Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

One-dimensional trapped atoms: critical coupling parameter and critical number of particles

In this paper we consider the case of a Bose gas in low dimension in order to illustrate the applicability of a method that allows us to construct analytical relations, valid for a broad range of coupling parameters, for a function which asymptotic expansions are known. The method is well suitable to investigate the problem of stability of a collection of Bose particles trapped in one- dimensional configuration for the case where the scattering length presents a negative value. The eigenvalues for this interacting quantum one-dimensional many particle system become negative when the interactions overcome the trapping energy and, in this case, the system becomes unstable. Here we calculate the critical coupling parameter and apply for the case of Lithium atoms obtaining the critical number of particles for the limit of stability.

RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .1. THEORETICAL DEVELOPMENT

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three-dimensional scattering integral equations satisfying constraints of relativistic unitarity and convariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three-dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and convariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The three-particle equations we derive are very practical and suitable for performing relativistic scattering calculations. (C) 1994 Academic Press, Inc.

An interplanetary mission to Neptune system: Gravitational capture and maneuvers around triton

The gravitational capture was initially used to understand the capture of planetary satellites. However, in the 90's decade, this phenomenon was applied in spacecraft trajectories. Belbruno and Miller studied missions in the Earth-Moon system that uses this technique to save fuel during the insertion of the spacecraft in its final orbit around the Moon. Using a parameter defined as twice the two-body energy of the planet-particle system, Yamakawa also studied the gravitational capture in the Earth-Moon system. In the present paper, this technique is used to study a mission that goes to the Neptune system and perform a gravitational capture in the satellite Triton. The results show direct and retrograde trajectories, for different values of the initial conditions.

An infinite level atom coupled to a heat bath

Wir untersuchen die Mathematik endlicher, an ein Wärmebad gekoppelter Teilchensysteme. Das Standard-Modell der Quantenelektrodynamik für Temperatur Null liefert einen Hamilton-Operator H, der die Energie von Teilchen beschreibt, welche mit Photonen wechselwirken. Im Heisenbergbild ist die Zeitevolution des physikalischen Systems durch die Wirkung einer Ein-Parameter-Gruppe auf eine Menge von Observablen A gegeben: Diese steht im Zusammenhang mit der Lösung der Schrödinger-Gleichung für H. Um Zustände von A, welche das physikalische System in der Nähe des thermischen Gleichgewichts zur Temperatur T darstellen, zu beschreiben, folgen wir dem Ansatz von Jaksic und Pillet, eine Darstellung von A zu konstruieren. Die Vektoren in dieser Darstellung definieren die Zustände, die Zeitentwicklung wird mit Hilfe des Standard Liouville-Operators L beschrieben. In dieser Doktorarbeit werden folgende Resultate bewiesen bzw. hergeleitet: - die Konstuktion einer Darstellung - die Selbstadjungiertheit des Standard Liouville-Operators - die Existenz eines Gleichgewichtszustandes in dieser Darstellung - der Limes des physikalischen Systems für große Zeiten.

Convergence results for stochastic particle systems with social interaction

We consider stochastic individual-based models for social behaviour of groups of animals. In these models the trajectory of each animal is given by a stochastic differential equation with interaction. The social interaction is contained in the drift term of the SDE. We consider a global aggregation force and a short-range repulsion force. The repulsion range and strength gets rescaled with the number of animals N. We show that for N tending to infinity stochastic fluctuations disappear and a smoothed version of the empirical process converges uniformly towards the solution of a nonlinear, nonlocal partial differential equation of advection-reaction-diffusion type. The rescaling of the repulsion in the individual-based model implies that the corresponding term in the limit equation is local while the aggregation term is non-local. Moreover, we discuss the effect of a predator on the system and derive an analogous convergence result. The predator acts as an repulsive force. Different laws of motion for the predator are considered.

Stationarity of multivariate particle systems

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in RdRd and in some cases provide a full characterisation of the stationarity property. In particular, a full characterisation of stationary multivariate Brown–Resnick processes is given.

