338 research outputs found
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 (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 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
. 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 ) 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
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