Related Research Groups
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],
experimental realizations , and
relevance in different fields such as
quantum chaos [4,5],
ultracold atoms  and quantum
chromodynamics (QCD) . 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:
- The proposal that the QCD phase transitions
in QCD are induced by a metal-insulator transition in the QCD Dirac
operator . 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  based on ideas and
techniques borrowed from condensed matter.
- An explicit analytical expression of the dependence of the
Planck's and Stefan-Boltzmann's radiation laws
 on the size and shape of the blackbody.
These results are of relevance in cosmology, sonoluminiscence and the
definition of radiance standards.
- The development
 of a theory that predicts, based on
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
- The development  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.
- The development  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
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. GarcÃa-GarcÃa, 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. GarcÃa-GarcÃa and Jiao Wang, Phys. Rev. E 73, 03621(2006).
- 6. A.M. Garcia-Garcia, B.L. Altshuler, et.al., 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.