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The flow field behind spinning baseballs at two different seam orientations was investigated, and compared with a smooth sphere, to isolate effects of seams on the Magnus effect at Reynolds numbers of 5×104 and 1×105. The rotational speed of the three spheres varied from 0 to 2400 rpm, which are typical of spin rates imparted to a thrown baseball. These spin rates are represented nondimensionally as a relative spin rate relating the surface tangential velocity to the freestream velocity, and varied between 0 and 0.94. Mean velocity profiles, streamline patterns, and power spectral density of the velocity signals were taken using hot-wire anemometry and/or stereoscopic particle image velocimetry in the wake region. The sphere wake orientation changed over a range of relative spin rates, indicating an inverse Magnus effect. Vortex shedding at a Strouhal number of 0.25 was present on the sphere at low relative spin rates. However, the seams on the baseball prevented any consequential change in wake orientation and, at most spin rates, suppressed the shedding frequency exhibited by the sphere. Instead, frequencies corresponding to the seam rotation rates were observed in the wake flow. It was concluded that the so-called inverse Magnus effect recorded by previous investigators at specific combinations of Reynolds number and relative spin rate on a sphere exists for a smooth sphere or an axisymmetrically dimpled sphere but not for a baseball near critical Reynolds numbers, where the wake flow pattern is strongly influenced by the raised seams.

Thermodynamics with multiple conserved quantities offers a promising direction for designing novel devices. For example, Vaccaro and Barnett's [J. A. Vaccaro and S. M. Barnett, Proc. R. Soc. A 467, 1770 (2011)1364-502110.1098/rspa.2010.0577; S. M. Barnett and J. A. Vaccaro, Entropy 15, 4956 (2013)ENTRFG1099-430010.3390/e15114956] proposed information erasure scheme, where the cost of erasure is solely in terms of a conserved quantity other than energy, allows for new kinds of heat engines. In recent work, we studied the discrete fluctuations and average bounds of the erasure cost in spin angular momentum. Here we clarify the costs in terms of the spin equivalent of work, called spinlabor, and the spin equivalent of heat, called spintherm. We show that the previously found bound on the erasure cost of γ^{-1}ln2 can be violated by the spinlabor cost, and only applies to the spintherm cost. We obtain three bounds for spinlabor for different erasure protocols and determine the one that provides the tightest bound. For completeness, we derive a generalized Jarzynski equality and probability of violation which shows that for particular protocols the probability of violation can be surprisingly large. We also derive an integral fluctuation theorem and use it to analyze the cost of information erasure using a spin reservoir.

Hot-wire measurements were taken in the wake of ten finite length circular cylinders, six of which were also tapered, in a uniform flow in a low speed wind tunnel. The Reynolds number based on mean cylinder diameter ranged from 2100 ≤ Re ≤ 5500, the aspect ratio (AR) of the cylinders varied from 16 ≤ AR ≤ 64, and the taper ratio (RT) varied from 21.3 ≤ RT ≤ 96. The vortex shedding along the spans of the cylinders coalesced into discrete cells, the range of Strouhal numbers and the number of cells being a function of the cylinder aspect ratio and taper ratio. It was found that the number of discrete cells is linearly related to a cylinder geometry ratio (CGR) defined as CGR = AR(1 + AR/RT).

An experimental wind tunnel study was performed to assess the effect of aspect ratio and rotational speed of circular cylinders of varying diameter on the flow patterns behind the cylinders in the presence of a uniform upstream crossflow. Six circular cylinders of constant length but different diameters, producing aspect ratios 6 ≤ AR ≤ 32 were examined at a single upstream velocity such that the Reynolds number varied between 1920 ≤ Re ≤ 10240. Rotational speeds from stationary up to 3600 rpm were applied to the cylinders, so that the maximum relative velocity α = πfD/U∞ = 0.80. Mean velocity profiles were measured three diameters downstream of the cylinder axis at 6 equidistant locations, and PSD power spectral density were generated for 26 equidistant locations along the cylinder, to create a comprehensive record of spanwise variations under all rotational conditions. For the highest aspect ratio tested, the wake velocity profiles were independent of rotational speed at all spanwise locations, whereas at lower aspect ratios, the maximum velocity defect diminished with increasing rotational speed along most of the span and became asymmetric near the free end. Two distinct shedding cells were found only for a cylinder with an aspect ratio of twelve at three relative spin rates of 0.067, 0.27, and 0.4. In cases where only a single cell existed, increased rotational speed produced a higher vortex shedding frequency on a given aspect ratio cylinder.

