Comment on ``Protective measurements of the wave function of a single squeezed harmonic-oscillator state''

Alter and Yamamoto [Phys. Rev. A 53, R2911 (1996)] claimed to consider ``protective measurements'' [Phys. Lett. A 178, 38 (1993)] which we have recently introduced. We show that the measurements discussed by Alter and Yamamoto ``are not'' the protective measurements we proposed. Therefore, their results are irrelevant to the nature of protective measurements.Comment: 2 pages LaTe

Comment on "Attractive Forces between Electrons in 2 + 1 Dimensional QED"

It is shown that a model recently proposed for numerical calculations of bound states in QED$_3$ is in fact an improper truncation of the Aharonov-Bohm potential.Comment: 4 page

Weak Energy: Form and Function

The equation of motion for a time-independent weak value of a quantum mechanical observable contains a complex valued energy factor - the weak energy of evolution. This quantity is defined by the dynamics of the pre-selected and post-selected states which specify the observable's weak value. It is shown that this energy: (i) is manifested as dynamical and geometric phases that govern the evolution of the weak value during the measurement process; (ii) satisfies the Euler-Lagrange equations when expressed in terms of Pancharatnam (P) phase and Fubini-Study (FS) metric distance; (iii) provides for a PFS stationary action principle for quantum state evolution; (iv) time translates correlation amplitudes; (v) generalizes the temporal persistence of state normalization; and (vi) obeys a time-energy uncertainty relation. A similar complex valued quantity - the pointed weak energy of an evolving state - is also defined and several of its properties in PFS-coordinates are discussed. It is shown that the imaginary part of the pointed weak energy governs the state's survival probability and its real part is - to within a sign - the Mukunda-Simon geometric phase for arbitrary evolutions or the Aharonov-Anandan (AA) phase for cyclic evolutions. Pointed weak energy gauge transformations and the PFS 1-form are discussed and the relationship between the PFS 1-form and the AA connection 1-form is established.Comment: To appear in "Quantum Theory: A Two-Time Success Story"; Yakir Aharonov Festschrif

Interaction of confining vortices in SU(2) lattice gauge theory

Center projection of SU(2) lattice gauge theory allows to isolate magnetic vortices as confining configurations. The vortex density scales according to the renormalization group, implying that the vortices are physical objects rather than lattice artifacts. Here, the binary correlations between points at which vortices pierce a given plane are investigated. We find an attractive interaction between the vortices. The correlations show the correct scaling behavior and are therefore physical. The range of the interaction is found to be (0.4 +/- 0.2) fm, which should be compared with the average planar vortex density of approximately 2 vortices/fm^2. We comment on the implications of these results for recent discussions of the Casimir scaling behavior of higher dimensional representation Wilson loops in the vortex confinement picture.Comment: 9 pages LaTeX, 2 ps figures included via eps

Gas Seepage and Pockmark Formation From Subsurface Reservoirs:Insights From Table-Top Experiments

Pockmarks are morphological depressions commonly observed in ocean and lake floors. Pockmarks form by fluid (typically gas) seepage thorough a sealing sedimentary layer, deforming and breaching the layer. The seepage-induced sediment deformation mechanisms, and their links to the resulting pockmarks morphology, are not well understood. To bridge this gap, we conduct laboratory experiments in which gas seeps through a granular (sand) reservoir, overlaid by a (clay) seal, both submerged under water. We find that gas rises through the reservoir and accumulates at the seal base. Once sufficient gas over-pressure is achieved, gas deforms the seal, and finally escapes via either: (a) doming of the seal followed by dome breaching via fracturing; (b) brittle faulting, delineating a plug, which is lifted by the gas seeping through the bounding faults; or (c) plastic deformation by bubbles ascending through the seal. The preferred mechanism is found to depend on the seal thickness and stiffness: in stiff seals, a transition from doming and fracturing to brittle faulting occurs as the thickness increases, whereas bubble rise is preferred in the most compliant, thickest seals. Seepage can also occur by mixed modes, such as bubbles rising in faults. Repeated seepage events suspend the sediment at the surface and create pockmarks. We present a quantitative analysis that explains the tendency for the various modes of deformation observed experimentally. Finally, we connect simple theoretical arguments with field observations, highlighting similarities and differences that bound the applicability of laboratory experiments to natural pockmarks.</p

Continuous-time quantum walk on integer lattices and homogeneous trees

This paper is concerned with the continuous-time quantum walk on Z, Z^d, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous trees. In addition, we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases.Comment: The journal version (save for formatting); 19 page

Modelling the electric field applied to a tokamak

The vector potential for the Ohmic heating coil system of a tokamak is obtained in semi-analytical form. Comparison is made to the potential of a simple, finite solenoid. In the quasi-static limit, the time rate of change of the potential determines the induced electromotive force through the Maxwell-Lodge effect. Discussion of the gauge constraint is included.Comment: 13 pages, 7 figures, final versio

Perturbative Analysis of Nonabelian Aharonov-Bohm Scattering

We perform a perturbative analysis of the nonabelian Aharonov-Bohm problem to one loop in a field theoretic framework, and show the necessity of contact interactions for renormalizability of perturbation theory. Moreover at critical values of the contact interaction strength the theory is finite and preserves classical conformal invariance.Comment: 12 pages in LaTeX, uses epsf.sty, 5 uuencoded Postscript figures sent separately. MIT-CTP-228

Causal and localizable quantum operations

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate; it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete measurement superoperators are semilocalizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.Comment: 23 pages, 7 figures, REVTeX, minor changes and references adde