Quantum theory of an optical maser. 3 - Theory of photoelectron counting statistics
Photoelectron counting statistics produced by fully quantum mechanical laser
Lamb, W. E., Jr.↗
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Dynamical computation of photon correlations and counting statistics
Dynamical computation of photon correlations and counting statistics
PHOTON↗
Distinct universality classes of diffusive transport from full counting statistics
The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous site-resolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and nonintegrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. Here, we discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quantum theory of an optical maser. III - Theory of photoelectron counting statistics.
Quantum mechanics method for obtaining photocount distribution from optical maser photoelectron counting statistics
Lamb, W. E., Jr.↗
Full Counting Statistics of Charge in Chaotic Many-Body Quantum Systems
We investigate the full counting statistics of charge transport in U(1)-symmetric random unitary circuits. We consider an initial mixed state prepared with a chemical potential imbalance between the left and right halves of the system and study the fluctuations of the charge transferred across the central bond in typical circuits. Using an effective replica statistical mechanics model and a mapping onto an emergent classical stochastic process valid at large on-site Hilbert space dimension, we show that charge transfer fluctuations approach those of the symmetric exclusion process at long times, with subleading t –1/2 quantum corrections. Here, we discuss our results in the context of fluctuating hydrodynamics and macroscopic fluctuation theory of classical nonequilibrium systems and check our predictions against direct matrix-product state calculations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A Search for Neutrino Point-source Populations in 7 yr of IceCube Data with Neutrino-count Statistics
The presence of a population of point sources in a data set modifies the underlying neutrino-count statistics from the Poisson distribution. This deviation can be exactly quantified using the non-Poissonian template fitting technique, and in this work we present the first application of this approach to the IceCube high-energy neutrino data set. Using this method, we search in 7 yr of IceCube data for point-source populations correlated with the disk of the Milky Way, the Fermi bubbles, the Schlegel, Finkbeiner, and Davis dust map, or with the isotropic extragalactic sky. No evidence for such a population is found in the data using this technique, and in the absence of a signal, we establish constraints on population models with source-count distribution functions that can be described by a power law with a single break. Here, the derived limits can be interpreted in the context of many possible source classes. In order to enhance the flexibility of the results, we publish the full posterior from our analysis, which can be used to establish limits on specific population models that would contribute to the observed IceCube neutrino flux.
79 ASTRONOMY AND ASTROPHYSICS↗
Reduced Dynamics of Full Counting Statistics
We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Evidence of galaxy assembly bias in SDSS DR7 galaxy samples from count statistics
We present observational constraints on the galaxy–halo connection, focusing particularly on galaxy assembly bias from a novel combination of counts-in-cylinders statistics, P(N CIC ), with the standard measurements of the projected two-point correlation function w p (r p ), and number density n gal of galaxies. We measure n gal , w p (r p ), and P(N CIC ) for volume-limited, luminosity-threshold samples of galaxies selected from SDSS DR7, and use them to constrain halo occupation distribution (HOD) models, including a model in which galaxy occupation depends upon a secondary halo property, namely halo concentration. We detect significant positive central assembly bias for the M r < -20.0 and M r <-19.5 samples. Central galaxies preferentially reside within haloes of high concentration at fixed mass. Positive central assembly bias is also favoured in the M r < -20.5 and M r < -19.0 samples. We find no evidence of central assembly bias in the M r < -21.0 sample. We observe only a marginal preference for negative satellite assembly bias in the M r < -20.0 and M r < -19.0 samples, and non-zero satellite assembly bias is not indicated in other samples. Our findings underscore the necessity of accounting for galaxy assembly bias when interpreting galaxy survey data, and demonstrate the potential of count statistics in extracting information from the spatial distribution of galaxies, which could be applied to both galaxy–halo connection studies and cosmological analyses.