The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we use the fundamental principles of ergodicity (via Liouville's theorem), the self-similarity of correlations, and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long-range-interacting systems. Significantly, our formalism provides a justification for the well-studied nonextensive thermostatistics characterized by the Tsallis distribution, which it includes as a special case. We also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the Boltzmann-Gibbs-Shannon entropy. The consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics., Comment: 6 pages, 1 figure, 1 table, and 3 pages of supplemental material. v4: comments are welcome

Quantum coherence, the ability to control the phases in superposition states is a resource, and it is of crucial importance, therefore, to understand how it is consumed in use. It has been suggested that catalytic coherence is possible, that is repeated use of the coherence without degradation or reduction in performance. The claim has particular relevance for quantum thermodynamics because, were it true, it would allow free energy that is locked in coherence to be extracted $\textit{indefinitely}$. We address this issue directly with a careful analysis of the proposal by $\AA{}$berg. We find that coherence $\textit{cannot}$ be used catalytically, or even repeatedly without limit., Comment: 23 pages with 2 figures

An experimental investigation into the flow field behind baseballs at two different seam orientations as well as a smooth sphere of the same diameter was undertaken at Reynolds numbers of 5 × 104 and 1 × 105. The rotational speed of the three spheres varied from 0 to 2400 rpm, with data collected in increments of 400 rpm which correspond to relative spin rates between 0 and 0.94. Mean velocity profiles, turbulence in intensity profiles, and power spectral density of the signals were taken using hot-wire anemometry. The smooth sphere wake was seen to change in orientation over a range of relative rotational speeds. The Strouhal number remained constant around 0.24 for relatively low spin rates. The seams on the baseball suppressed any measurable vortex shedding once rotation began, also eliminating any significant change in wake orientation as evidenced by the mean velocity deficit and turbulence intensity profiles. It was concluded that the so-called inverse Magnus effect recorded by previous investigators at a specific Reynolds number / relative rotational speed of a sphere exists only for a smooth sphere and not for a sphere where the boundary layer separation is governed by raised seams.

Advances in our understanding of the physical universe have impacted dramatically on how we view ourselves. Right at the core of all modern thinking about the universe is the assumption that dynamics is an elemental feature that exists without question. However, ongoing research into the quantum nature of time is challenging this view: my recently-introduced quantum theory of time suggests that dynamics may be a phenomenological consequence of a fundamental violation of time reversal symmetry. I show here that there is consistency between the new theory and the block universe view. I also discuss the new theory in relation to the human experience of existing in the present moment, able to reflect on the past and contemplate a future that is yet to happen., 13 pages

A combined experimental and numerical investigation of flow control actuation in a short, rectangular, diffusing S-shape inlet duct using a two-dimensional tangential control jet was conducted. Experimental and numerical techniques were used in conjunction as complementary techniques, which are utilized to better understand the complex flow field. The compact inlet had a length-to-hydraulic diameter ratio of 1.5 and was investigated at a free-stream Mach number of 0.44. In contrast to the baseline flow, where the flow field was fully separated, the two-dimensional control jet was able to eliminate flow separation at the mid-span portion of the duct and changed considerably the three-dimensional flow field, and ultimately, the inlet performance. A comparison between the baseline (no actuation) and forced flow fields showed that secondary flow structures dominated both flow fields, which is inevitably associated with total pressure loss. Contrary to the baseline case, the secondary flow structures in the forced case were established from the core flow stagnating on the lower surface of the duct close to the aerodynamic interface plane. High fidelity spectral analysis of the experimental results at the inlet’s exit plane showed that the baseline flow field was dominated by pressure fluctuations corresponding to a Strouhal number based on hydraulic diameter of 0.26. Not only did the two-dimensional tangential control jet improve the time-averaged pressure recovery at the inlet exit plane (13.3% at the lower half of the aerodynamic interface plane), it essentially eliminated the energy content of the distinct unsteady fluctuations which characterized the baseline flow field. This result has several implications for the design of a realistic engine inlet; furthermore, it depicts that a single non-intrusive static pressure measurement at the surface of the duct can detect flow separation.

