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Antonio Garcia-Garcia

Anthony Garcia My expertise is in condensed matter theory with a strong interest in certain aspects of high energy physics. I am intrigued and fascinated by the phenomenon of Anderson localization. I have studied it from different points of views: theoretical understanding [1,2], possible experimental realizations [3], and relevance in different fields such as quantum chaos [4,5], ultracold atoms [3] and quantum chromodynamics (QCD) [2]. Motivated by the experimental difficulties to test localization effects in electronic systems, I focused my research on the role of localization in systems like cold atoms where it is easier to test it experimentally or in QCD where it may provide a novel mechanism to explain certain properties of the vacuum. One of my long term goals is to develop an analytical description of Anderson localization (very likely in the context of ultra cold atoms) accurate enough such that it can be used in experimental tests of quantum mechanics.

In recent times I have initiated a complementary line of research [6,7,8] aimed to develop a theoretical formalism to address finite size effects (in many cases combined with interactions) in situations in which quantum coherence is preserved and disorder is negligible. I would like to answer questions like: How do the physical properties of a system contained in a closed cavity/grain depend on its size and form?. For a given problem, in what range of sizes are these corrections relevant for experiments and practical applications?. I was surprised to know that these questions have been answered only in very few physical situations beyond the realm of electronic systems. My motivation here is rather practical: A comprehensive theoretical understanding of such effects would be an important step for the design and development of nano devices.

The most interesting results of my research so far are:

  1. The proposal that the QCD phase transitions in QCD are induced by a metal-insulator transition in the QCD Dirac operator [4]. This opens a novel way to address problems in non perturbative QCD by using condensed matter techniques and ideas. I have also put forward a phenomenological model of the QCD vacuum [2] based on ideas and techniques borrowed from condensed matter.

  2. An explicit analytical expression of the dependence of the Planck's and Stefan-Boltzmann's radiation laws [7] on the size and shape of the blackbody. These results are of relevance in cosmology, sonoluminiscence and the definition of radiance standards.

  3. The development [2] of a theory that predicts, based on the one parameter scaling theory for localization, the magnitude of the localization effects in the context of non-random Hamiltonians. Specifically I have determined in what situations a metal insulator transition is expected in quantum chaos and the conditions under which it could be studied experimentally by using ultra cold atoms techniques. I have also proposed exactly solvable random matrix models capable to describe the spectral correlations at the metal insulator transition [5].

  4. The development [6] of a theory for finite size effects in superconducting clean grains that describes how the superconducting gap depends on the shape, size and number of electrons inside the grain. For symmetric grains these effects may switch on and off superconductivity by just adding a small number of coopers pairs. These findings are of interest for practical (nanotechnological) applications. It is my intention to further explore this possibility in the near future.

  5. The development [1] of an analytical treatment of the Anderson (metal-insulator) transition valid for any dimension. This formalism predicts that the upper critical dimension is infinity and provides explicit expressions for different quantities describing the transition, such as level statistics and critical exponents, as a function of the dimensionality of the space. This the the first time that a really quantitative treatment of the metal-insulator transition is carried out.

Antonio Garcia's Homepage

S e l e c t e d P u b l i c a t i o n s:

1. A.M. Garcia-Garcia, K. Takahashi, Nucl. Phys. B, 700 (2004) 361, A.M. Garcia-Garcia Phys. Rev. E 69 (2004) 066216; A.M. Garcia-Garcia, arXiv:0709.1292.

2. A. M. Garcia-Garcia, J. C. Osborn, Nucl. Phys. A 769, 251 (2006); A. M. Garcia-Garcia, James C. Osborn, Phys.Rev. D75 (2007) 034503; A. M. Garcia-Garcia, James C. Osborn, Phys.Rev.Lett. 93 (2004) 132002;A.M Garcia-Garcia, J.J.M.Verbaarschot, Nucl. Phys. B 586 (2001) 668.

3. A. M. Garcia-Garcia, Wang Jiao, Phys. Rev. A 74, 063629 (2006).

4. A. M. Garcia-Garcia, J. Wang, Phys. Rev. Lett. 94, 244102 (2005); Phys. Rev. E 73, 03621(2006), arXiv:0707.3964; A. M. García-García, Phys. Rev. E 73, 026213 (2006).

5. A.M. Garcia-Garcia, J.J.M. Verbaarschot, Phys.Rev. E67 (2003) 046104;A.M. Garcia-Garcia , J.J.M. Verbaarschot, S. Nishigaki, Phys. Rev. E66 016132 (2002); A. M. García-García and Jiao Wang, Phys. Rev. E 73, 03621(2006).

6. A.M. Garcia-Garcia, B.L. Altshuler,, arXiv:0710.1593.

7. A.M. Garcia-Garcia, arXiv:arXiv:0709.1287.

8. A. M. Garcia-Garcia, Jorge G. Hirsch, and Alejandro Frank, Phys.Rev. C 74 (2006) 024324.


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