result demonstrates that in some instances, the combinatorial Phase retrieval problem can be solved by convex programming techniques. Finally, we also prove that our methodology is robust vis-a-vis additive noise. © 2012 Wiley Periodicals, Inc.
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Phaselift exact and stable signal recovery from magnitude measurements via convex programming
arXiv: Information Theory, 2011Co-Authors: Emmanuel J Candes, Thomas Strohmer, Vladislav VoroninskiAbstract:Suppose we wish to recover a signal x in C^n from m intensity measurements of the form | |^2, i = 1, 2,..., m; that is, from data in which Phase information is missing. We prove that if the vectors z_i are sampled independently and uniformly at random on the unit sphere, then the signal x can be recovered exactly (up to a global Phase Factor) by solving a convenient semidefinite program---a trace-norm minimization problem; this holds with large probability provided that m is on the order of n log n, and without any assumption about the signal whatsoever. This novel result demonstrates that in some instances, the combinatorial Phase retrieval problem can be solved by convex programming techniques. Finally, we also prove that our methodology is robust vis a vis additive noise.
Jian Qi Shen - One of the best experts on this subject based on the ideXlab platform.
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exact time dependent decoherence Factor and its adiabatic classical limit
Canadian Journal of Physics, 2003Co-Authors: Jian Qi Shen, Pan Chen, Hong MaoAbstract:The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis- Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence Factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what is obtained by other authors, and furthermore we obtain more general results concerning time-dependent nonadiabatic quantum decoherence. It is shown that the invariant theory is appropriate for treating both the time-dependent quantum decoherence and the geometric Phase Factor.
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exact solutions and geometric Phase Factor of time dependent three generator quantum systems
European Physical Journal D, 2003Co-Authors: Jian Qi Shen, Hongyi Zhu, Pan ChenAbstract:There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure, in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schrodinger equations governing various three-generator Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric Phase Factors and its adiabatic limit in time-dependent systems is briefly discussed.
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exact time dependent decoherence Factor and its adiabatic classical limit
arXiv: Quantum Physics, 2003Co-Authors: Jian Qi Shen, Pan Chen, Hong MaoAbstract:The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence Factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what obtained by other authors, and futhermore we obtain the more general results concerning the time-dependent non-adiabatic quantum decoherence. It is shown that the invariant theory is appropriate for treating both the time-dependent quantum decoherence and the geometric Phase Factor.