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  • Resultat 739921-739930 av 1641786
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739921.
  • Kailasvuori, Janik, 1975- (författare)
  • Quasiparticles in the Quantum Hall Effect
  • 2006
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing.This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory.The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2n-1, pertinent to nonabelian statistics, in the presence of 2n quasiholes in the Moore-Read state and generalise this result to 2n-k quasiholes and k quasielectrons.In the third approach, we study the topological nature of the degeneracy 2n-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-Tc superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2n-1 for 2n vortices.
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739922.
  • Kailath, Thomas, et al. (författare)
  • A Scattering Theory Framework for Fast Least-Squares Algorithms
  • 1976
  • Ingår i: Proceedings of the 4th International Symposium on Mulitvariate Analysis. - 9780720405200
  • Konferensbidrag (refereegranskat)abstract
    •  In scattering theory the Riccati equation arises in a natural family of equations evolving forwards as well as backwards in time. The authors show how this framework allows an interesting derivation of the fast Chandrasekhar-type equations for linear least-squares filtering of processes generated by a time-invariant, finite-dimensional linear system driven by white noise. The processes are not required to be stationary. The same ideas can be used to obtain Levinson- and Cholesky-type differential equations for the impulse responses of the whitening filter and the innovations representation of such processes. The scattering framework brings out clearly both the significance of the time-invariance of the parameters of the underlying finite-dimensional system and of the associated family of nonstationary processes. For stationary processes, it also becomes clear that the assumption of finite-dimensionality is unnecessary, but the proper extension of the nonstationary class of processes raises some interesting questions.
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739923.
  • Kailath, Thomas, et al. (författare)
  • Explicit Strict Sense State-Space Realizations of Nonstationary Processes
  • 1985
  • Ingår i: International Journal of Control. - : Taylor & Francis. - 0020-7179 .- 1366-5820. ; 42:5, s. 971-988
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper addresses the following problem: Given a possibly non-stationary second-order or Gaussian stochastic process over a certain time interval, find all state-space realizations that produce the given process as their output. A constructive solution to this problem is described. In particular, the degrees of freedom left in this problem are explicitly displayed in terms of additional random variables and processes injected into the state-space description. Special attention is paid to output-induced, or internal, state-space realizations, that is, those for which the state vector is completely determined by the given process. The development is self-contained, the approach and proofs are fairly elementary, and explicit formulas are given for the various realizations.
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739924.
  • Kailath, Thomas, et al. (författare)
  • Fast Time-Invariant Implementations of Gaussian Signal Detectors
  • 1978
  • Ingår i: IEEE Transactions on Information Theory. - : IEEE Information Theory Society. - 0018-9448 .- 1557-9654. ; 24:4, s. 469-477
  • Tidskriftsartikel (refereegranskat)abstract
    • A new implementation is presented for the optimum likelihood ratio detector for stationary Gaussian signals in white Gaussian noise that uses only two causal time-invariant filters. This solution also has the advantage that fast algorithms based on the Levinson and Chandrasekhar equations can he used for the determination of these time-invariant filters. By using a notion of "closeness to stationarity,' there is a natural extension of the above results for nonstationary signal processes.
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739925.
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739926.
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739927.
  • Kailath, Thomas, et al. (författare)
  • Recursive Input-Output and State Space Solutions for Continuous-Time Linear Estimation Problems
  • 1981
  • Rapport (övrigt vetenskapligt/konstnärligt)abstract
    • A general linear least-squares estimation problem is considered. It is shown how the optimal filters for filtering and smoothing can be recursively and efficiently calculated under certain structural assumptions about the covariance functions involved. This structure is related to an index known as the displacement rank, which is a measure of non-Toeplitzness of a covariance kernel. When a state space type structure is added, it is shown how the Chandrasekhar equations for determining the gain of the Kalman-Bucy filter can be derived directly from the covariance function information; thus we are able to imbed this class of state-space problems into a general input-output framework.
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739928.
  • Kailath, Thomas, et al. (författare)
  • Recursive Input-Output and State Space Solutions for Continuous-Time Linear Estimation Problems
  • 1983
  • Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 28:9, s. 897-906
  • Tidskriftsartikel (refereegranskat)abstract
    • A general linear least-squares estimation problem is considered. It is shown how the optimal filters for filtering and smoothing can be recursively and efficiently calculated under certain structural assumptions about the covariance functions involved. This structure is related to an index known as the displacement rank, which is a measure of non-Toeplitzness of a covariance kernel. When a state space type structure is added, it is shown how the Chandrasekhar equations for determining the gain of the Kalman-Bucy filter can be derived directly from the covariance function information; thus we are able to imbed this class of state-space problems into a general input-output framework.
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739929.
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739930.
  • Kailath, Thomas, et al. (författare)
  • The Factorization and Representation of Operators in the Algebra Generated by Toeplitz Operators
  • 1979
  • Ingår i: SIAM Journal on Applied Mathematics. - : SIAM. - 0036-1399 .- 1095-712X. ; 37:3, s. 467-484
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we study the factorization and the representation of Fredholm operators belonging to the algebra $\mathcal{R}$ generated by inversion and composition of Toeplitz integral operators. The operators in $\mathcal{R}$ have the interesting property of being close to Toeplitz (in a sense quantifiable by an integer-valued index $\alpha $) and, at the same time, of being dense in the space of arbitrary kernels. By using these properties, we derive a set of efficient algorithms (generalized fast-Cholesky and Levinson recursions) for the factorization and the inversion of arbitrary Fredholm operators. The computational burden of these algorithms depends on how close (as measured by the index $\alpha $) these operators are to being Toeplitz.We also obtain several important representation theorems for the decomposition of operators in $\mathcal{R}$ in terms of sums of products of lower times upper triangular Toeplitz operators. These results can be used to approximate operators corresponding to noncausal and time-variant systems in terms of operators representing causal and anticausal time-invariant systems, a property that has a large number of potential applications in signal processing problems.
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