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Blog de Luis Mochán.

Blog de Luis Mochán del Instituto de Ciencias Físicas.

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Luis Mochán
mochan@fis.unam.mx
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Seminar of Sir Michael Berry

Yesterday, Sir Michael Berry gave a talk at the Institute of Physics of UNAM, about the Ahoronov Bohm effect. The effect consists in an observable phase change in the wave-function of electrons that travel along magnetic field free regions of space, due to a magnetic flux in a region unaccessible to the electrons. Thus, it seems that there is a non-local interaction with the magnetic field, which seems unacceptable. or a local interaction with the vector potential, which is also unacceptable due to the non-uniqueness of the gauge.

The Ahoronov-Bohm effect was predicted by Ehrenberg and Siday in 1948 using an argument based on the Dirac's phase exp(i\int d\vec l\cdot\vec A) around the flux line. The argument was not exact, as it did not take into account that an electron can turn many times around the shielded magnetic flux, and it yielded a non-single-valued result. Ahoronv and Bohm rediscovered the effect in 1959 finding an exact solution for the quantum mechanical problem of an electron moving in a multiply connected space pierced by a magnetic flux. Dr. Berry showed us that the exact single valued result may be obtained as a Poisson topological sum of whirling waves, each of whose terms corresponds to a given number of turns around the flux and is not si9ngle valued, but the sum is indeed single valued.

Chambers in the 60's provided experimental verification of the effect, but it rouse certain controversy. Was the effect due to the return fields? to the switching electric fields? The controversies seem to have been solved now.

There are actually four A-B efects, as the wave and the flux could each be quantum or classical. For example, ripples scattered by a vortex in a fluid is a classical-classical instance of the A-B effect. Another analogy is a simple interferometer.

There is a close connection between the A-B effect and scattering by a semi-infinite half-wave plane. This is made explicit by using the edge gauge. in which the vector potential is different from zero only in a half plane that ends at the flux line. Thus, the tools of optics, i.e., Fresnel diffraction integrals, may be used to study the effect.

He mentioned an application to quantum chaos in billiards, in which a flux line would break down time reversal symmetry but would leave the classical trajectories unchanged. This has been discussed with Thomas Seligman.

Finally, he mentioned that the physically relevant field is not the magnetic field, nor the vector potential, nor the line integral of the vector potential but its imaginary exponential.

Cargado a las 09:46 en /mochan/noticiasFisica / 20100309Berry, | Etiquetas: electrodynamics, quantum mechanics, unam | liga permanente

Effective dielectric response of Metamaterials
Effective dielectric response of Metamaterials, Guillermo P. Ortiz, Brenda E. Martínez-Zérega, Bernardo S. Mendoza and W. Luis Mochán, Phys. Rev. B 79, 245132 (2009). (URL: http://link.aps.org/abstract/PRB/v79/e245132, DOI: 10.1103/PhysRevB.79.245132). A copy is here. We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency dependent macroscopic dielectric response tensor $\epsilon^M_{ij}(\omega)$ of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating $\epsilon^M_{ij}(\omega)$ for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response which may change from conductor-like at low $\omega$ to dielectric-like with resonances at large $\omega$, attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

Cargado a las 16:37 en /mochan/noticiasFisica / ortiz20100124, | Etiquetas: extraordinary transmission, metamaterials, nanoparticles, papers | liga permanente

Energy transfer to an harmonic diatomic system
Récamier, José and Mochán, W. Luis, Energy transfer to an anharmonic diatomic system, Molecular Physics, 107: 14, 1467 -- 1472 (2009) [DOI: 10.1080/00268970902942268, URL: http://dx.doi.org/10.1080/00268970902942268]. A copy is here. We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.

Cargado a las 16:21 en /mochan/noticiasFisica / collisions20100124, | Etiquetas: anharmonic oscillator, creation and anhilation operators, deformed operators, harmonic oscillator, morse oscillator, papers | liga permanente

Non-local derivation of Poynting's theorem
My paper with Rubén Barrera was accepted in Physica B. In it we discuss an expression for Poynting's vector within non-local media. We find that besides ExB, there is a contribution -ExM to the energy flow (as is well known) but it originates in the non-locality of the dielectric response within true magnetic materials, and also within dielectric metamaterials or colloids whose non-local response mimics an effective magnetic contribution. We obtain further corrections useful for transverse and for longitudinal fields.

Cargado a las 17:13 en /mochan/noticiasFisica / poynting20100117, | Etiquetas: colloids, electrodynamics, metamaterials, papers, Poynting | liga permanente

Portal de Física en la Wikipedia
Hallé que la Wikipedia tiene un Portal de física.

Cargado a las 16:42 en /mochan/noticiasFisica / wikipediaPhysics20091230, | Etiquetas: física, wiki | liga permanente

Obituario del Dr. Marcos Moshinsky
Obituario del Dr. Marcos Moshinsky preparado por el Dr. Alejandro Frank y que aparecerá en Physics Today. WLM

Cargado a las 23:03 en /mochan/noticiasFisica / moshinsky, | Etiquetas: personajes | liga permanente

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