Research plans and outlook for the future Antonio M. García-García Lecturer and Marie Curie fellow Princeton University Research lines Research lines Research organization Research organization Anderson localization Mesoscopic physics in clean systems Non perturbative QCD Money In Money Out Interdisciplinary ERC, ERG Visitors

Anderson Localization (1957) a = ? D quan =f(d,dis)? t D clas t D quan t D quan t a Quantum diffusion in a random potential stops due to interference effects. Numerical simulations d = 1, 2 Localization for any disorder d > 2 Localization for disorder strong enough Analytical calculations d < 3 Well understood d  3 Not well understood Localization Delocalization What? State of the art: ? Anderson transition

Why is the localization problem still interesting? 1. Universal quantum phenomenon 2. No accurate experimental verification yet!!! Electrons (problem with interactions), light (problem with absorbtion) Why is it interesting now ? Cold atoms in speckle (and kicked) potentials promise a very, very precise verification of Anderson localization. Main Contribution:

Sep (2007) Two recent examples: The effective random potential is in both cases correlated

Main Project: (strong) localization in d =3 these results to the correlated potentials typical of cold atoms. what quantities can be measured with the highest precision. goal analytical predictions with the goal of: 1. Gora Shlyapnikov, cold atoms 2. Emilio Cuevas, numerical simulations. 3. Jiao Wang and G. Gong, cold atoms in quantum chaos. Collaborators Test localization and quantum mechanics itself Describe Adapt Determine Provide

2. Finite size effects in clean systems: I plan to carry out a systematic analytical study of the impact of finite size effects in quantum interacting systems and quantum gases in the range of parameters in which quantum coherence is preserved. In other words: I want to determine how the relevant observables of a given quantum (interacting) system depend on the size and shape of the grain/cavity/confining potential. What? To what extent is that known? 1. Nuclear physics 1. Nuclear physics (magic numbers). 2. Cold atoms 2. Cold atoms (Heiselberg, Mottelson). 3. Atomic clusters. 4. Superconductivity 4. Superconductivity (Parmenter, Devreese, numerics).

arXiv: Main contributions Gap dependence (cube) Gap  (size) dependence (cube)  = mean level spacing  0 ~ 0.2mV L < 15nmAl Finite size effects relevant:

Gap energy dependence  = E -E F Al grains 8-12nm

R = 2cm T = 5K Aper = 0.1cm arXiv: Density of Energy

Projects: 1. Extend this analytical treatment to other types of interactions. 2. In each case study the dependence on temperature, magnetic field, size and shape of the grain 3. Analysis of thermodynamical properties. 1. E. Yuzbashian (superconductivity related ussues) 2. K. Richter and J. Urbina, semiclassical techniques Collaborators d-wave superconductors (high Tc superconductivity) Strong coupling superconductivity BEC-BCS crossover Combined effect of Coulomb and pairing interactions. Examples Free and interacting gases

Why is this relevant? Increase the critical temperature of a superconductor!. Sonoluminiscence.Cosmology(?). Quality control for the manufacture of cavities of a certain shape. Radiance standards. Superconductivity Bosonic gases

3. Condensed matter approach to non perturbative QCD State of the art T = 0 low energy What?How? 1. Lattice QCD 2. Effective models: Instantons…. Chiral Symmetry breaking and Confinement T = T c Chiral and deconfinement transition Universality (Wilczek and Pisarski) T > T c Quark- gluon plasma QCD non perturbative! AdS-CFT N =4 Super Yang Mills μ large Color superconductivityBulk BCS

Main contribution At the same T that the Chiral Phase transition "A metal-insulator transition in the Dirac operator induces the QCD chiral phase transition" metal - insulator undergo a metal - insulator transition with J. Osborn Phys.Rev. D75 (2007) Nucl.Phys. A770 (2006) 141

Projects: 1. James Osborn, Lattice QCD. 2. Diego Rodriguez, AdS-CFT 3. Emil Yuzbashian, Superconductivity. Collaborators AdS-CFT Localization Quark-gluon plasma Ultra cold atoms Color superconductivity QCD phase transitions Confinement Other Condensed matter systems Finite size effects Entanglement entropy Spectral characterization Coulomb interactions

Research organization: 1. Reintegration grants EU: 4 years 2. European Research Council: 5 years 3. Spanish Ministry of Education (already). Money In: Money Out: 2. Vigorous visitor program: a) Leading scientists (international visibility) b) Current and prospective collaborators. (from a few days to a few months) c) Leading scientists outside my field (what’s hot!). 1. Group: one PhD student, one postdoc.

Test of localization by Cold atoms Role of localization in QCD phase transition and color superconductivity Finite size effects in clean interacting in clean interactingsystems GOALS Comparison with experiments of ultrasmallsuperconductinggrains Numerical and theoretical analysis of experimental random (correlated and uncorrelated) potentials Comparison with experiments (cold atoms)‏ Relation of order parameters to localization by lattice to localization by lattice simulations and AdS-CFT Combination of semiclassical and many body techniques Comparison quark gluon plasma (LHC) gluon plasma (LHC) Comparison with experiments(sonoluminiscence)‏ Semiclassical techniques to find finite size corrections in the blackbody radiation and thermodynamical functions IDEA THEORY REALITY CHECK Exp. verification of localization BadGood Mesoscopiccorrections in statistical mechanics mechanics Great! GoodBad Superconducting circuits with higher critical temperature Qualitiy control manufacturedcavities J. Osborn,D.Rodriguez, I. Klebanov? Test of quantum mechanics B. Altshuler, K. Richter graduate student G. Slyapnikov, A. Aspect ? Novel understanding of non perturbative non perturbativeQCD Localization outside disordered systems 053 Time (years)‏ EasyMediumDifficultMilestone