79 ASTRONOMY AND ASTROPHYSICS↗
Interpretation of gamma-ray burst source count statistics
Ever since the discovery of gamma-ray bursts, the so-called log N-log S relation has been used for determination of their distances and distribution. This task has not been straightforward because of varying thresholds for the detection of bursts. Most of the current analyses of these data are couched in terms of ambiguous distributions, such as the distribution of Cp/Clim, the ratio of peak to threshold photon count rates, or the distribution of V/Vmax = (Cp/Clim) exp -3/2. It is shown that these distributions are not always a true reflection of the log N-log S relation. Some kind of deconvolution is required for obtaining the true log N-log S. Therefore, care is required in the interpretation of results of such analyses. A new method of analysis of these data is described, whereby the bivariate distribution of Cp and Clim is obtained directly from the data.
Petrosian, Vahe↗
A convergence metric for counting statistics in time-resolved small angle neutron scattering
Here, this work introduces a model-independent, dimensionless metric for predicting optimal measurement duration in time-resolved small-angle neutron scattering using early-time data. Built on a Gaussian process regression framework, the method reconstructs scattering profiles with quantified uncertainty, even from sparse or noisy measurements. Demonstrated on the EQ-SANS instrument at the Spallation Neutron Source, the approach generalizes to general SANS instruments with a two-dimensional detector. A key result is the discovery of a dimensionless convergence metric revealing a universal power-law scaling in profile evolution across soft matter systems. When time is normalized by a system-specific characteristic time t*, the variation in inferred profiles collapses onto a single curve with an exponent between −2 and −1. This trend emerges within the first ten time steps, enabling early prediction of measurement sufficiency. The method supports real-time experimental optimization and is especially valuable for maximizing efficiency in low-flux environments such as compact accelerator-based neutron sources.
Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗
Effect of photon counting shot noise on total internal reflection microscopy
Total internal reflection microscopy (TIRM) measures changes in the distance between a colloidal particle and a transparent substrate by measuring the scattering intensity of the particle illuminated by an evanescent wave. From the distribution of the recorded separation distances, the height-dependent effective potential φ(z) between the colloidal particle and the substrate can be measured. In this work, we show that spatial resolution with which TIRM can measure φ(z) is limited by the photon counting statistics of the scattered laser light. Here, we develop a model to evaluate the effect of photon counting statistics on different potential profiles using Brownian dynamics simulations and experiments. Our results show that the effect of photon counting statistics depends on spatial gradients ∂φ/∂z of the potential, with the result that sharp features tend to be significantly blurred. We further establish the critical role of photon counting statistics and the intensity integration time τ in TIRM measurements, which is a trade-off between narrowing the width of the photon counting distribution and capturing the instantaneous position of the probe particle.
47 OTHER INSTRUMENTATION↗
The flat fielding and achievable signal-to-noise of the MAMA detectors
The Space Telescope Imaging Spectrograph (STIS) was designed to achieve a signal-to-noise (S/N) of at least 100:1 per resolution element. Multi-Anode Microchannel Arrays (MAMA) observations during Servicing Mission Orbital Verification (SMOV) confirm that this specification can be met. From analysis of a single spectrum of GD153, with counting statistics of approximately 165 a S/N of approximately 125 is achieved per spectral resolution element in the far ultraviolet (FUV) over the spectral range of 1280A to 1455A. Co-adding spectra of GRW+7OD5824 to increase the counting statistics to approximately 300 yields a S/N of approximately 190 per spectral resolution element over the region extending from 1347A to 1480A in the FUV. In the near ultraviolet (NUV), a single spectrum of GRW+7OD5824 with counting statistics of approximately 200 yields a S/N of approximately 150 per spectral resolution element over the spectral region extending from 2167 to 2520A. Details of the flat field construction, the spectral extraction, and the definition of a spectral resolution element will be described in the text.
Kaiser, Mary Elizabeth↗
Elemental Composition Variations for Large Dusty and Rocky Regions on Mars Using Gamma-Ray Data from the Mars Odyssey Gamma-Ray Spectrometer
The Gamma-Ray Spectrometer (GRS) on the Mars Odyssey spacecraft has been mapping the elemental composition of the surface materials since June 2002. To study elemental composition variations on the martian surface, seven large regions of Mars were selected: three very dusty ones and four mainly rocky ones. Large regions were used to get good counting statistics on as many gamma-ray peaks as possible from spectrum accumulated by the GRS experiment on Mars Odyssey, including elements with poor counting statistics. Data from TES were used to help select these regions. Gamma-ray peaks for several elements were analyzed. Some results and trends are reported.
