Decoherence in Phase Space

Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\"{o}dinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger "cat" state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.Comment: in press in Laser Phys.13(2003

Phase space path integral in curved space

Phase space path integral is worked out in a riemannian geometry, by employing a prescription for the infinitesimal propagator that takes riemannian normal coordinates and momenta on an equal footing. The operator ordering induced by this prescription leads to the DeWitt curvature coupling in the Schrodinger equation.Comment: 11 page

Tilted phase space measurements

We show that the phase shift of {\pi}/2 is crucial for the phase space translation covariance of the measured high-amplitude limit observable in eight-port homodyne detection. However, for an arbitrary phase shift {\theta} we construct explicitly a different nonequivalent projective representation of R$^2$ such that the observable is covariant with respect to this representation. As a result we are able to determine the measured observable for an arbitrary parameter field and phase shift. Geometrically the change in the phase shift corresponds to the tilting of one axis in the phase space of the system.Comment: 4 pages, 4 figure

Phase Moduli Space of Supertubes

We study possible deformations of BPS supertubes keeping their conserved charges fixed. We show that there is no flat direction to closed supertubes of circular cross section with uniform electric and magnetic fields, and also to open planar supertubes. We also find that there are continuously infinite flat deformations to supertubes of general shape under certain conditions.Comment: 12 pages, reference adde

Disordered Systems in Phase Space

As a function of the disorder strength in a mesoscopic system, the electron dynamics crosses over from the ballistic through the diffusive towards the localized regime. The ballistic and the localized situation correspond to integrable or regular behavior while diffusive conductors correspond to chaotic behavior. The chaotic or regular character of single wave functions can be inferred from phase space concepts like the Husimi distribution and the Wehrl entropy. These quantities provide useful information about the structure of states in disordered systems. We investigate the phase space structure of one dimensional (1d) and 2d disordered systems within the Anderson model. The Wehrl entropy of the eigenstates allows to detect the crossover between the ballistic, diffusive and localized regime.Comment: 4 pages, requires annmod.cls (included). A version with full resolution figures is available from http://www.physik.uni-augsburg.de/theo1/ingold/e/publrev.htm

Quantum Nonlocality in Phase Space

We propose an experiment demonstrating the nonlocality of a quantum singlet-like state generated from a single photon incident on a beam splitter. Each of the two spatially separated apparatuses in the setup performs a strongly unbalanced homodyning, employing a single photon counting detector. We show that the correlation functions violating the Bell inequalities in the proposed experiment are given by the joint two-mode Q-function and the Wigner function of the optical singlet-like state. This establishes a direct relationship between two intriguing aspects of quantum mechanics: the nonlocality of entangled states and the noncommutativity of quantum observables, which underlies the nonclassical structure of phase space quasidistribution functions.Comment: 4 pages, REVTe

Surface bubble nucleation phase space

Recent research has revealed several different techniques for nanoscopic gas nucleation on submerged surfaces, with findings seemingly in contradiction with each other. In response to this, we have systematically investigated the occurrence of surface nanobubbles on a hydrophobised silicon substrate for various different liquid temperatures and gas concentrations, which we controlled independently. We found that nanobubbles occupy a distinct region of this phase space, occurring for gas concentrations of approximately 100-110%. Below the nanobubble phase we did not detect any gaseous formations on the substrate, whereas micropancakes (micron wide, nanometer high gaseous domains) were found at higher temperatures and gas concentrations. We moreover find that supersaturation of dissolved gases is not a requirement for nucleation of bubbles.Comment: 4 pages, 4 figure