Landauer's erasure principle is a cornerstone of thermodynamics and information theory [R. Landauer, IBM J. Res. Dev. 5, 183 (1961)]. According to this principle, erasing information incurs a minimum energy cost. Recently, Vaccaro and Barnett [J. A. Vaccaro and S. M. Barnett, Proc. R. Soc. A 467, 1770 (2011)] explored information erasure in the context of multiple conserved quantities and showed that the erasure cost can be solely in terms of spin angular momentum. As Landauer's erasure principle plays a fundamental role in heat engines, their result considerably widens the possible configurations that heat engines can have. Motivated by this, we propose here an optical heat engine that operates under a single thermal reservoir and a spin angular momentum reservoir coupled to a three-level system with two energy degenerate ground states. The proposed heat engine operates without producing waste heat and goes beyond the traditional Carnot engine where the working fluid is subjected to two thermal baths at different temperatures.

Information is central to thermodynamics, providing the grounds to the formulation of the theory in powerful abstract statistical terms. One must not forget, however, that, as put by Landauer, {\it information is physical}. This means that the processing of information will be unavoidably linked to the costs of manipulating the real physical systems carrying the information. Here we will focus on the particular process of erasing information, which plays a fundamental role in the description of heat engines. We will review Landauer's principle and the associated erasure energy cost. We will also show, following the recent contributions from Vaccaro and Barnett, that cost of erasing does not need to be paid with energy, but with any other conserved quantity. Finally, we will address the issue of designing heat engines based on these new concepts.

An experimental study was undertaken to investigate the influence of leading edge geometry and of relative curvature on the formation of a boundary layer on the surface of a cylinder aligned axially in a uniform flow. Hot wire anemometry was used to measure mean and fluctuating velocity components at a number of axial locations from the leading edge of cylinders of three different relative curvatures and two different leading edge shapes. In all cases a minimum relative axial length of greater than ten radii was examined, hence allowing adequate inspection of the formation region. Six cylinders were employed in the study, three with a blunt leading edge, and three with an ellipsoid of 3:1 ratio leading to the constant radius length. The Reynolds number based on cylinder radius (Rea = Uoa/v) varied from 3000 ≤ Rea ≤ 9000. The elliptical leading edge cylinders experienced laminar boundary layers, and the blunt cylinders created a separated bubble region followed by the development of a turbulent boundary layer. The laminar boundary layer was smaller than what a flat plate would produce at a corresponding length, and its experimental data generated profiles could be universalized with previously developed similarity variables. The turbulent boundary layer assumed a nearly constant velocity profile in the region 10 ≤ x/a ≤ 40, and its height grew proportionally to x1/3 rather than to x4/5 as for a flat plate. Streamwise turbulence intensities diminished rapidly with vertical distance from the surface of the cylinder, and also assumed a constant profile as relative axial distance increased. Over the limited range examined, changes in curvature were of secondary importance on relative boundary layer growth.

A combined experimental and numerical investigation of the flow field in a short, rectangular, diffusing S-shape inlet duct was conducted. The inlet duct had a length-to-hydraulic diameter ratio of 1.5 and an inflow Mach number of 0.44. The flow field was diagnosed utilizing stereoscopic particle image velocimetry, surface static pressure measurements, and high frequency total pressure measurements both on the lower surface and at the duct’s aerodynamic interface plane. To complement the experimental investigation and to aid in understanding the flow field associated with this complex geometry, a numerical flow simulation was undertaken. The flow field exhibited massive flow separations and shear layer formations at both turns of the compact inlet. Moreover, secondary flow structures along the duct’s lower surface and along the duct’s side walls were identified. It was shown that the two counter-rotating flow structures along the duct’s lower surface resulted in high levels of total pressure loss at the aerodynamic interface plane. A high fidelity spectral analysis of the pressure signals at the aerodynamic interface plane and along the lower surface was conducted and demonstrated that a high frequency surface static pressure sensor could identify flow separation in a non-intrusive fashion, allowing for future use in a closed-loop control scheme for active flow control. This work was part of a more comprehensive study which was to utilize active flow control to improve performance metrics of such compact inlets.

