Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas

We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that the two-particle reduced density matrix exhibits maximal off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement we show that during an expansion the momentum distribution undergoes a "dynamical bosonization", approaching that of an ideal Bose gas without violating the Pauli exclusion principle.Comment: v3: 4 pages, 2 figures, revtex4. Section on the fermionic TG gas on a ring revised, emphasizing degeneracy of ground state for even N and resultant high sensitivity to external fields. Submitted to PR

Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory

It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T^1\times S^2, where T^1 is R^1 or S^1. Namely, imposing SO(3)-invariance and some reality conditions, we consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the \phi^4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R^{1,1}\times S^2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R^1\times S^1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R^1\times S^1\times S^2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). We also describe similar solutions in Euclidean SU(N) gauge theory on S^1\times S^3 interpreted as chains of n instanton-antiinstanton pairs.Comment: 16 pages; v2: subsection on topological charges added, title expanded, some coefficients corrected, version to appear in PR

Statistical properties of Klauder-Perelomov coherent states for the Morse potential

We present in this paper a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach . We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated

Nanotube-based scanning rotational microscope

A scheme of the scanning rotational microscope is designed. This scheme is based on using carbon nanotubes simultaneously as a probe tip and as a bolt/nut pair which converts translational displacements of two piezo actuators into pure rotation of the probe tip. First-principles calculations of the interaction energy between movable and rotational parts of the microscope confirms the capability for its operation. The scanning rotational microscope with a chemically functionalized nanotube-based tip can be used to study how the interaction between individual molecules or a molecule and a surface depends on their relative orientation.Comment: 4 pages, 3 figure

Multidimensional Worldline Instantons

We extend the worldline instanton technique to compute the vacuum pair production rate for spatially inhomogeneous electric background fields, with the spatial inhomogeneity being genuinely two or three dimensional, both for the magnitude and direction of the electric field. Other techniques, such as WKB, have not been applied to such higher dimensional problems. Our method exploits the instanton dominance of the worldline path integral expression for the effective action.Comment: 22 pages, 13 figure

Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transition with control fields

We show that atoms from wide velocity interval can be concurrently involved in Doppler-free two-photon resonant far from frequency degenerate four-wave mixing with the aid of auxiliary electromagnetic field. This gives rise to substantial enhancement of the output radiation generated in optically thick medium. Numerical illustrations addressed to typical experimental conditions are given.Comment: LaTeX2e, hyperref, 7 pages, 5 figures, to appear in PRA 1 august 200