Scaling near Quantum Chaos Border in Interacting Fermi Systems

The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution $P(s)$ as function of interaction strength $U$ and the excitation energy $\epsilon$ above the Fermi level. As $U$ increases, $P(s)$ undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z = (U \epsilon^{\alpha}-u_0) \epsilon^{1/2\nu}$, where $u_0$ is a constant. While the exponent $\alpha$, which determines the global change of the chaos border, is indecisive within a broad range of $0.9 \sim 2.0$, finite value of $\nu$, which comes from the increase of the Fock space size with $\epsilon$, suggests that the transition becomes sharp as $\epsilon$ increases.Comment: 4 pages, 4 figures, to appear in Phys. Rev. E (Rapid Communication

The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions

Interacting fermions are ubiquitous in nature and understanding their thermodynamics is an important problem. We measure the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.Comment: 28 pages, 7 figure

Microbiology and atmospheric processes: research challenges concerning the impact of airborne micro-organisms on the atmosphere and climate

For the past 200 years, the field of aerobiology has explored the abundance, diversity, survival and transport of micro-organisms in the atmosphere. Micro-organisms have been explored as passive and severely stressed riders of atmospheric transport systems. Recently, an interest in the active roles of these micro-organisms has emerged along with proposals that the atmosphere is a global biome for microbial metabolic activity and perhaps even multiplication. As part of a series of papers on the sources, distribution and roles in atmospheric processes of biological particles in the atmosphere, here we describe the pertinence of questions relating to the potential roles that air-borne micro-organisms might play in meteorological phenomena. For the upcoming era of research on the role of air-borne micro-organisms in meteorological phenomena, one important challenge is to go beyond descriptions of abundance of micro-organisms in the atmosphere toward an understanding of their dynamics in terms of both biological and physico-chemical properties and of the relevant transport processes at different scales. Another challenge is to develop this understanding under contexts pertinent to their potential role in processes related to atmospheric chemistry, the formation of clouds, precipitation and radiative forcing. This will require truly interdisciplinary approaches involving collaborators from the biological and physical sciences, from disciplines as disparate as agronomy, microbial genetics and atmosphere physics, for example

Hydrodynamic Modes in a Trapped Strongly Interacting Fermi Gases of Atoms

The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for collective frequencies of the radial and the axial breathing modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. It is shown that the method gives nearly exact solutions.Comment: 11 page

Hydrodynamic modes of a 1D trapped Bose gas

We consider two regimes where a trapped Bose gas behaves as a one-dimensional system. In the first one the Bose gas is microscopically described by 3D mean field theory, but the trap is so elongated that it behaves as a 1D gas with respect to low frequency collective modes. In the second regime we assume that the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger model. In both regimes we find the frequency of the lowest compressional mode by solving the hydrodynamic equations. This is done by making use of a method which allows to find analytical or quasi-analytical solutions of these equations for a large class of models approaching very closely the actual equation of state of the Bose gas. We find an excellent agreement with the recent results of Menotti and Stringari obtained from a sum rule approach.Comment: 15 pages, revtex, 1 figure

Ultra-cold Polarized Fermi Gases

Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half- century old open problem in condensed matter physics, and raised new interrogations of their own.Comment: 27 pages; 8 figures; Published in Report in Rep. Prog. Phys. 73 112401 (2010

Low energy transition in spectral statistics of 2D interactingfermions

We study the level spacing statistics $P(s)$ and eigenstate properties of spinless fermions with Coulomb interaction on a two dimensional lattice at constant filling factor and various disorder strength. In the limit of large lattice size, $P(s)$ undergoes a transition from the Poisson to the Wigner-Dyson distribution at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature.Comment: revtex, 5 pages, 4 figures; new data for eigenfunctions are adde

Decoherence in Nearly-Isolated Quantum Dots

Decoherence in nearly-isolated GaAs quantum dots is investigated using the change in average Coulomb blockade peak height upon breaking time-reversal symmetry. The normalized change in average peak height approaches the predicted universal value of 1/4 at temperatures well below the single-particle level spacing, but is greatly suppressed for temperature greater than the level spacing, suggesting that inelastic scattering or other dephasing mechanisms dominate in this regime.Comment: Significant revisions to include comparison to theory. Related papers available at http://marcuslab.harvard.ed

Limits to error correction in quantum chaos

We study the correction of errors that have accumulated in an entangled state of spins as a result of unknown local variations in the Zeeman energy (B) and spin-spin interaction energy (J). A non-degenerate code with error rate kappa can recover the original state with high fidelity within a time kappa^1/2 / max(B,J) -- independent of the number of encoded qubits. Whether the Hamiltonian is chaotic or not does not affect this time scale, but it does affect the complexity of the error-correcting code.Comment: 4 pages including 1 figur