The Hamiltonian defines the dynamical properties of the universe. Evidence from particle physics shows that there is a different version of the Hamiltonian for each direction of time. As there is no physical basis for the universe to be asymmetric in time, both versions must operate equally. However, conventional physical theories accommodate only one version of the Hamiltonian and one direction of time. This represents an unexplained anomaly in conventional physics and calls for a reworking of the concepts of time and space. Here I explain how the anomaly can be resolved by allowing dynamics to emerge phenomenologically. The resolution offers a picture of time and space that lies below our everyday experience, and one in which their differences are epiphenomenal rather than elemental.

An experimental study was undertaken to examine two phenomena associated with a jet issuing from a forward-facing circular cylinder (with a length to outer radius ratio of 6.8) into a counterflow: (1) the effect of the counterflow on the internal velocity profile near the injector exit, and (2) the combined jet and counterflow influence on the external surface boundary layer profiles. Wind tunnel experiments, utilizing hot-wire anemometry, were conducted at very low jet-to-counterflow velocity ratios between 0 and 0.41 and Reynolds numbers based on cylinder outer diameter of 2.6×104 and 5.2×104. It was found that the flow at the internal location was negligibly affected by the counterflow, with the profiles exhibiting typical turbulent pipe flow behavior. However, close to the injector exit plane, the counter-flow accelerated the exiting jet in an annular region adjacent to the cylinder inner wall, creating a high velocity region which reversed direction upon exiting. The exit flow reversal around the lip of the cylinder was manifested downstream as an addition of momentum to the flow field. Boundary layer measurements were taken at seven streamwise locations along the upper surface of the cylinder. A dimensionless parameter constructed from both a traditional flat plate turbulent boundary layer scaling and a geometric curvature ratio was used to plot all data, which collapsed to a single curve at all locations in the absence of a jet, while in the presence of the jet, the only differences in the profiles were close to the surface. Independently of jet-to-counterflow velocity ratio, the boundary layer on the cylinder was seen to grow in the streamwise direction at a rate proportional to x25 rather than x45 as occurs with a turbulent boundary layer on a flat plate, even though the boundary layer height to curvature ratio was relatively low (≈ 1), and hence would have been expected to approximate flat plate behavior.

Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators., 20 pages, 3 figures

Active flow control using fluidic actuators, via arrays of synthetic jet actuators, was used to provide control power for the Stingray unmanned aerial vehicle in the longitudinal (pitch) and lateral (roll) directions at low angles of attack. Using this technique, the pitch and roll moments were altered such that the effect is similar to that of a deflection of conventional control effectors. The control effectiveness of the synthetic jets on the aerodynamic performance of the Stingray unmanned aerial vehicle was investigated experimentally in a wind tunnel. Global flow measurements were conducted, where the moments and forces on the vehicle were measured using a six-component sting balance. The effect of the actuation was also examined on the surface static pressure at two spanwise locations. In addition, a particle image velocimetry technique was used to quantify the flowfield over the model, both the global flowfield as well as the localized interaction domain near the synthetic jet orifice. The synthetic jets were able to alter the local streamlines and displace the boundary layer through the formation of a small quasi-steady interaction region on the suction surface of the Stingray unmanned aerial vehicle's wing. Phase-locked particle image velocimetry data were acquired to provide insight into the growth, propagation, and decay of the synthetic jets impulse and their interaction with the crossflow. Furthermore, the changes induced on the moments and forces can be proportionally controlled by either changing the momentum coefficient or by driving the synthetic jets with a pulse modulation waveform. This can lead the way for future development of closed-loop control models.

According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with an intrinsically discrete degree of freedom. Here we study the discrete fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.

