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The thermodynamic stability of quantized vortex patterns in rotating Bose-Einstein condensates is assessed at finite temperature using complex Langevin sampling. We construct a temperature-rotation frequency phase diagram and find that that vortices are stabilized at lower rotation speeds by the addition of quantum and thermal fluctuations. The coherent states field theoretic representation of the imaginary time path integral enables efficient simulation of large systems at finite temperature, and the complex Langevin simulation scheme bypasses the sign problems that arise from the complex-valued coherent states fields as well as the gauge potential describing solid body rotation. Field operators allow us to generate high-resolution images of particle and momentum density of the cloud. Quantized vortices appear as dark spots on density images, and vector plots of cloud momentum detail circulation around each vortex.

Can quantum mechanical thermodynamic engines outperform their classical counterparts? To address one aspect of this question, we experimentally realize and characterize an isentropic thermodynamic engine that uses a Bose-condensed working fluid. In this engine, an interacting quantum degenerate gas of bosonic lithium is subjected to trap compression and relaxation strokes interleaved with strokes strengthening and weakening interparticle interactions. We observe a significant enhancement in efficiency and power when using a Bose-condensed working fluid, compared to the case of a non-degenerate thermal gas. We demonstrate reversibility, and measure power and efficiency as a function of engine parameters including compression ratio and cycle time. Results agree quantitatively with interacting finite temperature field-theoretic simulations that closely replicate the length and energy scales of the working fluid., Comment: 8 pages, 6 figures

This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx {{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance, $k$ is a real wavenumber, and $\omega(k)$ is a wavelength-dependent complex frequency. In a previous paper, King et al (Stability of algebraically unstable dispersive flows, \textit{Phys. Rev. Fluids}, 1(073604), 2016) demonstrates that when Im$[\omega(k)]$=0 for all $k$, it is possible for a system response to grow or damp algebraically as $h\approx {{t}^{s}}$ where $s$ is a fractional power. The growth is deduced through an asymptotic analysis of the Fourier integral that inherently invokes the superposition of an infinite number of modes. In this paper, the more typical case associated with the transition from stability to instability is examined in which Im$[\omega(k)]$=0 for a single mode (i.e., for one value of $k$) at neutral stability. Two partial differential equation systems are examined, one that has been constructed to elucidate key features of the stability threshold, and a second that models the well-studied problem of rectilinear Newtonian flow down an inclined plane. In both cases, algebraic growth/decay is deduced at the neutral stability boundary, and the propagation features of the responses are examined.

We analyze extensions of the Poisson process in which any interarrival time that exceeds a fixed value $r$ is counted as an interarrival of duration $r$. In the engineering application that initiated this work, one part is tested at a time, and $N(t)$ is the number of parts that, by time $t$, have either failed, or if they have reached age $r$ while still functioning, have been replaced. We refer to $\{N(t), t \geq 0\}$ as a replace-after-fixed-time process. We extend this idea to the case where the replacement time for the process is itself random, and refer to the resulting doubly stochastic process as a replace-after-random-time process.