Search results for " equilibrium."
showing 10 items of 518 documents
Ein iteratives numerisches verfahren zur auswertung von elutionsanalysen an eng verteilten polymeren
1972
Ein iteratives Rechenverfahren zur Bestimmung der Molekulargewichtsverteilungsfunktionen aus experimentellen, mit der isothermen Elution ermittelten Daten – speziell fur Polymere kleiner Uneinheitlichkeit – wird beschrieben. Hierbei wird die klassisch gewonnene Verteilung als Naherung betrachtet, rechnerisch auf der Basis des Phasengleichgewichts erneut fraktioniert und aus den ermittelten Fraktionen die Zusatzinformation zur Konstruktion einer besseren Naherung gewonnen. Um die Stabilitat der Konvergenz des Verfahrens zu zeigen, wurde eine Simulationsrechnung durchgefuhrt. Schlieslich wird das Verfahren an experimentell gewonnenen Daten eines aus zwei gut bekannten, eng verteilten Polystyr…
ERGODICITY IN RANDOMLY COLLIDING QUBITS
2009
The dynamics of a single qubit randomly colliding with an environment consisting of just two qubits is discussed. It is shown that the system reaches an equilibrium state which coincides with a pure random state of three qubits. Furthermore the time average and the ensemble averages of the quantities used to characterize the approach to equilibrium (purity and tangles) coincide, a signature of ergodic behavior.
Robust control of unstable nonlinear quantum systems
2020
Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that, in the context of driven nonlinear Hamiltonian systems, adiabatic passage becomes highly non-robust when the target is unstable. We show this result for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point in the classical phase space featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially non-adiabatic trajectories. They localize at the approach of the target near the stable manifold of the separatrix, which drives the dynamics towards the ta…
Scale-free relaxation of a wave packet in a quantum well with power-law tails
2013
We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.
Atomic transition probabilities of F I spectral lines from3s−3pand3p−3dtransition arrays
1999
We have measured the relative transition probabilities of about $100 3s\ensuremath{-}3p$ and $3p\ensuremath{-}3d$ lines of neutral fluorine in the visible and near-infrared spectrum with a wall-stabilized high-current arc, which is operated under conditions very close to partial local thermodynamic equilibrium. The set of measured lines includes about 40 intersystem transitions. Our data have been placed on an absolute scale by normalizing several strong transitions to the results of the OPACITY Project calculations, which are expected to be quite accurate for such transitions. We estimate that the uncertainties of our absolute transition probability values are in the \ifmmode\pm\else\textp…
Minimum main sequence mass in quadratic Palatini f(R) gravity
2019
General relativity yields an analytical prediction of a minimum required mass of roughly $\ensuremath{\sim}0.08--0.09\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for a star to stably burn sufficient hydrogen to fully compensate photospheric losses and, therefore, to belong to the main sequence. Those objects below this threshold (brown dwarfs) eventually cool down without any chance to stabilize their internal temperature. In this work we consider quadratic Palatini $f(\mathcal{R})$ gravity and show that the corresponding Newtonian hydrostatic equilibrium equation contains a new term whose effect is to introduce a weakening/strengthening of the gravitational interaction inside astrophysical…
One-dimensional Ising-like systems: an analytical investigation of the static and dynamic properties, applied to spin-crossover relaxation
2000
We investigate the dynamical properties of the 1-D Ising-like Hamiltonian taking into account short and long range interactions, in order to predict the static and dynamic behavior of spin crossover systems. The stochastic treatment is carried out within the frame of the local equilibrium method [1]. The calculations yield, at thermodynamic equilibrium, the exact analytic expression previously obtained by the transfer matrix technique [2]. We mainly discuss the shape of the relaxation curves: (i) for large (positive) values of the short range interaction parameter, a saturation of the relaxation curves is observed, reminiscent of the behavior of the width of the static hysteresis loop [3]; …
Truncated thermalization of incoherent optical waves through supercontinuum generation in photonic crystal fibers
2013
We revisit the process of optical wave thermalization through supercontinuum generation in photonic crystal fibers. We report theoretically and numerically a phenomenon of `truncated thermalization': The incoherent optical wave exhibits an irreversible evolution toward a Rayleigh-Jeans thermodynamic equilibrium state characterized by a compactly supported spectral shape. The theory then reveals the existence of a frequency cut-off which regularizes the ultraviolet catastrophe inherent to ensembles of classical nonlinear waves. This phenomenon sheds new light on the mechanisms underlying the formation of bounded supercontinuum spectra in photonic crystal fibers.
Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators
2018
This paper deals with collisionless transport equationsin bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonallyinvariant velocity measure $\bm{m}(\d v)$ with support $V\subset \R^{d}$ and stochastic partly diffuse boundary operators $\mathsf{H}$ relating the outgoing andincoming fluxes. Under very general conditions, such equations are governedby stochastic $C_{0}$-semigroups $\left( U_{\mathsf{H}}(t)\right) _{t\geq 0}$ on $%L^{1}(\Omega \times V,\d x \otimes \bm{m}(\d v)).$ We give a general criterion of irreducibility of $%\left( U_{\mathsf{H}}(t)\right) _{t\geq 0}$ and we show that, under very natural assumptions, if an …
Propagation of fourth sound in turbulent superfluids via extended thermodynamics
2011
The work deals with further developments of a study previously initiated, in which a macroscopic one-fluid model of inhomogeneous turbulent superfluids, based on extended thermodynamics, had been formulated. In this work the study is carried on. First the influence of the remnant vortices on the propagation of the first and second sound is studied. Then a boundary condition able to explain the reversible flow of superfluid flowing through a thin capillary is postulated and two vector fields, which have the dimensions of velocity and can be interpreted as the velocities of normal and superfluid components, are introduced. By using these new fields, a comparison between this model and the Hal…