Clock shift in a strongly interacting two-dimensional Fermi gas

We derive universal relations for the radio-frequency (rf) spectroscopy of a two-dimensional Fermi gas consisting of two spin states with a resonant S-wave interaction. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like $1/(\omega^2 \ln^2 \omega)$. Its coefficient is proportional to $\ln^2(a_{2D}'/a_{2D})$, where $a_{2D}$ and $a_{2D}'$ are the 2-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to $\ln(a_{2D}'/a_{2D})$. If $|\ln(a_{2D}'/a_{2D})| \gg 1$, the clock shift arises as a cancellation between much larger contributions proportional to $\ln^2(a_{2D}'/a_{2D})$ from bound-bound and bound-free rf transitions.Comment: 4 pages, 1 figur

Quantum Fluctuations in the Chirped Pendulum

An anharmonic oscillator when driven with a fast, frequency chirped voltage pulse can oscillate with either small or large amplitude depending on whether the drive voltage is below or above a critical value-a well studied classical phenomenon known as autoresonance. Using a 6 GHz superconducting resonator embedded with a Josephson tunnel junction, we have studied for the first time the role of noise in this non-equilibrium system and find that the width of the threshold for capture into autoresonance decreases as the square root of T, and saturates below 150 mK due to zero point motion of the oscillator. This unique scaling results from the non-equilibrium excitation where fluctuations, both quantum and classical, only determine the initial oscillator motion and not its subsequent dynamics. We have investigated this paradigm in an electrical circuit but our findings are applicable to all out of equilibrium nonlinear oscillators.Comment: 5 pages, 4 figure

Tomografische Rekonstruktion der Raumtemperaturverteilung aus einer Raumimpulsantwort

Temperature can be estimated by acoustic propagation time measurements along known sound paths. By using a multitude of known sound paths in combination with a tomographic reconstruction technique a spatial and temporal resolution of the temperature field can be achieved. Based on it, this article focuses on an experimental method in order to determine the spatially differentiated development of room temperature with only one loudspeaker and one microphone. The theory of geometrical room acoustics is being used to identify sound paths under consideration of reflections. The propagation time along a specific sound path is derived from the room impulse response. Temporal variances in room impulse response can be attributed primarily to a change in air temperature and airflow. It is shown that in the absence of airflow a three-dimensional acoustic monitoring of the room temperature can be realized with a fairly limited use of hardware.Die Temperatur kann mithilfe von akustischen Laufzeitmessungen auf definierten Schallstrecken ermittelt werden. Der Einsatz multipler Schallstrecken, in Verbindung mit einem tomografischen Rekonstruktionsverfahren, erlaubt eine räumliche Auflösung der genannten klimatologischen Größe. Aufbauend darauf, befasst sich dieser Artikel mit einer experimentellen Methode zur Erfassung der räumlich und zeitlich aufgelösten Entwicklung der Raumtemperatur mit lediglich einem Lautsprecher und einem Mikrofon. Die Theorie der geometrischen Raumakustik wird genutzt, um Schallstrecken, unter der Berücksichtigung von Reflexionen, zu identifizieren. Die zu den Ausbreitungswegen gehörenden Laufzeiten werden aus einer gemessenen Raumimpulsantwort abgeleitet. Zeitliche Varianzen in Raumimpulsantworten sind in erster Linie auf die Veränderung der Lufttemperatur und von Strömungsverhältnissen zurückzuführen. Es wird gezeigt, dass bei Abwesenheit von Raumluftströmungen, eine dreidimensionale, akustische Überwachung der Raumtemperatur mit einem sehr geringen Einsatz an Messtechnik realisiert werden kann

Clinically relevant dual probe difference specimen imaging (DDSI) protocol for freshly resected breast cancer specimen staining

Background: Re-excision rates following breast conserving surgery (BCS) remain as high as ~ 35%, with positive margins detected during follow-up histopathology. Additional breast cancer resection surgery is not only taxing on the patient and health care system, but also delays adjuvant therapies, increasing morbidity and reducing the likelihood of a positive outcome. The ability to precisely resect and visualize tumor margins in real time within the surgical theater would greatly benefit patients, surgeons and the health care system. Current tumor margin assessment technologies utilized during BCS involve relatively lengthy and labor-intensive protocols, which impede the surgical work flow. Methods: In previous work, we have developed and validated a fluorescence imaging method termed dual probe difference specimen imaging (DDSI) to accurately detect benign and malignant tissue with direct correlation to the targeted biomarker expression levels intraoperatively. The DDSI method is currently on par with touch prep cytology in execution time (~ 15-min). In this study, the main goal was to shorten the DDSI protocol by decreasing tissue blocking and washing times to optimize the DDSI protocol to \u3c 10-min whilst maintaining robust benign and malignant tissue differentiation. Results: We evaluated the utility of the shortened DDSI staining methodology using xenografts grown from cell lines with varied epidermal growth factor receptor (EGFR) expression levels, comparing accuracy through receiver operator characteristic (ROC) curve analyses across varied tissue blocking and washing times. An optimized 8-min DDSI methodology was developed for future clinical translation. Conclusions: Successful completion of this work resulted in substantial shortening of the DDSI methodology for use in the operating room, that provided robust, highly receptor specific, sensitive diagnostic capabilities between benign and malignant tissues

Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh

Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in 2D and 3D. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA

Tan relations in one dimension

We derive exact relations that connect the universal $C/k^4$-decay of the momentum distribution at large $k$ with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact interactions. The relations are analogous to those obtained by Tan in the three-dimensional case and are derived from an operator product expansion of the one- and two-particle density matrix. They extend earlier results by Olshanii and Dunjko [Phys. Rev. Lett. 91, 090401 (2003)] for the bosonic Lieb-Liniger gas. As an application, we calculate the pair distribution function at short distances and the dimensionless contact in the limit of infinite repulsion. The ground state energy approaches a universal constant in this limit, a behavior that also holds in the three-dimensional case. In both one and three dimensions, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.Comment: 8 figures, 27 pages - Updated to status of published versio

Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy

We study the excitation energy for slow changes of the hopping parameter in the Falicov-Kimball model with nonequilibrium dynamical mean-field theory. The excitation energy vanishes algebraically for long ramp times with an exponent that depends on whether the ramp takes place within the metallic phase, within the insulating phase, or across the Mott transition line. For ramps within metallic or insulating phase the exponents are in agreement with a perturbative analysis for small ramps. The perturbative expression quite generally shows that the exponent depends explicitly on the spectrum of the system in the initial state and on the smoothness of the ramp protocol. This explains the qualitatively different behavior of gapless (e.g., metallic) and gapped (e.g., Mott insulating) systems. For gapped systems the asymptotic behavior of the excitation energy depends only on the ramp protocol and its decay becomes faster for smoother ramps. For gapless systems and sufficiently smooth ramps the asymptotics are ramp-independent and depend only on the intrinsic spectrum of the system. However, the intrinsic behavior is unobservable if the ramp is not smooth enough. This is relevant for ramps to small interaction in the fermionic Hubbard model, where the intrinsic cubic fall-off of the excitation energy cannot be observed for a linear ramp due to its kinks at the beginning and the end.Comment: 24 pages, 6 figure