Statistical properties of one dimensional attractive Bose gas

Using classical field approximation we present the first study of statistical properties of one dimensional Bose gas with attractive interaction. The canonical probability distribution is generated with the help of a Monte Carlo method. This way we obtain not only the depletion of the condensate with growing temperature but also its fluctuations. The most important is our discovery of a reduced coherence length, the phenomenon observed earlier only for the repulsive gas, known as quasicondensation.Comment: 4 pages, 4 figure

Dust reference frame in quantum cosmology

We give a formulation of quantum cosmology with a pressureless dust and arbitrary additional matter fields. The system has the property that its Hamiltonian constraint is linear in the dust momentum. This feature provides a natural time gauge, leading to a physical hamiltonian that is not a square root. Quantization leads to Schr{\"o}dinger equation for which unitary evolution is directly linked to geodesic completeness. Our approach simplifies the analysis of both Wheeler-deWitt and loop quantum cosmology (LQC) models, and significantly broadens the applicability of the latter. This is demonstrated for arbitrary scalar field potential and cosmological constant in LQC.Comment: 8 pages, iopart style + BibTe

Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC

A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator $(1/2)\pi^2 B - H$ is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schroedinger-like quantum mechanics with a generalized Hamiltonian $\sqrt{B^{-1} H}$. In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schroedinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases considered in the paper correspond to the negative and, respectively, positive cosmological constant. Our results should be also applicable in many other general relativistic contexts.Comment: RevTex4, 32 page

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

Closed FRW model in Loop Quantum Cosmology

The basic idea of the LQC applies to every spatially homogeneous cosmological model, however only the spatially flat (so called $k=0$) case has been understood in detail in the literature thus far. In the closed (so called: k=1) case certain technical difficulties have been the obstacle that stopped the development. In this work the difficulties are overcome, and a new LQC model of the spatially closed, homogeneous, isotropic universe is constructed. The topology of the spacelike section of the universe is assumed to be that of SU(2) or SO(3). Surprisingly, according to the results achieved in this work, the two cases can be distinguished from each other just by the local properties of the quantum geometry of the universe. The quantum hamiltonian operator of the gravitational field takes the form of a difference operator, where the elementary step is the quantum of the 3-volume derived in the flat case by Ashtekar, Pawlowski and Singh. The mathematical properties of the operator are studied: it is essentially self-adjoint, bounded from above by 0, the 0 itself is not an eigenvalue, the eigenvectors form a basis. An estimate on the dimension of the spectral projection on any finite interval is provided.Comment: 19 pages, latex, no figures, high quality, nea

On non-existence of static vacuum black holes with degenerate components of the event horizon

We present a simple proof of the non-existence of degenerate components of the event horizon in static, vacuum, regular, four-dimensional black hole spacetimes. We discuss the generalisation to higher dimensions and the inclusion of a cosmological constant.Comment: latex2e, 9 pages in A

UDZIAŁ POLSKI W POCZĄTKOWYCH DZIAŁANIACH NA RZECZ REALIZACJI POSTANOWIEŃ KONWENCJI

In the period between ratification of the Convention and its coming into effect in 1977, Poland became an important centre for shaping the global identification and cultural heritage preservation system. The 1976 Warsaw Governmental Experts Conference concerning protection and role of historic and traditional complexes allowed for adopting a definition thereof. “A meeting of experts on the improvement and harmonization of systems on the inventories and catalogues of monuments” which took place in Warsaw in 1977, was the next stage.Polish delegate, who had been chosen a vice-president of the Committee during the first session thereof in 1977, submitted a set of comments on operational directives on the criteria for historical value, authenticity, urban complexes, and technological artefacts. Polish nominations provided illustration of this intricate matter. These included: urban complex of Cracow, Wieliczka Salt Mine, Warsaw Old Town (rebuilt after WW2), and the former Concentration CampAuschwitz-Birkenau. Polish ICOMOS presented the “Protection and Management in Cities of Exceptional Monumental Value” programme in 1995, which was subsequently accepted by UNESCO.In the period between ratification of the Convention and its coming into effect in 1977, Poland became an important centre for shaping the global identification and cultural heritage preservation system. The 1976 Warsaw Governmental Experts Conference concerning protection and role of historic and traditional complexes allowed for adopting a definition thereof. “A meeting of experts on the improvement and harmonization of systems on the inventories and catalogues of monuments” which took place in Warsaw in 1977, was the next stage.Polish delegate, who had been chosen a vice-president of the Committee during the first session thereof in 1977, submitted a set of comments on operational directives on the criteria for historical value, authenticity, urban complexes, and technological artefacts. Polish nominations provided illustration of this intricate matter. These included: urban complex of Cracow, Wieliczka Salt Mine, Warsaw Old Town (rebuilt after WW2), and the former Concentration CampAuschwitz-Birkenau. Polish ICOMOS presented the “Protection and Management in Cities of Exceptional Monumental Value” programme in 1995, which was subsequently accepted by UNESCO