Positivity violations of the density operator in the Caldeira-Leggett master equation

The Caldeira-Leggett master equation as an example of Markovian master equation without Lindblad form is investigated for mathematical consistency. We explore situations both analytically and numerically where the positivity violations of the density operator occur. We reinforce some known knowledge about this problem but also find new surprising cases. Our analytical results are based on the full solution of the Caldeira-Leggett master equation obtained via the method of characteristics. The preservation of positivity is mainly investigated with the help of the density operator's purity and we give also some numerical results about the violation of the Robertson-Schr\"odinger uncertainty relation.Comment: 13 pages, 12 figure

An entropy production based method for determining the position diffusion's coefficient of a quantum Brownian motion

Quantum Brownian motion of a harmonic oscillator in the Markovian approximation is described by the respective Caldeira-Leggett master equation. This master equation can be brought into Lindblad form by adding a position diffusion term to it. The coefficient of this term is either customarily taken to be the lower bound dictated by the Dekker inequality or determined by more detailed derivations on the linearly damped quantum harmonic oscillator. In this paper, we explore the theoretical possibilities of determining the position diffusion term's coefficient by analyzing the entropy production of the master equation.Comment: 13 pages, 10 figure

Ion beamlet steering for two-grid electrostatic thrusters

An experimental study of ion beamlet steering in which the direction of beamlets emitted from a two grid aperture system is controlled by relative translation of the grids, is described. The results can be used to design electrostatic accelerating devices for which the direction and focus of emerging beamlets are important. Deflection and divergence angle data are presented for two grid systems as a function of the relative lateral displacement of the holes in these grids. At large displacements, accelerator grid impingements become excessive and this determines the maximum allowable displacement and as a result the useful range of beamlet deflection. Beamlet deflection is shown to vary linearly with grid offset angle over this range. The divergence of the beamlets is found to be unaffected by deflection over the useful range of beamlet deflection. The grids of a typical dished grid ion thruster are examined to determine the effects of thermally induced grid distortion and prescribed offsets of grid hole centerlines on the characteristics of the emerging beamlets. The results are used to determine the region on the grid surface where ion beamlet deflections exceed the useful range. Over this region high accelerator grid impingement currents and rapid grid erosion are predicted

Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check

We investigate the exact master equation of Hu, Paz, and Zhang for a quantum harmonic oscillator at zero temperature with a Lorentz-Drude type Ohmic spectral density. This master equation plays an important role in the study of quantum Brownian motion and in various applications. In this paper, we give an analytical evaluation of the coefficients of this non-Markovian master equation without Lindblad form, which allows us to investigate consistencies of the solutions, the positivity of the stationary density operator, and the boundaries of the model's parameters.Comment: 17 pages, 8 figure

Range of applicability of the Hu-Paz-Zhang master equation

We investigate a case of the Hu-Paz-Zhang master equation of the Caldeira-Leggett model without Lindblad form obtained in the weak-coupling limit up to the second-order perturbation. In our study, we use Gaussian initial states to be able to employ a sufficient and necessary condition, which can expose positivity violations of the density operator during the time evolution. We demonstrate that the evolution of the non-Markovian master equation has problems when the stationary solution is not a positive operator, i.e., does not have physical interpretation. We also show that solutions always remain physical for small-times of evolution. Moreover, we identify a strong anomalous behavior, when the trace of the solution is diverging. We also provide results for the corresponding Markovian master equation and show that positivity violations occur for various types of initial conditions even when the stationary solution is a positive operator. Based on our numerical results, we conclude that this non-Markovian master equation is superior to the corresponding Markovian one.Comment: 14 pages, 19 figure

The diminishing state of shared reality on US television news

The potential for a large, diverse population to coexist peacefully is thought to depend on the existence of a ``shared reality:'' a public sphere in which participants are exposed to similar facts about similar topics. A generation ago, broadcast television news was widely considered to serve this function; however, since the rise of cable news in the 1990s, critics and scholars have worried that the corresponding fragmentation and segregation of audiences along partisan lines has caused this shared reality to be lost. Here we examine this concern using a unique combination of data sets tracking the production (since 2012) and consumption (since 2016) of television news content on the three largest cable and broadcast networks respectively. With regard to production, we find strong evidence for the ``loss of shared reality hypothesis:'' while broadcast continues to cover similar topics with similar language, cable news networks have become increasingly distinct, both from broadcast news and each other, diverging both in terms of content and language. With regard to consumption, we find more mixed evidence: while broadcast news has indeed declined in popularity, it remains the dominant source of news for roughly 50\% more Americans than does cable; moreover, its decline, while somewhat attributable to cable, appears driven more by a shift away from news consumption altogether than a growth in cable consumption. We conclude that shared reality on US television news is indeed diminishing, but is more robust than previously thought and is declining for somewhat different reasons

Newton's identities and positivity of trace class integral operators

We provide a countable set of conditions based on elementary symmetric polynomials that are necessary and sufficient for a trace class integral operator to be positive semidefinite, which is an important cornerstone for quantum theory in phase-space representation. We also present a new, efficiently computable algorithm based on Newton's identities. Our test of positivity is much more sensitive than the ones given by the linear entropy and Robertson-Schr\"odinger's uncertainty relations; our first condition is equivalent to the non-negativity of the linear entropy.Comment: 15 pages, 6 figure

Derandomizing Codes for the Binary Adversarial Wiretap Channel of Type II

We revisit the binary adversarial wiretap channel (AWTC) of type II in which an active adversary can read a fraction $r$ and flip a fraction $p$ of codeword bits. The semantic-secrecy capacity of the AWTC II is partially known, where the best-known lower bound is non-constructive, proven via a random coding argument that uses a large number (that is exponential in blocklength $n$) of random bits to seed the random code. In this paper, we establish a new derandomization result in which we match the best-known lower bound of $1-H_2(p)-r$ where $H_2(\cdot)$ is the binary entropy function via a random code that uses a small seed of only $O(n^2)$ bits. Our random code construction is a novel application of pseudolinear codes -- a class of non-linear codes that have $k$-wise independent codewords when picked at random where $k$ is a design parameter. As the key technical tool in our analysis, we provide a soft-covering lemma in the flavor of Goldfeld, Cuff and Permuter (Trans. Inf. Theory 2016) that holds for random codes with $k$-wise independent codewords

Wetting behaviour and reactivity between liquid Gd and ZrO2 substrate

The wetting behavior and reactivity between molten pure Gd and polycrystalline 3YSZ substrate (ZrO2 stabilized with 3 wt% of Y2O3)were experimentally determined by a sessile drop method using a classical contact heating coupled with drop pushing procedure. The test was performed under an inert flowing gas atmosphere (Ar) at two temperatures of 1362°C and 1412°C. Immediately after melting (Tm=1341°C), liquid Gd did not wet the substrate forming a contact angle of θ=141°. The non-wetting to wetting transition (θ < 90°) took place after about 110 seconds of interaction and was accompanied by a sudden decrease in the contact angle value to 67°. Further heating of the couple to 1412 °C did not affect wetting (θ=67°±1°). The solidified Gd/3YSZ couple was studied by means of optical microscopy and scanning electron microscopy coupled with X-ray energy dispersive spectroscopy. Structural investigations revealed that the wettability in the Gd/3YSZ system is of a reactive nature associated with the formation of a continuous layer of a wettable reaction product Gd2Zr2O7