Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in \cite{Ristivojevic} and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan's contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions

Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature

We study the effect of thermal and quantum fluctuations on the dynamical response of a one-dimensional strongly-interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeau-impenetrable-boson limit to obtain the dynamic structure factor of the strongly-interacting fluid at finite temperature. Then, we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.Comment: 13 pages, 11 figure

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of non-analyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of $\mathbb{Z}_2$ symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.Comment: journal article, 15 pages, 12 figures. Final versio

Fast logarithmic Fourier-Laplace transform of nonintegrable functions

We present an efficient and very flexible numerical fast Fourier-Laplace transform, that extends the logarithmic Fourier transform (LFT) introduced by Haines and Jones [Geophys. J. Int. 92(1):171 (1988)] for functions varying over many scales to nonintegrable functions. In particular, these include cases of the asymptotic form $f(\nu\to0)\sim\nu^a$ and $f(|\nu|\to\infty)\sim\nu^b$ with arbitrary real $a>b$. Furthermore, we prove that the numerical transform converges exponentially fast in the number of data points, provided that the function is analytic in a cone $|\Im{\nu}|<\theta|\Re{\nu}|$ with a finite opening angle $\theta$ around the real axis and satisfies $|f(\nu)f(1/\nu)|<\nu^c$ as $\nu\to 0$ with a positive constant $c$, which is the case for the class of functions with power-law tails. Based on these properties we derive ideal transformation parameters and discuss how the logarithmic Fourier transform can be applied to convolutions. The ability of the logarithmic Fourier transform to perform these operations on multiscale (non-integrable) functions with power-law tails with exponentially small errors makes it the method of choice for many physical applications, which we demonstrate on typical examples. These include benchmarks against known analytical results inaccessible to other numerical methods, as well as physical models near criticality.Comment: 14 pages, 8 figure

On the Transition from Accretion Powered to Rotation Powered Millisecond Pulsars

The heating associated with the deposition of $\gamma$-rays in an accretion disk is proposed as a mechanism to facilitate the transformation of a low mass X-ray binary to the radio millisecond pulsar phase. The $\gamma$-ray emission produced in the outer gap accelerator in the pulsar magnetosphere likely irradiates the surrounding disk, resulting in its heating and to the possible escape of matter from the system. We apply the model to PSR J1023+0038, which has recently been discovered as a newly born rotation powered millisecond pulsar. The predicted $\gamma$-ray luminosity $\sim 6 \times 10^{34}~\mathrm{erg~s^{-1}}$ can be sufficient to explain the disappearance of the truncated disk existing during the 8~month$\sim 2$~yr period prior to the 2002 observations of J1023+0038 and the energy input required for the anomalously bright optical emission of its companion star.Comment: 13 pages, 3 figures, accepted in ApJ

Energy Management for Hypervisor-Based Virtual Machines

Current approaches to power management are based on operating systems with full knowledge of and full control over the underlying hardware; the distributed nature of multi-layered virtual machine environments renders such approaches insufficient. In this paper, we present a novel framework for energy management in modular, multi-layered operating system structures. The framework provides a unified model to partition and distribute energy, and mechanisms for energy-aware resource accounting and allocation. As a key property, the framework explicitly takes the recursive energy consumption into account, which is spent, e.g., in the virtualization layer or subsequent driver components. Our prototypical implementation targets hypervisor- based virtual machine systems and comprises two components: a host-level subsystem, which controls machine-wide energy constraints and enforces them among all guest OSes and service components, and, complementary, an energy-aware guest operating system, capable of fine-grained applicationspecific energy management. Guest level energy management thereby relies on effective virtualization of physical energy effects provided by the virtual machine monitor. Experiments with CPU and disk devices and an external data acquisition system demonstrate that our framework accurately controls and stipulates the power consumption of individual hardware devices, both for energy-aware and energyunaware guest operating systems

Amplitude distribution of stochastic oscillations in biochemical networks due to intrinsic noise

Intrinsic noise is a common phenomenon in biochemical reaction networks and may affect the occurence and amplitude of sustained oscillations in the states of the network. To evaluate properties of such oscillations in the time domain, it is usually required to conduct long-term stochastic simulations, using for example the Gillespie algorithm. In this paper, we present a new method to compute the amplitude distribution of the oscillations without the need for long-term stochastic simulations. By the derivation of the method, we also gain insight into the structural features underlying the stochastic oscillations. The method is applicable to a wide class of non-linear stochastic differential equations that exhibit stochastic oscillations. The application is exemplified for the MAPK cascade, a fundamental element of several biochemical signalling pathways. This example shows that the proposed method can accurately predict the amplitude distribution for the stochastic oscillations even when using further computational approximations

Dynamical Quantum Phase Transitions: A Geometric Picture

The Loschmidt echo (LE) is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model (FC-TFIM) as an example, we show that this indeed is not the case, and that a simple semiclassical approximation to systems well described by mean-field theory (MFT) is in fact in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the post-quench dynamics provided in the supplemental material visualize this new point of view.Comment: Accepted version. 7 pages with 4 Figures in main file. 3 pages including 2 Figures of supplemental material. 3 videos linked in the references of the main fil

Administration of Tramadol or Buprenorphine via the drinking water for post-operative analgesia in a mouse-osteotomy model

Adequate analgesia is essential whenever pain might occur in animal experiments. Unfortunately, the selection of suitable analgesics for mice in bone-linked models is limited. Here, we evaluated two analgesics - Tramadol [0.1 mg/ml (Tlow) vs. 1 mg/ml (Thigh)] and Buprenorphine (Bup; 0.009 mg/ml) - after a pre-surgical injection of Buprenorphine, in a mouse-osteotomy model. The aim of this study was to verify the efficacy of these opioids in alleviating pain-related behaviors, to provide evidence for adequate dosages and to examine potential side effects. High concentrations of Tramadol affected water intake, drinking frequency, food intake and body weight negatively in the first 2-3 days post-osteotomy, while home cage activity was comparable between all groups. General wellbeing parameters were strongly influenced by anesthesia and analgesics. Model-specific pain parameters did not indicate more effective pain relief at high concentrations of Tramadol. In addition, ex vivo high-resolution micro computed tomography (µCT) analysis and histology analyzing bone healing outcomes showed no differences between analgesic groups with respect to newly formed mineralized bone, cartilage and vessels. Our results show that high concentrations of Tramadol do not improve pain relief compared to low dosage Tramadol and Buprenorphine, but rather negatively affect animal wellbeing