Search

Suppose that a system is known to be in one of two quantum states. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of determining with one measurement which state the system is in. However, because a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states, it is always possible to choose this inner product so that the two states are orthogonal. Thus, it is possible to perform a simulated quantum state discrimination with a single measurement in which a perfect state discrimination is realized probabilistically.

The potential of a piezoelectric, double-amplifier active-skin with structural acoustic sensing (SAS) is demonstrated for the reduction of broadband acoustic radiation from a clamped, aluminum plate. The active-skin is a continuous covering of the vibrating portions of the plate with active, independently controllable piezoelectric, double-amplifier elements and is designed to affect control by altering the continuous structural radiation impedance rather than structural vibration. In simulation, acoustic models are sought for the primary and secondary sources that incorporate finite element methods. Simulation indicates that a total radiated power attenuation in excess of 10 dB may be achieved between 250 and 750 Hz with microphone error sensing, while under SAS the radiated power is reduced by nearly 8 dB in the same frequency range. In experiment, the adaptive feed forward filtered-x LMS (least mean square) algorithm, implemented on a Texas Instruments C40 DSP, was used in conjunction with the 6I6O control system. With microphone error sensing, 11.8-dB attenuation was achieved in the overall radiated power between 175 and 600 Hz. while inclusion of SAS resulted in a 7.3-dB overall power reduction in this frequency band.

In recent years, hybrid absorption systems have been implemented which achieve high sound absorption over a broad frequency range. This work is an experimental study of a broadband hybrid absorption system which is comprised of a layer of sound-absorbing material (the passive component) positioned at a distance from a movable wall (the active component) inside an impedance tube. The movable wall is used to impose desired boundary conditions in the cavity behind the passive layer, thereby increasing the absorption of the system at frequencies where the passive material is not independently effective. Both pressure-release (i.e., minimizing the pressure at the back surface of the layer) and impedance-matching (i.e., minimizing the reflected wave from the layer) boundary conditions are studied. The performance of the hybrid system for these two boundary conditions is compared for broadband disturbances over a frequency range of 100-1000 Hz. The unmodified passive system showed absorption coefficients greater than 0.7 only above 500 Hz, while the impedance-matching condition yielded absorption coefficients of 0.8 to 1.0 over the 100-1000-Hz range. The impedance-matching condition provided significantly better absorption than that achieved with the pressure-release condition. The sensitivity of these control approaches to system parameters is also investigated.

A natural geometry, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is used to study the symmetry properties of real-space renormalisation group (RG) flow. In the projective state space this flow is shown to have two contributions: a gradient term, which generates a projective automorphism of the state space for each given length scale; and an explicit correction. We then argue that this structure implies the absence of any symmetry of a geodesic type for the RG flow when restricted to the parameter space submanifold of the state space. This is demonstrated explicitly via a study of the one dimensional Ising model in an external field. In this example we construct exact expressions for the beta functions associated with the flow induced by infinitesimal rescaling. These constitute a generating vector field for RG diffeomorphisms on the parameter space manifold, and we analyse the symmetry properties of this transformation. The results indicate an approximate conformal Killing symmetry near the critical point, but no generic symmetry of the RG flow globally on the parameter space., Comment: 16 pages, RevTeX, 3 postscript figures

Using real-space renormalisation techniques we analyse the Ising model on a Sierpi\'nski gasket with anisotropic microscopic couplings, and observe a restoration of isotropy on macroscopic scales. In particular, via use of a decimation procedure directly on the fractal lattice, we calculate explicitly the exponential anisotropy decay coefficients near the isotropic regime for both ferromagnetic and antiferromagnetic systems. The results suggest the universality of the phenomenon in lattice field theories on fractals., Comment: 10 pages, RevTeX, 4 postscript figures, to appear in Phys. Lett. A