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Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian forms

It is shown that the fidelity of the dynamically evolved system with its earlier time-density matrix provides a signature of non-Markovian dynamics. Also, the fidelity associated with the initial state and the dynamically evolved state is shown to be larger in the non-Markovian evolution compared to that in the corresponding Markovian case. Starting from the Kraus representation of quantum evolution, the Markovian and non-Markovian features are discerned in its short-time structure. These two features are in concordance with each other and they are illustrated with the help of four models of interaction of the system with its environment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Adiabatically steered open quantum systems: Master equation and optimal phase

We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a nonsteered system in the first superadiabatic basis. It is potentially efficient in obtaining higher-order equations. Furthermore, we show how to select the phases of the adiabatic eigenstates to minimize the local adiabatic parameter and how this selection leads to states which are invariant under a local gauge change. We also discuss the effects of the adiabatic noncyclic geometric phase on the master equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-Markovian dynamics of an open quantum system with nonstationary coupling

The spectral, dissipative, and statistical properties of the damped quantum oscillator are studied in the case of non-Markovian and nonstationary system-heat bath coupling. The dissipation of collective energy is shown to be slowed down, and the decoherence rate and entropy grow with modulation frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Proceedings of the 2010 Monitoring Research Review: Ground-Based Nuclear Explosion Monitoring Technologies

These proceedings contain papers prepared for the Monitoring Research Review 2010: Ground-Based Nuclear Explosion Monitoring Technologies, held 21-23 September, 2010 in Orlando, Florida,. These papers represent the combined research related to ground-based nuclear explosion monitoring funded by the National Nuclear Security Administration (NNSA), Air Force Research Laboratory (AFRL), US Army Space and Missile Defense Command, National Science Foundation (NSF), Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO), and other invited sponsors. The scientific objectives of the research are to improve the United States capability to detect, locate, and identify nuclear explosions. The purpose of the meeting is to provide the sponsoring agencies, as well as potential users, an opportunity to review research accomplished during the preceding year and to discuss areas of investigation for the coming year. For the researchers, it provides a forum for the exchange of scientific information toward achieving program goals, and an opportunity to discuss results and future plans. Paper topics include: seismic regionalization and calibration; detection and location of sources; wave propagation from source to receiver; the nature of seismic sources, including mining practices; hydroacoustic, infrasound, and radionuclide methods; on-site inspection; and data processing.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Proceedings of the 2011 Monitoring Research Review: Ground-Based Nuclear Explosion Monitoring Technologies

These proceedings contain papers prepared for the Monitoring Research Review 2011: Ground-Based Nuclear Explosion Monitoring Technologies, held 13-15 September, 2011 in Tucson, Arizona. These papers represent the combined research related to ground-based nuclear explosion monitoring funded by the National Nuclear Security Administration (NNSA), Defense Threat Reduction Agency (DTRA), Air Force Research Laboratory (AFRL), US Army Space and Missile Defense Command, Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO), National Science Foundation (NSF), and other invited sponsors. The scientific objectives of the research are to improve the United States' capability to detect, locate, and identify nuclear explosions. The purpose of the meeting is to provide the sponsoring agencies, as well as potential users, an opportunity to review research accomplished during the preceding year and to discuss areas of investigation for the coming year. For the researchers, it provides a forum for the exchange of scientific information toward achieving program goals, and an opportunity to discuss results and future plans. Paper topics include: seismic regionalization and calibration; detection and location of sources; wave propagation from source to receiver; the nature of seismic sources, including mining practices; hydroacoustic, infrasound, and radionuclide methods; on-site inspection; and data processing.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Scalable and Memory-Efficient Algorithms for Controlling Networked Epidemic Processes Using Multiplicative Weights Update Method

We study the problem of designing scalable algorithms to find effective intervention strategies for controlling stochastic epidemic processes on networks. This is a common problem arising in agent based models for epidemic spread. Previous approaches to this problem focus on either heuristics with no guarantees or approximation algorithms that scale only to networks corresponding to county-sized populations, typically, with less than a million nodes. In particular, the mathematical-programming based approaches need to solve the Linear Program (LP) relaxation of the problem using an LP solver, which restricts the scalability of this approach. In this work, we overcome this restriction by designing an algorithm that adapts the multiplicative weights update (MWU) framework, along with the sample average approximation (SAA) technique, to approximately solve the linear program (LP) relaxation for the problem. To scale this approach further, we provide a memory-efficient algorithm that enables scaling to large networks, corresponding to country-size populations, with over 300 million nodes and 30 billion edges. Furthermore, we show that this approach provides near-optimal solutions to the LP in practice.

