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Boris Altshuler
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Nancy Tate
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Institute for Nuclear Theory Program 02-2

Chaos and Interactions: from Nuclei to
Quantum Dots

July 1 - September 6, 2002

This program will explore outstanding problems in the physics of mesoscopic systems such as quantum dots from an interdisciplinary perspective. Theoretical approaches to mesoscopic systems have benefited from the ideas and methods of several fields, including nuclear physics, quantum chaos, strongly correlated electron systems, and atomic physics. The program will encourage an exchange of ideas between these communities. Theoretical progress in mesoscopic physics has been closely tied to experimental work, and several experimentalists are expected to take part in the program.

Quantum dots are small enough to be governed by the laws of quantum mechanics and exhibit a rich variety of behavior depending on their size, geometry, and external conditions. Their conductance can be readily measured, and their physical parameters are easily controlled. Small dots with harmonic-like confining potentials are characterized by shell structure, leading to the magic number phenomenon familiar to nuclear physicists. For larger dots, the symmetry responsible for shells disappears, and the single-electron dynamics are mostly chaotic. Random-matrix theory- introduced by Wigner and Dyson to explain the statistical properties of the neutron resonances in compound nuclei-has proven useful for describing the mesoscopic fluctuations of the conductance in such dots.

Despite the early success of theories based on a single particle picture, recent experiments have identified important discrepancies that are likely signatures of interactions. In almost-isolated dots the charge is quantized, and electron-electron interactions play an important role. A central topic of the program will be the interplay between mean-field behavior, one-body chaos (or disorder) and interactions.

The program will also address spin-related phenomena in mesoscopic systems. In general, the exchange interaction is minimized for a spin-polarized Hund state (typical in atoms), while the one-body kinetic energy favors the Pauli state of minimal spin (typical of bulk metallic systems). How does disorder (or chaos) affect the spin properties? Other key issues are spin transport and the possibility of manipulating spin, a problem relevant to quantum computers.

Recent exciting advances include the fabrication of conducting nanostructures even smaller than quantum dots, e.g., metallic nanoparticles and carbon nanotubes. These systems provide additional insight into the physics of small, coherent quantum systems, and part of the program will be devoted to them.

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