Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics

We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure (POVM) of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.Comment: 12 pages, 3 figure

An analytical and experimental study of a short s-shaped subsonic diffuser of a supersonic inlet

A subscale HiMAT forebody and inlet was investigated over a range of Mach numbers to 1.4. The inlet exhibited a transitory separation within the diffuser but steady state data indicated reattachment at the diffuser exit. A finite difference procedure for turbulent compressible flow in axisymmetric ducts was used to successfully model the HiMAT duct flow. The analysis technique was further used to estimate the initiation of separation and delineate the steady and unsteady flow regimes in similar S-shaped ducts

The thick-thin decomposition and the bilipschitz classification of normal surface singularities

We describe a natural decomposition of a normal complex surface singularity $(X,0)$ into its "thick" and "thin" parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin. The thin part is empty if and only if the singularity is metrically conical; the link of the singularity is then Seifert fibered. In general the thin part will not be empty, in which case it always carries essential topology. Our decomposition has some analogy with the Margulis thick-thin decomposition for a negatively curved manifold. However, the geometric behavior is very different; for example, often most of the topology of a normal surface singularity is concentrated in the thin parts. By refining the thick-thin decomposition, we then give a complete description of the intrinsic bilipschitz geometry of $(X,0)$ in terms of its topology and a finite list of numerical bilipschitz invariants.Comment: Minor corrections. To appear in Acta Mathematic

Preparation of pure and mixed polarization qubits and the direct measurement of figures of merit

Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.Comment: 5 pages, 3 figures, 1 tabl

The second law, Maxwell's daemon and work derivable from quantum heat engines

With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium

Probing of the Kondo peak by the impurity charge measurement

We consider the real-time dynamics of the Kondo system after the local probe of the charge state of the magnetic impurity. Using the exactly solvable infinite-degeneracy Anderson model we find explicitly the evolution of the impurity charge after the measurement.Comment: 4 pages, 1 eps figure, revte

Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival

Repeated measurements of a quantum particle to check its presence in a region of space was proposed long ago [G. R. Allcock, Ann. Phys. {\bf 53}, 286 (1969)] as a natural way to determine the distribution of times of arrival at the orthogonal subspace, but the method was discarded because of the quantum Zeno effect: in the limit of very frequent measurements the wave function is reflected and remains in the original subspace. We show that by normalizing the small bits of arriving (removed) norm, an ideal time distribution emerges in correspondence with a classical local-kinetic-energy distribution.Comment: 5 pages, 4 figures, minor change

Suppression of Zeno effect for distant detectors

We describe the influence of continuous measurement in a decaying system and the role of the distance from the detector to the initial location of the system. The detector is modeled first by a step absorbing potential. For a close and strong detector, the decay rate of the system is reduced; weaker detectors do not modify the exponential decay rate but suppress the long-time deviations above a coupling threshold. Nevertheless, these perturbing effects of measurement disappear by increasing the distance between the initial state and the detector, as well as by improving the efficiency of the detector.Comment: 4 pages, 4 figure

A computerized Langmuir probe system

For low pressure plasmas it is important to record entire single or double Langmuir probe characteristics accurately. For plasmas with a depleted high energy tail, the accuracy of the recorded ion current plays a critical role in determining the electron temperature. Even for high density Maxwellian distributions, it is necessary to accurately model the ion current to obtain the correct electron density. Since the electron and ion current saturation values are, at best, orders of magnitude apart, a single current sensing resistor cannot provide the required resolution to accurately record these values. We present an automated, personal computer based data acquisition system for the determination of fundamental plasma properties in low pressure plasmas. The system is designed for single and double Langmuir probes, whose characteristics can be recorded over a bias voltage range of ±70 V with 12 bit resolution. The current flowing through the probes can be recorded within the range of 5 nA–100 mA. The use of a transimpedance amplifier for current sensing eliminates the requirement for traditional current sensing resistors and hence the need to correct the raw data. The large current recording range is realized through the use of a real time gain switching system in the negative feedback loop of the transimpedance amplifier