Sambaturu, Prathyush↗

REST-UV ABSORPTION LINES AS METALLICITY ESTIMATOR: THE METAL CONTENT OF STAR-FORMING GALAXIES AT z ∼ 5

We measure a relation between the depth of four prominent rest-UV absorption complexes and metallicity for local galaxies and verify it up to z∼3. We then apply this relation to a sample of 224 galaxies at 3.5 9 is characterized by 0.3–0.4 dex (in units of 12+log(O/H)) lower metallicities than at z ∼ 2, but comparable to z∼3.5. We find galaxies with weak or no Lyα emission to have metallicities comparable to z ∼ 2 galaxies and therefore may represent an evolved subpopulation of z∼5 galaxies. We find a correlation between metallicity and dust in good agreement with local galaxies and an inverse trend between metallicity and star-formation rate consistent with observations at z ∼ 2. The relation between stellar mass and metallicity (MZ relation) is similar to z∼3.5, but there are indications of it being slightly shallower, in particular for the young, Lyα-emitting galaxies. We show that, within a “bathtub” approach, a shallower MZ relation is expected in the case of a fast (exponential) build-up of stellar mass with an e-folding time of 100–200 Myr. Because of this fast evolution, the process of dust production and metal enrichment as a function of mass could be more stochastic in the first billion years of galaxy formation compared to later times.

79 ASTRONOMY AND ASTROPHYSICS↗

Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes

We develop a viscosity solution theory for a system of nonlinear degenerate parabolic integro-partial differential equations (IPDEs) related to stochastic optimal switching and control problems or stochastic games. In the case of stochastic optimal switching and control, we prove via dynamic programming methods that the value function is a viscosity solution of the IPDEs. In our setting the value functions or the solutions of the IPDEs are not smooth, so classical verification theorems do not apply.

97 MATHEMATICS AND COMPUTING↗

Three qubits in a symmetric environment: Dissipatively generated asymptotic entanglement

We study the asymptotic entanglement of three identical qubits under the action of a Markovian open system dynamics that does not distinguish them. We show that by adding a completely depolarized qubit to a special class of two-qubit states, by letting them reach the asymptotic state and by finally eliminating the added qubit, can provide more entanglement than by direct immersion of the two qubits within the same environment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Studying the effect of meteorological factors on the SO2 and PM10 pollution levels with refined versions of the SARIMA model

Numerous time series methods are used in environmental sciences allowing the detailed investigation of air pollution processes. The goal of this study is to present the empirical analysis of various aspects of stochastic modeling and in particular the ARIMA/SARIMA methods. The subject of investigation is air pollution in the town of Kardzhali, Bulgaria with 2 problematic pollutants – sulfur dioxide (SO2) and particulate matter (PM10). Various SARIMA Transfer Function models are built taking into account meteorological factors, data transformations and the use of different horizons selected to predict future levels of concentrations of the pollutants.

54 ENVIRONMENTAL SCIENCES↗

Nonlinear thermodynamic quantum master equation: Properties and examples

The quantum master equation obtained from two different thermodynamic arguments is seriously nonlinear. We argue that, for quantum systems, nonlinearity occurs naturally in the step from reversible to irreversible equations and we analyze the nature and consequences of the nonlinear contribution. The thermodynamic nonlinearity naturally leads to canonical equilibrium solutions and extends the range of validity to lower temperatures. We discuss the Markovian character of the thermodynamic quantum master equation and introduce a solution strategy based on coupled evolution equations for the eigenstates and eigenvalues of the density matrix. The general ideas are illustrated for the two-level system and for the damped harmonic oscillator. Several conceptual implications of the nonlinearity of the thermodynamic quantum master equation are pointed out, including the absence of a Heisenberg picture and the resulting difficulties with defining multitime correlations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations: A nanocavity coupled to a coupled-resonator optical waveguide

In this paper, the exact non-Markovian dynamics of open quantum systems in the presence of initial system-reservoir correlations is investigated for a photonic cavity system coupled to a general non-Markovian reservoir. The exact time-convolutionless master equation incorporating with initial system-reservoir correlations is obtained. The non-Markovian dynamics of the reservoir and the effects of the initial correlations are embedded into the time-dependent coefficients in the master equation. We show that the effects induced by the initial correlations play an important role in the non-Markovian dynamics of the cavity but they are washed out in the steady-state limit in the Markovian regime. Moreover, the initial two-photon correlation between the cavity and the reservoir can induce nontrivial squeezing dynamics to the cavity field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Characterization of decoherence from an environmental perspective

For the case of phase damping (pure decoherence) we investigate the extent to which environmental traits are imprinted on an open quantum system. The dynamics is described using the quantum channel approach. We study what the knowledge of the channel may reveal about the nature of its underlying dynamics and, conversely, what the dynamics tell us about how to consistently model the environment. We find that, for a Markov phase-damping channel (i.e., a channel compatible with a time-continuous Markovian evolution), the environment may adequately be represented by a mixture of only a few coherent states. For arbitrary Hilbert space dimension N{>=}4 we refine the idea of quantum phase damping, for which we show a means of identification. Symmetry considerations are used to identify decoherence-free subspaces of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Excitation energy transfer: Study with non-Markovian dynamics

