Publication

Lagrangian Reductions and Integrable Systems in Condensed Matter

Tudor Ratiu, François Gay-Balmaz
2015
Journal Articles

Abstract

We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrability of several one dimensional texture equations arising in liquid Helium phases and neutron stars.

Official source

https://infoscience.epfl.ch/entities/publication/92731c46-88bd-4f57-9730-3f3759153f6f

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Tudor Ratiu, François Gay-Balmaz
2015
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/92731c46-88bd-4f57-9730-3f3759153f6f

About this result

Related concepts (26)

Integrable system

In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space.

Spontaneous symmetry breaking

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.

Helium

Helium (from helios) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is the lowest among all the elements, and it does not have a melting point at standard pressure. It is the second-lightest and second most abundant element in the observable universe, after hydrogen. It is present at about 24% of the total elemental mass, which is more than 12 times the mass of all the heavier elements combined.

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