T violation has previously been shown to induce destructive interference between different paths that the universe can take through time and leads to a new quantum equation of motion called bievolution. Here we examine further details of the interference and clarify the conditions needed for the bievolution equation., Comment: 12 pages with 6 figures. Final accepted version

An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental, is represented by equations of motion and conservation laws that operate differently over time and space. If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, the formalism treats time and space symmetrically such that states of matter are localised both in space and in time. In this case, equations of motion and conservation laws are undefined or inapplicable. However if T symmetry is violated, the same sum over paths formalism yields states that are localised in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schr\"{o}dinger equation) and conservation laws apply. This suggests that the time-space asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution., Comment: Final published version: 22 pages, 5 figures. Published article is available as Open Access from publisher

We derive stochastic Schr\"odinger equations describing the evolution of an optical linear amplifier conditioned on the state-selective detection of the source atoms. By applying a classical pulse to each atom immediately before the detection process we generate different stochastic Schr\"odinger equations including that of the quantum-jump method and quantum-state diffusion. We also study the transition from the distinct jumps of the quantum-jump method to the diffusive behavior of quantum-state diffusion and trace the effect of the information gained by the detection of the state of the atom on the state of the field.

Observation of transient effects in electromagnetically induced transparency (EIT) is reported in ${\mathrm{Rb}}^{85}$ cooled in a magneto-optical trap. The transmission of a weak probe beam in resonance with the ${5S}_{1/2}(F=3)$ to ${5P}_{3/2}(F=3)$ hyperfine transition increased transiently when a relatively strong coupling field in resonance with the ${5S}_{1/2}(F=2)$ to ${5P}_{3/2}(F=3)$ hyperfine transition was switched on rapidly using a Pockels cell. The probe transient showed an initial Rabi half-cycle overshoot before settling down to steady-state EIT. The results agreed well with computations using a three-state model of the \ensuremath{\Lambda} system. The computations also suggest that transient gain should be observed with coupling field power only four times larger than that presently available to us.

The Galilei invariance under displacements of position and momentum is a defining property of Wigner's quasi-probability function Wpm. The analogous defining property of the number-phase Wigner function WNP is invariance under discrete upward shifts in photon number and shifts in phase. We use these different invariance properties to highlight distinct differences and similarities between the two quasi-probability functions Wpm and WNP. In the process we introduce the number-shifted coherent states in analogy with the displaced number states and discuss their properties.

We report experiments demonstrating the effects of optical pumping, coherent population trapping and light polarisation on electromagnetically induced transparency in simple Λ-type configurations of rubidium 87 where the relevant coherences are within the three Zeeman substates of the F=1 component of the 5S1/2 ground level. Inversionless gain is also demonstrated. The sample is cooled to below 1 mK in a magneto-optic trap operating without repumping light to give a working population of F=1 ground state atoms. The experimental results are compared with master equation computations of a closed seven-substate-model representing the ground level (F=1) and the excited levels F′=0 and F′=1.

We show that the violation of time reversal invariance (T) observed in meson decay may have a profound effect on the direction of time. Our starting point is a universe without a presumed direction of time. Time evolution is modeled by taking an equal superposition of steps in both directions of time. This gives rise to multiple paths through time. The presence of T violating processes is shown to give rise to destructive interference between all paths except for the two that comprise continuously forwards and continuously backwards steps. We show that this leads to a new kind of irreversibility that is quite unlike that found in thermodynamics.

We outline the theory of a practical Bragg scattering technique for studying the long-range spatial order of atoms localized in one-dimensional optical lattices and we demonstrate the technique using and F = 1 → 1 transitions with lin ⊤ lin laser cooling fields. The latter transition gives a dark optical lattice. We show that the scattering by a spin grating, which may also be present, can be completely or partially filtered out by varying the polarizations of the cooling fields while holding the polarization of the probe and the detector analyser fixed. This allows the fraction of atoms that are localized to be measured. The probe field is treated as a pulse and so the technique also allows time-resolved details of the spatial structure to be studied.

