Dark solitons revealed in Lieb-Liniger eigenstates

We study how dark solitons, i.e. solutions of one-dimensional single-particle nonlinear time-dependent Schr\"odinger equation, emerge from eigenstates of a linear many-body model of contact interacting bosons moving on a ring, the Lieb-Liniger model. This long-standing problem was addressed by various groups, which presented different, seemingly unrelated, procedures to reveal the solitonic waves directly from the many-body model. Here, we propose a unification of these results using a simple Ansatz for the many-body eigenstate of the Lieb-Liniger model, which gives us access to systems of hundreds of atoms. In this approach, mean-field solitons emerge in a single-particle density through repeated measurements of particle positions in the Ansatz state. The post-measurement state turns out to be a wave packet of yrast states of the reduced system.Comment: 8 pages of the main text + 7 pages of appendice

Beyond Gross-Pitaevskii equation for 1D gas: Quasiparticles and solitons

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.Comment: 27 pages, 11 figures. Submission to SciPos

Maximum likelihood models and algorithms for gene tree evolution with duplications and losses

<p>Abstract</p> <p>Background</p> <p>The abundance of new genomic data provides the opportunity to map the location of gene duplication and loss events on a species phylogeny. The first methods for mapping gene duplications and losses were based on a parsimony criterion, finding the mapping that minimizes the number of duplication and loss events. Probabilistic modeling of gene duplication and loss is relatively new and has largely focused on birth-death processes.</p> <p>Results</p> <p>We introduce a new maximum likelihood model that estimates the speciation and gene duplication and loss events in a gene tree within a species tree with branch lengths. We also provide an, in practice, efficient algorithm that computes optimal evolutionary scenarios for this model. We implemented the algorithm in the program DrML and verified its performance with empirical and simulated data.</p> <p>Conclusions</p> <p>In test data sets, DrML finds optimal gene duplication and loss scenarios within minutes, even when the gene trees contain sequences from several hundred species. In many cases, these optimal scenarios differ from the lca-mapping that results from a parsimony gene tree reconciliation. Thus, DrML provides a new, practical statistical framework on which to study gene duplication.</p

Preliminary studies of sediments from the Dobczyce drinking water reservoir

The analysis of river and lake sediments indicates that the physical, chemical, biochemical and geochemical processes that influence the fate of toxic compounds and elements in sediments are numerous and complex (for example: sorption - desorption, oxidation - reduction, ion-exchange, biological activity). Due to the above-mentioned general statement, only a long term and complex research programme can lead to satisfactory answers to the questions relating to possible changes of water and environmental quality in the future. The aim of our study consisted in physical and chemical characterisation of sediments in in-depth profiles taken from the Dobczyce reservoir in southern Poland that is a main source of drinking water for the city of Kraków. Due to morphological reasons, 7 layers of sediment samples were distinguished from the ground level to about 90 cm below (total thickness of the sediments in the sampling site). Analysis of grain size distribution and application of x-ray diffraction method, enabled mineralogical description of sediments. The use of proton-induced x-ray emission (PIXE) and atomic absorption spectrometry (AAS) revealed elemental composition of the samples (Al, P, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn). Concentrations of natural 40K and artificial 137Cs radionuclides were determined by the use of gamma spectrometry. The following facts were established: 1) the oldest (deepest) and newest, recently deposited layers of sediments are similar in their physical and chemical properties. It means that the inflow of contaminants and biogenic compounds to the reservoir has changed little since it was constructed and filled with water; 2) the severe flood in 1997 changed significantly sediment composition and, in fact, led to purification of sediments in the Dobczyce reservoir

Novel Potent Muscarinic Receptor Antagonists: Investigation on the Nature of Lipophilic Substituents in the 5- and/or 6-Positions of the 1,4-Dioxane Nucleus

A series of novel 1,4-dioxane analogues of the muscarinic acetylcholine receptor (mAChR) antagonist 2 was synthesized and studied for their affinity at M1-M5 mAChRs. The 6-cyclohexyl-6-phenyl derivative 3b, with a cis configuration between the CH2N+(CH3)3 chain in the 2-position and the cyclohexyl moiety in the 6-position, showed pKi values for mAChRs higher than those of 2 and a selectivity profile analogous to that of the clinically approved drug oxybutynin. The study of the enantiomers of 3b and the corresponding tertiary amine 33b revealed that the eutomers are (2S,6S)-(-)-3b and (2S,6S)-(-)-33b, respectively. Docking simulations on the M3 mAChR-resolved structure rationalized the experimental observations. The quaternary ammonium function, which should prevent the crossing of the blood-brain barrier, and the high M3/M2 selectivity, which might limit cardiovascular side effects, make 3b a valuable starting point for the design of novel antagonists potentially useful in peripheral diseases in which M3 receptors are involved

Thermodynamic principles and implementations of quantum machines

The efficiency of cyclic heat engines is limited by the Carnot bound. This bound follows from the second law of thermodynamics and is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. By contrast, the efficiency of engines powered by quantum non-thermal baths has been claimed to surpass the thermodynamic Carnot bound. The key to understanding the performance of such engines is a proper division of the energy supplied by the bath to the system into heat and work, depending on the associated change in the system entropy and ergotropy. Due to their hybrid character, the efficiency bound for quantum engines powered by a non-thermal bath does not solely follow from the laws of thermodynamics. Hence, the thermodynamic Carnot bound is inapplicable to such hybrid engines. Yet, they do not violate the principles of thermodynamics. An alternative means of boosting machine performance is the concept of heat-to-work conversion catalysis by quantum non-linear (squeezed) pumping of the piston mode. This enhancement is due to the increased ability of the squeezed piston to store ergotropy. Since the catalyzed machine is fueled by thermal baths, it adheres to the Carnot bound. We conclude by arguing that it is not quantumness per se that improves the machine performance, but rather the properties of the baths, the working fluid and the piston that boost the ergotropy and minimize the wasted heat in both the input and the output.Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Recent Progress and Outlook", (Springer International Publishing