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Inverse z-Transform by Partial Fraction Expansion01:20

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The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
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The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
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Related Experiment Videos

Bridging Perturbative Expansions with Tensor Networks.

Laurens Vanderstraeten1, Michaël Mariën1, Jutho Haegeman1

  • 1Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.

Physical Review Letters
|September 27, 2017
PubMed
Summary
This summary is machine-generated.

We reframe perturbative expansions for quantum many-body systems using tensor networks. This novel approach naturally bridges quantum phase transitions and reveals new order parameters for topological phases.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Quantum Information Science

Background:

  • Perturbative expansions are crucial for understanding quantum many-body systems but struggle across quantum phase transitions.
  • Tensor networks offer a powerful framework for representing complex quantum states.
  • Characterizing quantum phase transitions and topological order requires robust theoretical tools.

Purpose of the Study:

  • To develop a unified framework for perturbative expansions in quantum many-body systems.
  • To enable interpolation of perturbative expansions across quantum phase transitions.
  • To establish tensor networks as a tool for analyzing entanglement Hamiltonians and topological order.

Main Methods:

  • Reformulating perturbative expansions within a tensor network framework.
  • Constructing tensor-network states with physically meaningful, few parameters.
  • Developing perturbative expansions for the entanglement Hamiltonian.

Main Results:

  • Demonstrated that perturbative expansions can be naturally expressed using tensor networks.
  • Introduced classes of tensor-network states yielding excellent variational energies.
  • Showcased the construction of entanglement Hamiltonian expansions and their relation to entanglement spectra.
  • Identified tensor-network-derived order parameters for topological phase transitions.

Conclusions:

  • Tensor network rephrasing of perturbative expansions provides a unified and powerful approach for quantum many-body systems.
  • This method facilitates the study of quantum phase transitions and topological phenomena.
  • The approach yields accurate variational energies and reveals new insights into entanglement and order parameters.