In thermodynamics one considers thermal systems and the maximization of entropy subject to the conservation of energy. A consequence is Landauer's erasure principle, which states that the erasure of 1 bit of information requires a minimum energy cost equal to $kT\ln(2)$ where $T$ is the temperature of a thermal reservoir used in the process and $k$ is Boltzmann's constant. Jaynes, however, argued that the maximum entropy principle could be applied to any number of conserved quantities which would suggest that information erasure may have alternative costs. Indeed we showed recently that by using a reservoir comprising energy degenerate spins and subject to conservation of angular momentum, the cost of information erasure is in terms of angular momentum rather than energy. Here we extend this analysis and derive the minimum cost of information erasure for systems where different conservation laws operate. We find that, for each conserved quantity, the minimum resource needed to erase 1 bit of memory is $\lambda^{-1}\ln(2)$ where $\lambda$ is related to the average value of the conserved quantity. The costs of erasure depend, fundamentally, on both the nature of the physical memory element and the reservoir with which it is coupled., Comment: 7 pages, 3 figures

The problem of reconstructing a wavefunction from probability distributions is re-examined in the context of whether a pure state vector of a single-mode optical field can be reconstructed from the...

We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density operator of any quantum system. We suggest a possible experimental implementation in quantum optics., Comment: RevTex, picture not included - see remark, 5 pages

We show that entropic uncertainty relations for photon number and phase, angle and angular momentum and for position and momentum may be derived from the entropic uncertainty relation for conjugate observables in a finite dimensional state space.

The phase properties of an initially coherent field propagating through a Kerr medium are examined using two different measures of phase uncertainty: (i) variance of periodic functions and (ii) the entropy. The variance of a periodic function of phase (with period 2\ensuremath{\pi}/m) is found to be minimized only at the times when the field evolves into a discrete superposition of n distinguishable coherent states (Schr\"odinger-cat states) where n is a factor of m. The phase entropy is found to be more sensitive, as it is minimized at the times when the field evolves into a superposition of an arbitrary number of distinguishable coherent states. The sum of the photon number and phase entropies is found to display behavior very similar to the Wehrl entropy for the evolving field, i.e., the sum is minimal at the times the cat states occur, and at these times it has a value that indicates the number of component coherent states in the cat states.

We show how Bell's idea on proving non-locality in phase space can be realized in quantum optics. The experiment, however, involves the generation of an appropriate superposition of Fock states.

We extend the Pegg-Barnett formalism, which describes the phase of a single-mode light field and is based on finite-dimensional Hilbert spaces, to the infinite-dimensional case. The infinite-dimensional versions of the Pegg-Barnett phase operators operate on a linear vector space which contains the conventionally used infinite-dimensional Hilbert space as a subspace.

We present a new quasiprobability function defined on Fock space whose marginal distributions are the number and phase probability distributions of the single mode light field (or, equivalently, a harmonic oscillator). The new function is shown to have analogous properties to that of the Wigner function associated with the position and momentum observables. Examples are given of the new function for specific states.

We show that the antinormal ordering introduced for the Susskind-Glogower phase operators can be justified formally from the Pegg-Barnett Ψ -space formalism. The Susskind-Glogower operators are the weak limits on the infinite-dimensional Hilbert space H of the corresponding operators in the Pegg-Barnett formalism. Because the weak limit of a product of two sequences of operators is not necessarily the product of the respective weak limits of the two sequences it follows that the algebra of the Pegg-Barnett operators will not be preserved by their weak limits on H . However, we show that the antinormal ordering of the Susskind-Glogower operators is just what is required to preserve the algebra for the weak limits on H .

We derive relationships between canonical and measured phase distributions for quantum-oscillator states in the semiclassical regime. First, we extend the formalism for the canonical phase to include external measurement-induced uncertainty. We require that a phase shifter shifts a phase distribution while a number shifter does not change it. These axioms determine pure canonical phase distributions uniquely while a noisy distribution can be interpreted as a weighted average of pure phase distributions. As a second step, we show that measured phase distributions, i.e., s-parametrized phase distributions fulfill approximately the axioms of noisy canonical phase, and we derive simple analytical expressions for the corresponding weight functions. Our analysis thus bridges all three conceptions of quantum-optical phase (canonical phase, s-parametrized phase, phase from measurements) and provides important physical insight into the relationship between them.

