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Domenico Oricchio: on 10/8/13 at 18:30pm UTC, wrote I am thinking that critical point in temperature physics near absolute zero...

Thomas Ray: on 10/1/13 at 14:52pm UTC, wrote Wow, I like this mathematical treatment, and I appreciate the amount of...

Ben Still: on 10/1/13 at 13:57pm UTC, wrote A mathematical method that determined an elementary link between two forces...


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Blogger Ben Still wrote on Oct. 1, 2013 @ 13:57 GMT
Image credit: Craig Ratcliffe
A mathematical method that determined an elementary link between two forces of nature has also led to a deeper understanding of what seems to be a fundamental link between solids, liquids and gases. The work is described in Scientific Reports 3, 2794 (2013) (http://arxiv.org/abs/1306.1892).

A process know as symmetry breaking is key to the theory of how the recently discovered Higgs boson gives mass to the fundamental building blocks and force carrying particles of nature. The mathematical procedure also shows, however, that there is an underlying connection between the electromagnetic force, responsible for chemistry and electricity, and the weak nuclear force, responsible for the processes making the Sun shine and radioactivity. Dima Bolmatov et al. at Queen Mary, University of London have now taken this idea out of the realm of particles and into the world of condensed matter physics.

In searching for an analytical approach to understanding the properties of liquids Dima Bolmatov and Kostya Trachenko have taken a different route to most. Most of their peers have sought to explain liquids as more heavily interacting gases but Bolmatov and Trachenko have looked at explaining liquids as solids that have more freedom. The research, titled the "phonon theory of liquids", explains how liquid properties are derived from solids with less restrictions on their relative movement. Bolmatov describes it as "cutting springs" which constrain the movement of individual atoms in a lattice.

Now an extension to this idea points to an underlying connection that allows all three states of matter and the transitions between them to be explained in one theory.

Breaking a symmetry

A symmetry is any series of manipulations that takes some object and ends up with the same object. For example one can take a picture of a square on a page and rotate it 90o to return to an identical square. You could also reflect the image of the square in a mirror and see an identical square. These rotational and reflection symmetries are individual manipulations but even if we combined them they too would also be a symmetry.

A circle has an infinite rotational symmetry; no matter by how much or how many times you rotate a circle you always end up with an identical circle at the end. What now if we were to draw a straight line from the centre to one point on the circle. No longer can we rotate the circle by any amount and get an identical circle. There is only one orientation in which the circle looks that specific way – the rotational symmetry the circle once had has been broken. We have removed this particular symmetry and in essence taken away what was once a true degree of freedom.

This exact same process is performed within the mathematics of the Higgs mechanism in particle physics. The drawing of a line above is executed in the maths by specifying a preferred direction in space. This in combination with the Higgs field results in particles gaining a mass when at rest.

Broken Symmetry and States of Matter

Dima Bolmatov, Edvard Musaev and Kostya Trachenko of Queen Mary, University of London have now proposed that a new idea using the same procedure can define a unified description of all three states of matter. If one thinks of matter as a solid but with different degrees of freedom then breaking of a symmetry distinguishes its phases (solid, liquid and gas). Although the symmetries themselves are different the process as described follows exactly the same route as the Higgs mechanism.

Mathematically, this was realised by introducing an interacting phonon Hamiltonian with ground state configurations minimising the potential energy. Symmetry breaking SO(3) to SO(2), from the group of rotations in reciprocal space to its subgroup, leads to emergence of energy gaps of transverse excitations. As a consequence of the Goldstone theorem it readily results in the emergence of energy spectra of solid, liquid and gas phases.

Glass transition and critical phenomena are among other challenging problems that can be considered in this framework.

--

Ben Still is a physicist at Queen Mary, University of London.

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Thomas Howard Ray wrote on Oct. 1, 2013 @ 14:52 GMT
Wow, I like this mathematical treatment, and I appreciate the amount of work it must have taken to make it short and simple.

In re eqns 8 & 13:

" ... the symmetry breaking SO(3) --> SO(2) acquires a microscopic meaning in real space. Namely, no symmetry breaking takes place in solids where atoms do not jump, giving ¯x^a = 0. In liquids and gases, on the other hand, symmetry breaking is due to particle jumps, i.e. spontaneous translations with amplitudes ¯x^a ."

A big hint of where to go with a continuous field theory -- for if we can isolate quantum jumps as a function of phase transition states, we may have a classical "skeleton" key to unlock quantum behavior at every scale.

Thanks, Ben!

Tom

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Domenico Oricchio wrote on Oct. 8, 2013 @ 18:30 GMT
I am thinking that critical point in temperature physics near absolute zero contain information on the structure of the matter, and fundamental interactions.

If there is a pure chemical element (so that there is a simplification of the interaction), then the wave function of the material particles is broad: there is an overlapping of the electrons, protons and neutrons (there is a complete mixing of the wave functions, until obtain a single wave function of the material with near zero entropy).

If there is a fluid dynamics of the system then the large scale vortexes, because of the shielding of the potential (it can be that exist a potential that give the Pauli exclusion principle: virtual photon connect fermion, if they are not shielded), then it is possible the overlapping over the inner structure of the nuclear potential.

If there is a mathematical description of the large scale quantum state, then it is possible to obtain elementary particles description using the vortexes.

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