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Related Concept Videos

Thermal Electrocyclic Reactions: Stereochemistry01:17

Thermal Electrocyclic Reactions: Stereochemistry

The stereochemistry of electrocyclic reactions is strongly influenced by the orbital symmetry of the polyene HOMO. Under thermal conditions, the reaction proceeds via the ground-state HOMO.
Selection Rules: Thermal Activation
Conjugated systems containing an even number of π-electron pairs undergo a conrotatory ring closure. For example, thermal electrocyclization of (2E,4E)-2,4-hexadiene, a conjugated diene containing two π-electron pairs, gives trans-3,4-dimethylcyclobutene.
Thermal Sigmatropic Reactions: Overview01:16

Thermal Sigmatropic Reactions: Overview

Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred to as...
Thermal and Photochemical Electrocyclic Reactions: Overview01:26

Thermal and Photochemical Electrocyclic Reactions: Overview

Electrocyclic reactions are reversible reactions. They involve an intramolecular cyclization or ring-opening of a conjugated polyene. Shown below are two examples of electrocyclic reactions. In the first reaction, the formation of the cyclic product is favored. In contrast, in the second reaction, ring-opening is favored due to the high ring strain associated with cyclobutene formation.
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
Cycloaddition Reactions: MO Requirements for Thermal Activation01:16

Cycloaddition Reactions: MO Requirements for Thermal Activation

Thermal cycloadditions are reactions where the source of activation energy needed to initiate the reaction is provided in the form of heat. A typical example of a thermally-allowed cycloaddition is the Diels–Alder reaction, which is a [4 + 2] cycloaddition. In contrast, a [2 + 2] cycloaddition is thermally forbidden.
Types of Semiconductors01:20

Types of Semiconductors

Intrinsic semiconductors are highly pure materials with no impurities. At absolute zero, these semiconductors behave as perfect insulators because all the valence electrons are bound, and the conduction band is empty, disallowing electrical conduction. The Fermi level is a concept used to describe the probability of occupancy of energy levels by electrons at thermal equilibrium. In intrinsic semiconductors, the Fermi level is positioned at the midpoint of the energy gap at absolute zero. When...

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Published on: August 2, 2019

Sufficient conditions for thermal rectification in hybrid quantum structures.

Lian-Ao Wu1, Dvira Segal

  • 1Chemical Physics Group, Department of Chemistry and Center for Quantum Information and Quantum Control, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada.

Physical Review Letters
|April 28, 2009
PubMed
Summary

This study identifies conditions for thermal rectification in quantum systems. Two rectifier types are found: one with dissimilar reservoirs and another with differing particle statistics.

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Area of Science:

  • Quantum thermodynamics
  • Condensed matter physics
  • Materials science

Background:

  • Thermal rectification, the directional flow of heat, is crucial for thermal management.
  • Understanding rectification mechanisms in quantum systems is key to designing advanced thermal devices.

Purpose of the Study:

  • To analytically identify sufficient conditions for thermal rectification in two-terminal quantum junctions.
  • To classify different types of thermal rectifiers based on their underlying mechanisms.

Main Methods:

  • Utilizing the quantum master equation formalism.
  • Analyzing two-terminal junctions connected to two reservoirs.
  • Investigating systems with dissimilar reservoir energy structures and systems with differing particle statistics.

Main Results:

  • Identified two distinct classes of thermal rectifiers.
  • Type A rectifiers exhibit rectification due to dissimilar reservoir energy structures.
  • Type B rectifiers show rectification from asymmetric coupling to particles with differing statistics, even with identical baths.

Conclusions:

  • Sufficient conditions for thermal rectification in quantum systems are analytically established.
  • The findings apply to diverse hybrid junctions, including metals, dielectrics, and spin systems.
  • This work provides a theoretical framework for designing quantum thermal rectifiers.