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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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Translation01:31

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Lesson: Translation
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Translation is the process of synthesizing proteins from the genetic information carried by messenger RNA (mRNA). Following transcription, it constitutes the final step in the expression of genes. This process is carried out by ribosomes, complexes of protein and specialized RNA molecules. Ribosomes, transfer RNA (tRNA), and other proteins produce a chain of amino acids—the polypeptide—as the end product of translation.
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Initiating translation is complex because it involves multiple molecules. Initiator tRNA, ribosomal subunits, and eukaryotic initiation factors (eIFs) are all required to assemble on the initiation codon of mRNA. This process consists of several steps that are mediated by different eIFs.
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The large ribosomal subunit has several important structures essential to translation. These include the peptidyl transferase center (PTC) - which is the site where the peptide bond is formed - and a large, internal, water-filled tube through which the nascent polypeptide moves. This latter structure is called the Peptide Exit Tunnel, and it begins at the PTC and spans the body of the large ribosomal subunit. During translation, as the nascent polypeptide chain is synthesized, it passes through...
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Uhlmann number in translational invariant systems.

Luca Leonforte1, Davide Valenti2,3, Bernardo Spagnolo2,4,5

  • 1Department of Physics and Chemistry - Emilio Segrè, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy. luca.leonforte@unipa.it.

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We introduce the Uhlmann number to describe topology in 2D fermionic systems at finite temperatures. This new topological invariant connects geometric properties to measurable quantities like conductivity.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory

Background:

  • Topological invariants like the Chern number characterize quantum systems.
  • Understanding topological properties at finite temperatures is crucial for realistic systems.

Purpose of the Study:

  • To define and utilize the Uhlmann number for characterizing the topology of 2D fermionic systems at finite temperatures.
  • To investigate topological phase transitions in paradigmatic systems using the Uhlmann number.

Main Methods:

  • Definition of the Uhlmann number as an extension of the Chern number.
  • Application of linear response theory to connect geometric quantities with physical observables.
  • Derivation of a finite-temperature generalization of the Thouless-Kohmoto-Nightingale-den Nijs formula.

Main Results:

  • The Uhlmann number successfully describes the topology of 2D fermionic systems at finite temperatures.
  • The mean Uhlmann curvature and Uhlmann number are linked to dynamical susceptibility and conductivity, respectively.
  • A generalized Thouless-Kohmoto-Nightingale-den Nijs formula valid at non-zero temperatures is derived.

Conclusions:

  • The Uhlmann number provides a powerful tool for analyzing topological properties of quantum systems at finite temperatures.
  • The established links between geometric and physical quantities offer new avenues for experimental verification.