Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation

Bistable systems present two degenerate metastable configurations separated by an energy barrier. Thermal or quantum fluctuations can promote the transition between the configurations at a rate which depends on the dynamical properties of the local environment (i.e., a thermal bath). In the case of classical systems, strong system-bath interaction has been successfully modelled by the Generalised Langevin Equation (GLE) formalism. Here we show that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014) can be extended to include some crucial aspects of the quantum fluctuations. In particular, the expected isotopic effect is observed along with the convergence of the quantum and classical transition rates in the strong coupling limit. Saturation of the transition rates at low temperature is also retrieved, in qualitative, yet not quantitative, agreement with the analytic predictions. The discrepancies in the tunnelling regime are due to an incorrect sampling close to the barrier top. The domain of applicability of the quasiclassical GLE is also discussed.Comment: 21 pages, 5 figures. Presented at the NESC16 conference: Advances in theory and simulation of non-equilibrium system

Applications of the Generalised Langevin Equation: towards a realistic description of the baths

The Generalised Langevin Equation (GLE) method, as developed in Ref. [Phys. Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalises toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.Comment: accepted for publication in PR

Relativistic precession around rotating neutron stars: Effects due to frame-dragging and stellar oblateness

General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the precession frequencies of circular orbits around rapidly rotating neutron stars for a variety of masses and equations of state. The precession frequencies computed are expressed as numerical functions of the orbital frequency observed at infinity. The post-Newtonian expansion of the exact precession formula is examined to identify the relative magnitudes of the precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole effect and relativistic corrections. The first post-Newtonian correction to the Newtonian quadrupole precession is derived in the limit of slow rotation. We show that the post-Newtonian precession formula is a good approximation to the exact precession close to the neutron star in the slow rotation limit (up to \sim 400 Hz in the present context). The results are applied to recent RXTE observations of neutron star low-mass X-ray binaries, which display kHz quasi-periodic oscillations and, within the framework of beat frequency models, allow the measurement of both the neutron star spin frequency and the Keplerian frequency of the innermost ring of matter in the accretion disk around it. For a wide range of realistic equations of state, we find that the predicted precession frequency of this ring is close to one half of the low-frequency (\sim 20 - 35 Hz) quasi-periodic oscillations seen in several Atoll sources.Comment: 35 pages including 10 figures and 6 tables. To appear in the Astrophysical Journa

Nonequilibrium processes from Generalised Langevin Equations: realistic nanoscale systems connected to two thermal baths

We extend the Generalised Langevin Equation (GLE) method [Phys. Rev. B 89, 134303 (2014)] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nose-Hoover thermostats). We concentrate on the steady state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e. ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.Comment: present version accepted for publication in Phys. Rev. B (Apr 2016

Steady-state analysis of shortest expected delay routing

We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with non-identical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product-forms that can be determined recursively. The resulting series expression is directly amenable for numerical calculations and it also provides insight in the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.Comment: 41 pages, 13 figure

Warping modes in discs around accreting neutron stars

The origin and stability of a thin sheet of plasma in the magnetosphere of an accreting neutron star is investigated. First the radial extension of such a magnetospheric disc is explored. Then a mechanism for magnetospheric accretion is proposed, reconsidering the bending wave explored by Agapitou, Papaloizou & Terquem (1997), that was found to be stable in ideal MHD. We show that this warping becomes unstable and can reach high amplitudes, in a variant of Pringle's radiation-driven model for the warping of AGN accretion discs (Pringle (1996)). Finally we discuss how this mechanism might give a clue to explain the observed X-ray kHz QPO of neutron star binaries.Comment: Accepted for publication in MNRA

Nonequilibrium Generalised Langevin Equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths

We use a Generalised Langevin Equation (GLE) scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B {\bf 93}, 174303 (2016)]. We consider model Al systems, i.e. one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length $N$ and the temperature difference $\Delta T$ between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures ($T \gtrsim 500$ K) and temperature differences ($\Delta T \gtrsim 500$ K), the chains, with $N > 18$ atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures($T \lesssim 500$ K) and temperature differences ($\Delta T \lesssim 400$ K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains ($N \le 15$). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.Comment: Accepted for publication in J. Chem. Phy

Exploring the Role of Organisational Trust in Mergers and Acquisitions M/A Processes in Family Firms

In recent years, mergers and acquisitions (M/As) of family firms have started to play a more crucial role. But despite its increasing relevance this topic has not yet been studied in the family firm context. The existing theories on organisational trust in the M/A process might not necessarily apply in the family firm M/A (FF M/A) context as these companies are somehow unique, especially since the employees’ organisational trust in the family firm owners tends to be a key dynamic in merging family firms. Therefore, this thesis wants to close an application gap in research and explore how organisational trust can be applied to the family firm M/A context. M/As of German midsized family firms are explored in two different studies. In the quantitative study 1 data was collected in an employee survey (N=352). Data for the qualitative study 2 consists of 21 semi-structured interviews. In this thesis I generate an organisational trust framework in the context of family firms that have undergone M/As. This framework is valuable because it shows how family firms can use their specific nature as an asset to maintain their employees’ organisational trust even after an M/A. Therefore, M/As of family firms tend to be the less risky option for family firms that need to sell their businesses, and a way for them to maintain or restore their organisational trust. The three main contributions are the following: Firstly, there is not necessarily a trust breach under the premise of a “responsible” outcome. Secondly, there is an observation period in the M/A process where family firm employees will reserve judgement on the new family firm. Thirdly, the process of trust regain after the observation period is primarily based on trustworthiness demonstrated by role models, and especially by the new family firm owners. The analysis further shows that it should be a major concern of merging family firms to develop a reasonable, trust-enhancing concept because of the major consequences of a trust loss, such as a decrease of commitment and engagement. So from a practical point of view, this work’s framework can help family firms to prevent the employees’ loss of organisational trust due to M/As, and to establish a trusting relationship after the acquisition

Anomalous scaling due to correlations: Limit theorems and self-similar processes

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, justify their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance.Comment: Through text revision. 15 pages, 3 figure

Future X-ray timing missions

Thanks to the Rossi X-ray Timing Explorer (RXTE), it is now widely recognized that fast X-ray timing can be used to probe strong gravity fields around collapsed objects and constrain the equation of state of dense matter in neutron stars. We first discuss some of the outstanding issues which could be solved with an X-ray timing mission building on the great successes of RXTE and providing an order of magnitude better sensitivity. Then we briefly describe the 'Experiment for X-ray timing and Relativistic Astrophysics' (EXTRA) recently proposed to the European Space Agency as a follow-up to RXTE and the related US mission 'Relativistic Astrophysics Explorer' (RAE).Comment: To be published in `Proceedings of the Third Microquasar Workshop: Granada Workshop on galactic relativistic jet sources', Eds A. J. Castro-Tirado, J. Greiner and J. M. Paredes, Astrophysics and Space Science, in press. More about EXTRA can be found at: http://www.cesr.fr/~barret/extra.htm