In this paper, we investigate the non-Markovian dynamics of a model to mimic the excitation energy transfer (EET) between chromophores in photosynthesis systems. The numerical path integral method is used. This method includes the non-Markovian effects of the environmental affects, and it does not need the perturbation approximation in solving the dynamics of systems of interest. It implies that the coherence helps the EET between chromophores through lasting the transfer time rather than enhancing the transfer rate of the EET. In particular, the non-Markovian environment greatly increases the efficiency of the EET in the photosynthesis systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

The relationship between anatomic noise and volumetric breast density for digital mammography

Purpose: The appearance of parenchymal/stromal patterns in mammography have been characterized as having a Wiener power spectrum with an inverse power-law shape described by the exponential parameter, {beta}. The amount of fibroglandular tissue, which can be quantified in terms of volumetric breast density (VBD), influences the texture and appearance of the patterns formed in a mammogram. Here, a large study is performed to investigate the variations in {beta} in a clinical population and to indicate the relationship between {beta} and breast density. Methods: From a set of 2686 cranio-caudal normal screening mammograms, the parameter {beta} was extracted from log-log fits to the Wiener spectrum over the range 0.15-1 mm{sup -1}. The Wiener spectrum was calculated from regions of interest in the compression paddle contact region of the breast. An in-house computer program, Cumulus V, was used to extract the volumetric breast density and identify the compression paddle contact regions of the breast. The Wiener spectra were calculated with and without modulation transfer function (MTF) correction to determine the impact of VBD on the intrinsic anatomic noise. Results: The mean volumetric breast density was 25.5% ({+-}12.6%) over all images. The mean {beta} following a MTF correction which decreased the {beta} slightly ( Almost-Equal-To -0.08) was found to be 2.87. Varying the maximum of the spatial frequency range of the fits from 0.7 to 1.0, 1.25 or 1.5 mm{sup -1} showing small decreases in the result, although the effect of the quantum noise power component on reducing {beta} was clearly observed at 1.5 mm{sup -1}. Conclusions: The texture parameter, {beta}, was found to increase with VBD at low volumetric breast densities with an apparent leveling off at higher densities. The relationship between {beta} and VBD measured here can be used to create probabilistic models for computer simulations of detectability. As breast density is a known risk predictor for breast cancer, the correlation between {beta} and VBD suggests that {beta} may provide predictive information and this will be investigated in the future.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Toward in vivo lung's tissue incompressibility characterization for tumor motion modeling in radiation therapy

Purpose: A novel technique is proposed to characterize lung tissue incompressibility variation during respiration. Estimating lung tissue incompressibility parameter variations resulting from air content variation throughout respiration is critical for computer assisted tumor motion tracking. Continuous tumor motion is a major challenge in lung cancer radiotherapy, especially with external beam radiotherapy. If not accounted for, this motion may lead to areas of radiation overdosage for normal tissue. Given the unavailability of imaging modality that can be used effectively for real-time lung tumor tracking, computer assisted approach based on tissue deformation estimation can be a good alternative. This approach involves lung biomechanical model where its fidelity depends on input tissue properties. This investigation shows that considering variable tissue incompressibility parameter is very important for predicting tumor motion accurately, hence improving the lung radiotherapy outcome. Methods: First, an in silico lung phantom study was conducted to demonstrate the importance of employing variable Poisson's ratio for tumor motion predication. After it was established that modeling this variability is critical for accurate tumor motion prediction, an optimization based technique was developed to estimate lung tissue Poisson's ratio as a function of respiration cycle time. In this technique, the Poisson's ratio and lung pressure value were varied systematically until optimal values were obtained, leading to maximum similarity between acquired and simulated 4D CT lung images. This technique was applied in an ex vivo porcine lung study where simulated images were constructed using the end exhale CT image and deformation fields obtained from the lung's FE modeling of each respiration time increment. To model the tissue, linear elastic and Marlow hyperelastic material models in conjunction with variable Poisson's ratio were used. Results: The phantom study showed that the tumor motion trajectory and its final locations obtained from simulations with and without considering tissue incompressibility variation were very different. For example, tumor displacements in the z direction were -11.23 and -38.10 mm obtained with the Marlow hyperelastic material model in conjunction with constant and variable Poisson's ratio, respectively. By comparing the acquired 4D-CT image sequence of the porcine lung with their image sequence counterparts obtained from the hyperelastic model with constant and variable Poisson's ratio, it was shown that using variable tissue incompressibility reduced errors significantly in tumor motion prediction. Conclusions: This investigation demonstrates the importance of incompressibility variation estimation and utilization for accurate tumor tracking in computer assisted lung external beam radiation therapy. An optimization framework was developed to estimate a Poisson's ratio function in terms of respiration cycle time using experimental image data of the lung. Utilizing this function along with respiratory system FE modeling may lead to more effective tumor targeting, hence potentially improving the outcome of lung external beam radiation therapy techniques. This is particularly true for stereotactic body radiation therapy where only one or a few fraction treatments are applied, precluding the possibility of averaging out dosimetric deviations introduced by the respiratory motion.

60 APPLIED LIFE SCIENCES↗