The operator associated with the radially integrated Wigner function is found to lack justification as a phase operator., Comment: 4 pages + 2 figures. A comment on the paper arXiv:1009.4030v1 by T. Subeesh and V. Sudhir. Updated to the accepted journal version

We examine the effects of linear amplification and attenuation on the quantum-mechanical phase properties of light for fields with mean photon numbers of at least the order of 10. The phase probability density is found to satisfy a diffusion equation for both phase-insensitive and phase-sensitive amplifiers and attenuators. The solution is a convolution of the initial phase probability density with an infinite series of expanding Gaussians which clearly illustrates the diffusion of the phase. In particular, we find that for phase-insensitive amplification the phase of the field undergoes time-dependent uniform diffusion. In the limit of large amplification the diffusion ceases and the phase variance of the amplified light is given by the input phase variance plus an extra term which is equal to the phase variance of a coherent state of the same intensity as the initial field. We show that the reduced phase variance of phase-optimized states (relative to coherent states of the same intensity) is lost for power gains greater than the photon-cloning value of 2. In contrast, phase-sensitive amplifiers give rise to time-dependent nonuni form phase diffusion. The amount of phase diffusion depends on the relative phase angle between the light and the amplifier. If the peak of a relatively narrow phase probability density is near a minimum in the phase diffusion coefficient, then the phase noise added by the amplifier will be less than that found for a phase-insensitive amplifier. Further squeezing of the amplifier reduces the added phase noise proportionally. We find that it is possible, using phase-sensitive amplifiers, to amplify phaseoptimized states by power gains considerably larger than 2 and still retain a reduced phase variance.

Previous studies of the phase properties of optical linear amplifiers and attenuators have been restricted to situations where the effect on the phase of single-mode light is found to be diffusive. In this paper we give an analysis of phase-sensitive linear amplification and attenuation in the weak-field regime that clearly reveals a non-diffusive effect on the phase. Indeed we show that a weak field which has initially a uniform phase probability density can inherit non-random phase properties from both phase-sensitive attenuators and amplifiers. In contrast, we find that phase-insensitive amplifiers and attenuators have merely a diffusive effect on the phase of the light.

Objective. Because of the difficulty in determining patency of Double-J ureteral catheters, a study was devised at Madigan Army Medical Center to determine the best method to demonstrate stented ureteral patency. Methods. Forty-two patients requiring Double-J ureteral stenting for various clinical reasons were the study group. Outpatients underwent contrast retrograde cystography, nuclear cystography, and diuretic renography every four to six weeks during the stent duration or just prior to stent removal if the stents were indwelling for less than four weeks. In addition, four weeks after stent removal diuretic renography alone was done to evaluate for possible delayed obstructive effect of the ureteral stenting. Results. A total of 53 stents and 42 patients were evaluated. Seventy-seven sets of studies were obtained. In only four instances did all three imaging methods agree on the obstruction. In the remaining 73 sets of data, at least one imaging technique indicated stented ureteral patency. The contrast retrograde cystogram was positive for reflux 52 times (71 %). Nuclear cystography showed patency 54 times (74%) and an unobstructed diuretic renogram was obtained 59 times (81 %). In addition, five of the six diuretic renograms accomplished with patients in the supine position only and which showed obstruction were repeated with patients in the upright position, and they showed unobstructed function. The overall sensitivity for diuretic renography was 89 percent when the diuretic renogram was done with patients in the supine and upright positions. Conclusions. Diuretic renography is the most sensitive test for detecting stented ureteral patency. This test needs to be performed with patients in both the supine and upright positions.

The applicability is examined of the measured-phase operator describing a simple homodyne measurement scheme to states of the quantum optical field which have the minimum possible phase fluctuations. Such states necessarily have huge intensity fluctuations, so it is expected that this operator should be inapplicable because intensity fluctuations are deliberately ignored in its derivation. However, the surprising result found is that this operator can still provide a reasonably good approximation to the phase properties of fields even in this extreme limit.

Landauer argued that the process of erasing the information stored in a memory device incurs an energy cost in the form of a minimum amount of mechanical work. We find, however, that this energy cost can be reduced to zero by paying a cost in angular momentum or any other conserved quantity. Erasing the memory of Maxwell's demon in this way implies that work can be extracted from a single thermal reservoir at a cost of angular momentum and an increase in total entropy. The implications of this for the second law of thermodynamics are assessed., 8 pages with 1 figure. Final published version