Are topological defects such as domain walls really discontinuous?

In summary, the conversation discusses topological defects, such as domain walls, and whether they are truly discontinuous or only approximately so. The concept of "approximately discontinuous" is questioned and it is explained that topological defects can be one-dimensional cosmic strings or two-dimensional boundaries between regions of different symmetry breaking. The width or size of the discontinuity is also mentioned and it is noted that it varies depending on the specific theory.
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fhenryco
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TL;DR Summary
Are topological defects really discontinuous
Are topological defects such as domain walls really discontinuous (implying infinite slopes of the fields) or only approximately ?
 
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I don't know topology, but I do have a question. How can "discontinuous" not be a binary choice? What does "approximately discontinuous" mean?
 
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Likes jim mcnamara
  • #3
That's basically the definition of a topological defect, so yes, in a way.

They're not necessarily boundaries, though. Cosmic strings, for example, are one-dimensional structures where within the string the symmetry breaking that resulted in our observable universe is stuck in a different local minimum of symmetry of higher rest energy.

They can also be two-dimensional boundaries between different regions of distinct symmetry breaking (domain walls). If the rest energy differs, these domain walls will move at close to the speed of light.

As far as the width/size of the discontinuity, a quick Google search suggests that it depends upon the specific theory, but typical predictions around $10^{-32}$ meters (a thousand times the Planck length). I believe this is a thickness set by the energy at which the phase transition happens.
 

1. What are topological defects?

Topological defects are regions in a material or physical system where the order or symmetry of the system is disrupted. They can occur in a variety of systems, including crystals, liquid crystals, and superconductors.

2. How do topological defects form?

Topological defects can form through a process called spontaneous symmetry breaking, where a system transitions from a high-energy, symmetric state to a lower-energy, asymmetric state. This can occur due to changes in temperature, pressure, or other external factors.

3. What are domain walls?

Domain walls are a type of topological defect that occur in materials with broken symmetry. They are boundaries between regions of the material with different orientations or properties, and are characterized by a change in the order parameter of the material.

4. Are topological defects really discontinuous?

Yes, topological defects are considered to be discontinuous because they represent a sudden change in the order or symmetry of a system. However, they can also have continuous properties, such as a smoothly varying energy profile along the defect.

5. What applications do topological defects have?

Topological defects have a wide range of applications in physics and materials science. They can be used to study phase transitions, create novel materials with unique properties, and even in information storage and processing in devices such as magnetic memory. They also have potential applications in fields such as cosmology and particle physics.

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