Yoram Alhassid
Yale University
yoram.alhassid@yale.edu

Boris Altshuler
Columbia University
bla@phys.columbia.edu

Vladimir Fal'ko
Lancaster University, UK
v.falko@lancaster.ac.uk

Program Coordinator:
Laura Lee
lee@phys.washington.edu
(206) 685-3509

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The program will focus on correlated quantum systems in which finite-size effects are important: nuclei, quantum dots and nanostructures. It will aim to bring together the nuclear and mesoscopic physics/nanoscience communities as well as key researchers in the field of strongly correlated electron systems.

Mean-field theory has played an important role in the basic and qualitative understanding of nuclei. However, a more quantitative description requires the inclusion of correlations beyond the mean field, and this continues to be one of the outstanding problems in the field. In mesoscopic physics, the situation is quite similar. The single-particle degrees of freedom are by now well understood. Small quantum dots are characterized by shell structure familiar from nuclei and atoms, while larger dots exhibit chaotic single-particle dynamics and mesoscopic fluctuations that are well described by random matrix theory. However, in almost-isolated mesoscopic structures, many-body correlations are important and they modify the single-particle properties. An exceptional system where single-particle degrees of freedom are still being explored is a mesoscopic structure made of graphene. The latter attracted great interest, in part because of the chiral properties of its quasi-particles, mimicking a relativistic Dirac spectrum. The program will explore several topics that are of common interest to the nuclear and mesoscopic/nanoscience communities:

• Effective interactions to describe the low-energy degrees of freedom. A good recent example of an effective low-energy theory for chaotic electronic systems is the so-called universal Hamiltonian, in which spin exchange and Cooper-channel correlations contribute beyond the charging energy. The universal Hamiltonian is valid in GaAs dots, in which the interaction strength is moderate. Future experiments in Si dots will probe much stronger interactions, a regime that presents a challenge to theorists. Additional effective correlations can originate in an antiferromagnetic Kondo-like interaction, which competes with the exchange interaction, or a spin-orbit interaction, which breaks spin symmetry.

• Superfluidity or superconductivity in finite-size systems (e.g., nuclei and ultra-small metallic grains). Of particular interest is the crossover between the bulk BCS limit and the fluctuation-dominated regime, in which BCS theory is no longer valid. Methods have been developed in both communities to treat fluctuations in this regime. A particularly interesting problem in electronic systems is the competition between superconductivity and ferromagnetic exchange correlations.

• The coupling to the continuum. This is one of the outstanding problems in weakly bound nuclei. In quantum dots, the "continuum" corresponds to the conduction electrons in the leads. In particular, in the Kondo regime or for strong dot-leads coupling, the electrons in the dot and in the leads must be treated coherently.

• Quantum chaos in many-particle systems. While one-body chaos is by now rather well understood, many-body quantum chaos is much less so. Statistical properties of complex many-body systems are often described by random matrix models. The crossover between the regular (Poissonian) regime and random matrix regime has an interesting but not yet fully understood connection with the many-body Anderson localization problem.

• Cold trapped atomic condensates. The trapped condensate is a well-defined strongly interacting system, and it offers theorists in both the nuclear and mesoscopic communities a unique opportunity to explore various theoretical approaches.

• Quantum dynamics in confined geometries. The challenge is to describe the quantum evolution of a finite many-body system in which the coupling between its components is varied in time. Such quantum dynamics are of great interest in spin and superconducting qubits and in the transition between a Mott insulator and a superfluid in atomic systems. Nuclear spin dynamics has recently been found to play an important role in the coherent manipulation of quantum dot spin qubits.