Interaction-free measurements by quantum Zeno stabilization of ultracold atoms

Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object-realized by a laser beam-prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom. Contrary to existing proposals, our IFM does not require single-particle sources and is only weakly affected by losses and decoherence. We demonstrate confidence levels of 90%, well beyond previous optical experiments.

Conditional entropy and predictability for non-reversible Markov systems

The purpose of this thesis is to clarify the role of non-equilibrium stationary currents of Markov processes in the context of the predictability of future states of the system. Once the connection between the predictability and the conditional entropy is established, we provide a comprehensive approach to the definition of a multi-particle Markov system. In particular, starting from the well-known theory of random walk on network, we derive the non-linear master equation for an interacting multi-particle system under the one-step process hypothesis, highlighting the limits of its tractability and the prop- erties of its stationary solution. Lastly, in order to study the impact of the NESS on the predictability at short times, we analyze the conditional entropy by modulating the intensity of the stationary currents, both for a single-particle and a multi-particle Markov system. The results obtained analytically are numerically tested on a 5-node cycle network and put in correspondence with the stationary entropy production. Furthermore, because of the low dimensionality of the single-particle system, an analysis of its spectral properties as a function of the modulated stationary currents is performed.

Magnetic properties of Fe(3)O(4) nanoparticles coated with oleic and dodecanoic acids

Magnetic nanoparticles (NP) of magnetite (Fe(3)O(4)) coated with oleic acid (OA) and dodecanoic acid (DA) were synthesized and investigated through transmission electron microscopy (TEM), magnetization M, and ac magnetic susceptibility measurements. The OA coated samples were produced with different magnetic concentrations (78%, 76%, and 65%) and the DA sample with 63% of Fe(3)O(4). Images from TEM indicate that the NP have a nearly spherical geometry and mean diameter similar to 5.5 nm. Magnetization measurements, performed in zero-field cooled (ZFC) and field cooled processes under different external magnetic fields H, exhibited a maximum at a given temperature T(B) in the ZFC curves, which depends on the NP coating (OA or DA), magnetite concentration, and H. The temperature T(B) decreases monotonically with increasing H and, for a given H, the increase in the magnetite concentration results in an increase in T(B). The observed behavior is related to the dipolar interaction between NP, which seems to be an important mechanism in all samples studied. This is supported by the results of the ac magnetic susceptibility chi(ac) measurements, where the temperature in which chi' peaks for different frequencies follows the Vogel-Fulcher model, a feature commonly found in systems with dipolar interactions. Curves of H versus T(B)/T(B) (H=0) for samples with different coatings and magnetite concentrations collapse into a universal curve, indicating that the qualitative magnetic behavior of the samples may be described by the NP themselves, instead of the coating or the strength of the dipolar interaction. Below T(B), M versus H curves show a coercive field (H(C)) that increases monotonically with decreasing temperature. The saturation magnetization (M(S)) follows the Bloch's law and values of M(S) at room temperature as high as 78 emu/g were estimated, a result corresponding to similar to 80% of the bulk value. The overlap of M/M(S) versus H/T curves for a given sample and the low H(C) at high temperatures suggest superparamagnetic behavior in all samples studied. The overlap of M/M(S) versus H curves at constant temperature for different samples indicates that the NP magnetization behavior is preserved, independently of the coating and magnetite concentration. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3311611]

Direct detection of Kaluza-Klein particles in neutrino telescopes

In theories with universal extra dimensions, all standard model fields propagate in the bulk and the lightest state of the first Kaluza-Klein (KK) level can be made stable by imposing a Z(2) parity. We consider a framework where the lightest KK particle (LKP) is a neutral, extremely weakly interacting particle such as the first KK excitation of the graviton, while the next-to-lightest KK particle (NLKP) is the first KK mode of a charged right-handed lepton. In such a scenario, due to its very small couplings to the LKP, the NLKP is long-lived. We investigate the production of these particles from the interaction of high energy neutrinos with nucleons in the Earth and determine the rate of NLKP events in neutrino telescopes. Using the Waxman-Bahcall limit for the neutrino flux, we find that the rate can be as large as a few hundreds of events a year for realistic values of the NLKP mass.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

