This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

A quantized Hall plateau of ${\ensuremath{\rho}}_{\mathrm{xy}}=\frac{3h}{{e}^{2}}$, accompanied by a minimum in ${\ensuremath{\rho}}_{\mathrm{xx}}$, was observed at $Tl5$ K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is $\frac{1}{3}$ filled. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation.

https://link.aps.org/pdf/10.1103/PhysRevLett.48.1559

Two-Dimensional Magnetotransport in the Extreme Quantum Limit

http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

Bond-orientational order in molecular-dynamics simulations of supercooled liquids and in models of metallic glasses is studied. Quadratic and third-order invariants formed from bond spherical harmonics allow quantitative measures of cluster symmetries in these systems. A state with short-range translational order, but extended correlations in the orientations of particle clusters, starts to develop about 10% below the equilibrium melting temperature in a supercooled Lennard-Jones liquid. The order is predominantly icosahedral, although there is also a cubic component which we attribute to the periodic boundary conditions. Results are obtained for liquids cooled in an icosahedral pair potential as well. Only a modest amount of orientational order appears in a relaxed Finney dense-random-packing model. In contrast, we find essentially perfect icosahedral bond correlations in alternative "amorphon" cluster models of glass structure.

Bond-orientational order in liquids and glasses

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

The Casimir force is the attraction between uncharged metallic surfaces as a result of quantum mechanical vacuum fluctuations of the electromagnetic field. We demonstrate the Casimir effect in microelectromechanical systems using a micromachined torsional device. Attraction between a polysilicon plate and a spherical metallic surface results in a torque that rotates the plate about two thin torsional rods. The dependence of the rotation angle on the separation between the surfaces is in agreement with calculations of the Casimir force. Our results show that quantum electrodynamical effects play a significant role in such microelectromechanical systems when the separation between components is in the nanometer range.

https://science.sciencemag.org/content/sci/291/5510/1941.full.pdf

Quantum mechanical actuation of microelectromechanical systems by the Casimir force.

We have studied the superfluid transition of a thin two-dimensional helium film adsorbed on an oscillating substrate. The superfluid mass and dissipation when analyzed in terms of the dynamic theory of Ambegaokar, Halperin, Nelson, and Siggia support the Kosterlitz-Thouless picture of the phase transition in a two-dimensional superfluid. The value for the jump in the superfluid density at the transition given by Kosterlitz and Thouless, ${\ensuremath{\rho}}_{s}({{T}_{c}}^{\ensuremath{-}})=8\ensuremath{\pi}{k}_{\mathrm{B}}{(\frac{m}{h})}^{2}{T}_{c}$, is in good agreement with estimates from experiment.

Study of the Superfluid Transition in Two-Dimensional He 4 Films

Etude faite par un oscillateur mecanique au silicium a haut Q. La fusion du reseau de flux dans les deux supraconducteurs varie en fonction de l'orientation du champ magnetique

Evidence from mechanical measurements for flux-lattice melting in single crystals YBa2Cu3O7 and Bi2.2Sr2Ca0.8Cu2O8.

The Casimir force between uncharged metallic surfaces originates from quantum-mechanical zero-point fluctuations of the electromagnetic field. We demonstrate that this quantum electrodynamical effect has a profound influence on the oscillatory behavior of microstructures when surfaces are in close proximity $(\ensuremath{\le}100\mathrm{nm})$. Frequency shifts, hysteretic behavior, and bistability caused by the Casimir force are observed in the frequency response of a periodically driven micromachined torsional oscillator.

Nonlinear micromechanical Casimir oscillator.

We report on current-voltage measurements in clean, untwinned ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ single crystals with picovolt voltage sensitivity and millikelvin temperature resolution in magnetic fields ranging up to 7 T. We find evidence for a melting transition in the vortex lattice which is hysteretic in both temperature and magnetic field. The measured thermal and magnetic hysteresis widths are related by the local slope of the phase boundary. This strongly supports the picture that, in the clean limit, the melting transition of the Abrikosov vortex lattice is a first-order phase transition.

David J. Bishop

Papers

Quantum mechanical actuation of microelectromechanical systems by the Casimir force.

Study of the Superfluid Transition in Two-Dimensional He 4 Films

Evidence from mechanical measurements for flux-lattice melting in single crystals YBa2Cu3O7 and Bi2.2Sr2Ca0.8Cu2O8.

Nonlinear micromechanical Casimir oscillator.

Experimental evidence for a first-order vortex-lattice-melting transition in untwinned, single crystal YBa2Cu3O7.