Evans, L. G.↗
Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems
The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t 2/3 . This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The role of high resolution observations in determining energy release and transport processes
With present observations from the Solar Maximum Mission, we are seeing a very selective sample of spatially large flares in the soft part (10 to 50 keV) of the hard X-ray spectrum. The spatial resolution is at best 5600 km with a corresponding time resolution of 4.5 s for adequate count statistics. This resolution gives rise to the following problems: We cannot resolve the minor radii of the loops involved or tell where and how the energy release occurs. The manner in which loops interact and the relationship between the soft and hard or approx 00 keV) parts of hard X-rays remains elusive. We cannot see how energy propagates in most cases. Thus it is desirable to determine the minimum increase in spatial and temporal resolution required to solve these problems. Spatially we need to resolve the minor radius of a small loop which is about 800 km or 1 arc s. Upper limits to observed speeds of conduction fronts and shocks are approx km/s with theoretical limits running about a factor of 2 higher. Thus, a compatible minimum time resolution is in the range of 0.2 to 0.4 s. With these spatial and temporal resolutions, sufficient count statistics are required to go up to approx 120 keV with a sufficient number of energy bands to obtain spectra.
Smith, D. F.↗
Sensitive neutron transverse polarization analysis using a 3 He spin filter
Here we report an experimental implementation for neutron transverse polarization analysis that is capable of detecting a small angular change ($\ll$10 –3 rad) in neutron spin orientation. This approach is demonstrated for monochromatic beams, and we show that it could be extended to polychromatic neutron beams. Our approach employs a 3 He spin filter inside a solenoid with an analyzing direction perpendicular to the incident neutron polarization direction. The method was tested with polarized neutron beams and a spin rotator placed inside a μ -metal shield just upstream of the analyzer. No cryogenic superconducting shields or additional neutron spin manipulations are needed. With a counting detector, we experimentally show that the angular resolution δ θ = 1 / ( P n A N ) rad is only determined by the counting statistics for the total counts N and the product of the neutron polarization P n and the analyzing power A . With a high-flux neutron beam, 10 –6 rad angular sensitivity is feasible within a day. This simple, classical-quantum-limited transverse polarization analysis scheme may reduce the overall complexity of experimental implementation for applications requiring sensitive neutron polarimetry and improve the precision in fundamental science studies and polarized neutron imaging.
47 OTHER INSTRUMENTATION↗
Numerical least-square method for resolving complex pulse height spectra
Linear least-square method resolves complex pulse height spectra, allowing for calculation of relative intensity, of statistical variance based on counting statistics of the correlation between library components, and of the goodness-of-fit chi square. Some applications are to gamma-ray, X ray, and charged-particle spectroscopy.
Schmadebeck, R.↗
Towards a Counting Point Detector for Nanosecond Coherent X-ray Science
We present the technical realization of a high-speed hard X-ray single-photon counting-detection scheme based on a commercial avalanche silicon photodiode and high-speed oscilloscope. The development is motivated by the need to perform pulse-resolved photon-correlation and pump-probe studies at synchrotron sources with densely packed pulse patterns that result in high repetition rate pulses on the order of hundreds of MHz. Commissioning experiments are performed at the 1C PAL-KRISS beamline at PLS-II of South Korea operating at a burst mode maximum repetition rate of 500 MHz. In such a high count-rate measurement, detector dead-time can lead to a distortion of counting statistics. We are able to model the counting behavior of our detector under these conditions with a detector dead-time comparable to time between X-ray pulses, implying that nanosecond X-ray photon correlation spectroscopy should be possible at diffraction-limited light sources.
36 MATERIALS SCIENCE↗