Topic

# Transfer matrix

About: Transfer matrix is a(n) research topic. Over the lifetime, 3516 publication(s) have been published within this topic receiving 64660 citation(s).

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Abstract: It is shown how conformal invariance relates many numerically accessible properties of the transfer matrix of a critical system in a finite-width infinitely long strip to bulk universal quantities. Conversely, general properties of the transfer matrix imply constraints on the allowed operator content of the theory. We show that unitary theories with a finite number of primary operators must have a conformal anomaly number c < 1, and therefore must fall into the classification of Friedan, Qiu and Shenker. For such theories, we derive sum rules which constrain the numbers of operators with given scaling dimensions.

1,825 citations

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TL;DR: The existence conditions are equivalent to Scherer's results, but with a more elementary derivation, and the set of all H∞ controllers explicitly parametrized in the state space using the positive definite solutions to the LMIs is provided.

Abstract: This paper presents all controllers for the general H∞ control problem (with no assumptions on the plant matrices). Necessary and sufficient conditions for the existence of an H∞ controller of any order are given in terms of three Linear Matrix Inequalities (LMIs). Our existence conditions are equivalent to Scherer's results, but with a more elementary derivation. Furthermore, we provide the set of all H∞ controllers explicitly parametrized in the state space using the positive definite solutions to the LMIs. Even under standard assumptions (full rank, etc.), our controller parametrization has an advantage over the Q-parametrization. The freedom Q (a real-rational stable transfer matrix with the H∞ norm bounded above by a specified number) is replaced by a constant matrix L of fixed dimension with a norm bound, and the solutions (X, Y) to the LMIs. The inequality formulation converts the existence conditions to a convex feasibility problem, and also the free matrix L and the pair (X, Y) define a finite dimensional design space, as opposed to the infinite dimensional space associated with the Q-parametrization.

1,229 citations

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Abstract: The transfer matrix of a solid described by the stacking of principal layers is obtained by an iterative procedure which takes into account 2 layers after n iterations, in contrast to usual schemes where each iteration includes just one more layer. The Green function and density of states at the surface of the corresponding semi-infinite crystal are then given by well known formulae in terms of the transfer matrix. This method, especially convenient near singularities, is applied to the calculation of the spectral as well as the total densities of states for the (100) face of molybdenum. The Slater-Koster algorithm for the calculation of tight-binding parameters is used with a basis of nine orbitals per atom (4d, 5s, 5p). Surface states and resonances are first identified and then analysed into orbital components to find their dominant symmetry. Their evolution along the main symmetry lines of the two-dimensional Brillouin zone is given explicitly. The surface-state peak just below the Fermi level (Swanson hump) is not obtained. This is traced to the difficulty in placing an appropriate boundary condition at the surface with the tight-binding parameterisation scheme.

859 citations

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Abstract: It is shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed-loop system, formed by means of suitable linear feedback of the state. As an application of this result, it is shown that an open-loop system can be stabilized by linear feedback if and only if the unstable modes of its system matrix are controllable. A dual of this criterion is shown to be equivalent to the existence of an observer of Luenberger's type for asymptotic state identification.

822 citations

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01 Mar 1999-

Abstract: Part I. Thermodynamics of Non-Interacting Systems and Ground States on Interacting Systems: 1. Free energy and correlation functions of XY models 2. Systems with delta-function potential 3. Isotropic Heisenberg model 4. XXZ model 5. XYZ and eight-vertex models 6. Hubbard model Part II. Finite Temperature Integral Equations for Un-Nested Systems: 7. Repulsive delta-function bosons 8. Thermodynamics of the XXX chain 9. Thermodynamics of the XXZ model 10. Thermodynamics of the XYZ model 11. Low-temperature thermodynamics Part III. Finite Temperature Integral Equations for Nested Systems: 12. S=1/2 fermions with repulsive potential in the continuum 13. S=1/2 fermions with an attractive potential 14. Thermodynamics of the Hubbard model Part IV. Quantum Transfer Matrix and Recent Developments: 15. Transfer matrix and correlation length 16. The spin 1/2 XXZ model in a magnetic field 17. The XYZ model with no magnetic field 18. Recent developments and related topics.

820 citations