Finding the Kraus decomposition from a master equation and vice versa

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is reviewed for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N^2 x N^2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalising a related N^2 x N^2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a `best possible' master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.Comment: 16 pages, no figures. Appeared in special issue for conference QEP-16, Manchester 4-7 Sep 200

Quantum phenomena modelled by interactions between many classical worlds

We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here a `world' means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach each world evolves deterministically; probabilities arise due to ignorance as to which world a given observer occupies; and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds. We introduce a simple model of such a 'many interacting worlds' approach and show that it can reproduce some generic quantum phenomena---such as Ehrenfest's theorem, wavepacket spreading, barrier tunneling and zero point energy---as a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach. We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the double-slit interference phenomenon.Comment: Published version (including further discussion of interpretation and quantum limit

The complexity of the California recall election

The October 7, 2003 California Recall Election strained California’s direct democracy. In recent California politics there has not been a statewide election conducted on such short notice; county election officials were informed on July 24 that the election would be held on October 7. Nor has California recently seen a ballot with so many candidates running for a single statewide office (see Mueller 1970). Under easy ballot access requirements, Secretary of State Kevin Shelley certified 135 candidates for the official ballot on August 13^1. In the recall, voters cast votes on (1) whether to recall Governor Davis from office, and (2) his possible successor. These two voting decisions were made independent by the federal district court’s decision on July 29. The court’s decision invalidated a state law requiring a vote on the recall question in order for a vote on the successor election to be counted (Partnoy et al. 2003). The abbreviated election calendar also led to many improvisations, including a dramatically reduced number of precinct poll sites throughout the state and the unprecedented ability of military personnel, their dependents, and civilians living overseas to return their absentee ballots by fax. These problems produced litigation and speculation that substantial problems would mar the election and throw the outcome of both the recall and a possible successor’s election into doubt. In the end, the litigation failed to stall the recall election, and the large final vote margins on both the recall question and the successor ballot seemingly overwhelmed Election Day problems. In this paper, we concentrate on some of the problems produced by the complexity of the recall election, but we do not attempt an exhaustive presentation of these problems. We focus on polling place problems on election day, the problems associated with translating the complicated recall election ballot into six languages, how the long ballot influenced voter behavior, and voter difficulties with the ballot measured with survey data. We conclude with a short discussion of the possible impact of these problems on the recall election

Performance Modeling of Virtualized Custom Logic Computations

Virtualization of custom logic computations (i.e., by sharing a fixed function across distinct data streams) provides a means of reusing hardware resources, particularly when resources are limited. This is common practice in traditional processors where more than one user can share processor resources. In this paper, we virtualize a custom logic block using C-slow techniques to support fine-grain context-switching. We then develop and present an analytic model for several performance measures (throughput, latency, input queue occupancy) for both fine-grained and coarse-grained context switching (to a secondary memory). Next, we calibrate the analytic performance model with empirical measurements. We then validate the model via discrete-event simulation and use the model to predict the performance and develop optimal schedules for virtualized logic computations. We present results for a Taylor series expansion of a cosine function with added feedback and an AES encryption cipher

No-till Forage Establishment in Alaska

We assessed the effectiveness of no-till forage establishment at six Alaska locations: Anchor Point, Sterling, Point MacKenzie, Palmer, Delta Junction, and Fairbanks. Directly seeding grass into established grass stands generally did not improve forage yields or quality. Seeding rate had little effect on establishment of newly seeded forages in no-till. Grass yields were depressed when companion crop yields were high, and they typically did not recover in subsequent years. Red clover established well, producing high yields of good quality forage under no-till at Point MacKenzie, but established poorly at Anchor Point and Delta Junction. These results indicated that no-till seeding of most forage crops into declining grass stands is not likely to be successful in Alaska with current available technology

Acoustic, psychophysical, and neuroimaging measurements of the effectiveness of active cancellation during auditory functional magnetic resonance imaging

Functional magnetic resonance imaging (fMRI) is one of the principal neuroimaging techniques for studying human audition, but it generates an intense background sound which hinders listening performance and confounds measures of the auditory response. This paper reports the perceptual effects of an active noise control (ANC) system that operates in the electromagnetically hostile and physically compact neuroimaging environment to provide significant noise reduction, without interfering with image quality. Cancellation was first evaluated at 600 Hz, corresponding to the dominant peak in the power spectrum of the background sound and at which cancellation is maximally effective. Microphone measurements at the ear demonstrated 35 dB of acoustic attenuation [from 93 to 58 dB sound pressure level (SPL)], while masked detection thresholds improved by 20 dB (from 74 to 54 dB SPL). Considerable perceptual benefits were also obtained across other frequencies, including those corresponding to dips in the spectrum of the background sound. Cancellation also improved the statistical detection of sound-related cortical activation, especially for sounds presented at low intensities. These results confirm that ANC offers substantial benefits for fMRI research

Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems

We prove that for quantum lattice systems in d<=2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T=0. For systems with continuous symmetry the statement extends up to d<=4 dimensions. This establishes for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr. The extension of the proof to quantum systems is achieved by carrying out the analysis at the level of thermodynamic quantities rather than equilibrium states.Comment: This article presents the detailed derivation of results which were announced in Phys. Rev. Lett. 103 (2009) 197201 (arXiv:0907.2419). v3 incorporates many corrections and improvements resulting from referee comment

The X-ray Spectrum and Spectral Energy Distribution of FIRST J155633.8+351758: a LoBAL Quasar with a Probable Polar Outflow

We report the results of a new 60 ks Chandra X-ray Observatory Advanced CCD Imaging Spectrometer S-array (ACIS-S) observation of the reddened, radio-selected, highly polarized `FeLoBAL' quasar FIRST J1556+3517. We investigated a number of models of varied sophistication to fit the 531-photon spectrum. These models ranged from simple power laws to power laws absorbed by hydrogen gas in differing ionization states and degrees of partial covering. Preferred fits indicate that the intrinsic X-ray flux is consistent with that expected for quasars of similarly high luminosity, i.e., an intrinsic, dereddened and unabsorbed optical to X-ray spectral index of -1.7. We cannot tightly constrain the intrinsic X-ray power-law slope, but find indications that it is flat (photon index Gamma = 1.7 or flatter at a >99% confidence for a neutral hydrogen absorber model). Absorption is present, with a column density a few times 10^23 cm^-2, with both partially ionized models and partially covering neutral hydrogen models providing good fits. We present several lines of argument that suggest the fraction of X-ray emissions associated with the radio jet is not large. We combine our Chandra data with observations from the literature to construct the spectral energy distribution of FIRST J1556+3517 from radio to X-ray energies. We make corrections for Doppler beaming for the pole-on radio jet, optical dust reddening, and X-ray absorption, in order to recover a probable intrinsic spectrum. The quasar FIRST J1556+3517 seems to be an intrinsically normal radio-quiet quasar with a reddened optical/UV spectrum, a Doppler-boosted but intrinsically weak radio jet, and an X-ray absorber not dissimilar from that of other broad absorption line quasars.Comment: to be published in MNRA