Bogolyubov approximation for diagonal model of an interacting Bose gas

We study, using the Bogolyubov approximation, the thermodynamic behaviour of a superstable Bose system whose energy operator in the second-quantized form contains a nonlinear expression in the occupation numbers operators. We prove that for all values of the chemical potential satisfying $\mu > \lambda(0)$, where $\lambda (0)\leq 0$ is the lowest energy value, the system undergoes Bose--Einstein condensation

The perceived quality of process discovery tools

Process discovery has seen a rise in popularity in the last decade for both researchers and businesses. Recent developments mainly focused on the power and the functionalities of the discovery algorithm. While continuous improvement of these functional aspects is very important, non-functional aspects such as visualization and usability are often overlooked. However, these aspects are considered valuable for end-users and play an important part in the experience of these end-users when working with a process discovery tool. A questionnaire has been sent out to give end-users the opportunity to voice their opinion on available process discovery tools and about the state of process discovery as a domain in general. The results of 66 respondents are presented and compared with the answers of 63 respondents that were contacted through one particular software vendor's employee and customer base (i.e., Celonis)

A comparison of statistical models for short categorical or ordinal time series with applications in ecology

We study two statistical models for short-length categorical (or ordinal) time series. The first one is a regression model based on generalized linear model. The second one is a parametrized Markovian model, particularizing the discrete autoregressive model to the case of categorical data. These models are used to analyze two data-sets: annual larch cone production and weekly planktonic abundance.Comment: 18 page

Horizontal mergers for buyer power

Salant et al. (1983) showed in a Cournot setting that horizontal mergers are unprofitable because outsiders react by increasing their output. We show that this negative effect may be compensated by the positive effect that horizontal mergers have on the buyer power of merging firms in input markets.

The equilibrium states for a model with two kinds of Bose condensation

We study the equilibrium Gibbs states for a Boson gas model, defined by Bru and Zagrebnov, which has two phase transitions of the Bose condensation type. The two phase transitions correspond to two distinct mechanisms by which these condensations can occur. The first (non-conventional) Bose condensation is mediated by a zero-mode interaction term in the Hamiltonian. The second is a transition due to saturation quite similar to the conventional Bose-Einstein (BE) condensation in the ideal Bose gas. Due to repulsive interaction in non-zero modes the model manifests a generalized type III, i.e., non-extensive BE condensation. Our main result is that, as in the ideal Bose gas, the conventional condensation is accompanied by a loss of strong equivalence of the canonical and grand canonical ensembles whereas the non-conventional one, due to the interaction, does not break the equivalence of ensembles. It is also interesting to note that the type of (generalized) condensate, I, II, or III (in the terminology of van den Berg, Lewis and Pule), has no effect on the equivalence of ensembles. These results are proved by computing the generating functional of the cyclic representation of the Canonical Commutation Relation (CCR) for the corresponding equilibrium Gibbs states.Comment: 1+28 pages, LaTe

SISAL (Speleothem Isotopes Synthesis and AnaLysis Working Group) database version 1b

Note: This edition of the SISAL database was withdrawn on 13 July 2020. It has been superseded by a new edition available at http://dx.doi.org/10.17864/1947.256. Stable isotope records from speleothems provide information on past climate changes, most particularly information that can be used to reconstruct past changes in precipitation and atmospheric circulation. SISAL (Speleothem Isotope Synthesis and Analysis) is an international working group of the Past Global Changes (PAGES) project. The working group aims to provide a comprehensive compilation of speleothem isotope records for climate reconstruction and model evaluation. Version 1b of the SISAL database contains oxygen and carbon isotope measurements from 440 individual and 15 composite speleothem records from 221 cave systems worldwide, as well as metadata describing their cave settings and age-depth models. New records have been added and some metadata has been amended. The SISAL working group has also created SISAL chronologies for 20 entities, all of which had no published chronologies. In order to assure traceability, any presentation, report, or publication that uses the SISALv1b database should cite Atsawawaranunt et al. (2018) (The SISAL database: a global resource to document oxygen and carbon isotope records from speleothems; https://doi.org/10.5194/essd-10-1687-2018) and Comas-Bru et al. (2019) (Evaluating model outputs using integrated global speleothem records of climate change since the last glacial; https://doi.org/10.5194/cp-2019-25). If using individual sites or speleothems, the literature citations for published work provided in the database should also be cited. Contact information of data contributors of unpublished data is also provided and these should be contacted when unpublished records are used on an individual basis

Large systems of path-repellent Brownian motions in a trap at positive temperature

We study a model of $N$ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from escaping to infinity, and a pair-interaction Hamiltonian, which imposes a repellency of the $N$ paths. In fact, this interaction is an $N$-dependent regularisation of the Brownian intersection local times, an object which is of independent interest in the theory of stochastic processes. The time horizon (interpreted as the inverse temperature) is kept fixed. We analyse the model for diverging number of Brownian motions in terms of a large deviation principle. The resulting variational formula is the positive-temperature analogue of the well-known Gross-Pitaevskii formula, which approximates the ground state of a certain dilute large quantum system; the kinetic energy term of that formula is replaced by a probabilistic energy functional. This study is a continuation of the analysis in \cite{ABK04} where we considered the limit of diverging time (i.e., the zero-temperature limit) with fixed number of Brownian motions, followed by the limit for diverging number of motions. \bibitem[ABK04]{ABK04} {\sc S.~Adams, J.-B.~Bru} and {\sc W.~K\"onig}, \newblock Large deviations for trapped interacting Brownian particles and paths, \newblock {\it Ann. Probab.}, to appear (2004)

Large deviations for trapped interacting Brownian particles and paths

We introduce two probabilistic models for $N$ interacting Brownian motions moving in a trap in $\mathbb {R}^d$ under mutually repellent forces. The two models are defined in terms of transformed path measures on finite time intervals under a trap Hamiltonian and two respective pair-interaction Hamiltonians. The first pair interaction exhibits a particle repellency, while the second one imposes a path repellency. We analyze both models in the limit of diverging time with fixed number $N$ of Brownian motions. In particular, we prove large deviations principles for the normalized occupation measures. The minimizers of the rate functions are related to a certain associated operator, the Hamilton operator for a system of $N$ interacting trapped particles. More precisely, in the particle-repellency model, the minimizer is its ground state, and in the path-repellency model, the minimizers are its ground product-states. In the case of path-repellency, we also discuss the case of a Dirac-type interaction, which is rigorously defined in terms of Brownian intersection local times. We prove a large-deviation result for a discrete variant of the model. This study is a contribution to the search for a mathematical formulation of the quantum system of $N$ trapped interacting bosons as a model for Bose--Einstein condensation, motivated by the success of the famous 1995 experiments. Recently, Lieb et al. described the large-N behavior of the ground state in terms of the well-known Gross--Pitaevskii formula, involving the scattering length of the pair potential. We prove that the large-N behavior of the ground product-states is also described by the Gross--Pitaevskii formula, however, with the scattering length of the pair potential replaced by its integral.Comment: Published at http://dx.doi.org/10.1214/009117906000000214 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org