One-dimensional point interaction with three complex parameters

For a pair of non-Hermitian Hamiltonian H and its Hermitian adjoint H(dagger), there are situations in which their eigenfunctions form a biorthogonal system. We illustrate such a situation by means of a one-particle system with a one-dimensional point interaction in the form of the Fermi pseudo-potential. The interaction consists of three terms with three strength parameters g(i) (i = 1, 2 and 3), which are all complex. This complex point interaction is neither Hermitian nor PT-invariant in general. The S-matrix for the transmission reflection problem constructed with H (or with H(dagger)) in the usual manner is not unitary, but it conforms to the pseudo-unitarity that we define. The pseudounitarity is closely related to the biorthogonality of the eigenfunctions. The eigenvalue spectrum of H with the complex interaction is generally complex but there are cases where the spectrum is real. In such a case H and H(dagger) form a pseudo-Hermitian pair.

3D-partikkelit aloittelijoille : tarkastelussa 3D-Kalevala-projekti

Opinnäytteeni teososana on 3D-Kalevala projektinimellä tunnetun animaation partikkeliefektit. Tarkastelen tarkemmin elokuvan Lumi-, Kylä-, Paja- ja Luola-kohtauksia. 3D-Kalevala on tietokoneella tehty animaatio, joka kertoo Suomen kansalliseepoksen Kalevalan päähenkilöstä Väinämöisestä. Elokuvassa vanha Väinämöinen muistelee nuoruutensa tapahtumia. 3D-Kalevala-projekti käynnistettiin vuonna 2003, mutta sen alkuperäiset tekijät eivät saaneet sitä valmiiksi, ja projektin teko keskeytettiin vuonna 2005. Vuoden 2006 keväällä projektiin perustettiin uusi kahden verkkoviestinnän opiskelijan projektiryhmä, jonka tehtävänä oli saada elokuva valmiiksi vuoden 2007 kevääseen mennessä. Kun aloitimme projektin tekemisen, olin kolmiulotteisessa mallinnuksessa aloittelija. Tästä johtuen opinnäytteen kirjallinen osa on opas aloittelijoille partikkelien maailmaan. Selvitän raportissani miten elokuvan partikkeliefektit rakennettiin, mitä niiden tekeminen minulta vaati ja miten ne loppujen lopuksi mielestäni onnistuivat. Elokuvan efektit tehtiin 3D Studio Max-ohjelman versiolla 6.0, ja tämän takia kirjoitankin efektien rakentamisesta kyseisen ohjelman keinoin. Projektin suuruuden vuoksi molemmat tekijät pääsivät tekemään monenlaisia töitä, mutta päävastuualueet olivat selvät. Minun osani oli tehdä elokuvaan efektejä. Partikkeliefektit ovat proseduraalisia efektejä, joiden avulla on mahdollista tehdä aidon näköisiä luonnonilmiöitä, kuten tulta, savua, kipinöitä ja veden roiskeita. Koska partikkeliefektit mallintavat reaalimaailman ilmiöitä, on tekijän hyvä olla kiinnostunut selvittämään ilmiöiden käyttäytymistä luonnossa. Raportoin myös projektin aikana huomaamistani hyvistä tavoista opiskella itsenäisesti partikkelien rakentamiseen käytettyjä tekniikoita. On hyvä lukea 3D Studio Maxin tasokasta käyttöohjesovellusta, tutustua Internetissä löytyviin 3D-aiheisiin foorumeihin, käydä aiheesta tutoriaaleja läpi sekä tutustua ohjelman ominaisuuksiin kokeilemalla ja tutkimalla itsenäisesti. Elokuvan efektit onnistuivat mielestäni kiitettävästi ottaen huomioon lähtötasoni. Löysin tapoja kehittää itseäni ja helppoja keinoja toteuttaa realistista jälkeä efektien rakentamisessa. Toivon, että raportistani olisi jollekin 3D-partikkeliefekteistä kiinnostuneelle hyötyä.