270 research outputs found
Two-dimensional quantum-corrected black hole in a finite size cavity
We consider the gravitation-dilaton theory (not necessarily exactly
solvable), whose potentials represent a generic linear combination of an
exponential and linear functions of the dilaton. A black hole, arising in such
theories, is supposed to be enclosed in a cavity, where it attains thermal
equilibrium, whereas outside the cavity the field is in the Boulware state. We
calculate quantum corrections to the Hawking temperature , with the
contribution from the boundary taken into account. Vacuum polarization outside
the shell tend to cool the system. We find that, for the shell to be in the
thermal equilibrium, it cannot be placed too close to the horizon. The quantum
corrections to the mass due to vacuum polarization vanish in spite of non-zero
quantum stresses. We discuss also the canonical boundary conditions and show
that accounting for the finiteness of the system plays a crucial role in some
theories (e.g., CGHS), where it enables to define the stable canonical
ensemble, whereas consideration in an infinite space would predict instability.Comment: 21 pages. In v.2 misprints corrected. To appear in Phys. Rev.
Correlated N-boson systems for arbitrary scattering length
We investigate systems of identical bosons with the focus on two-body
correlations and attractive finite-range potentials. We use a hyperspherical
adiabatic method and apply a Faddeev type of decomposition of the wave
function. We discuss the structure of a condensate as function of particle
number and scattering length. We establish universal scaling relations for the
critical effective radial potentials for distances where the average distance
between particle pairs is larger than the interaction range. The correlations
in the wave function restore the large distance mean-field behaviour with the
correct two-body interaction. We discuss various processes limiting the
stability of condensates. With correlations we confirm that macroscopic
tunneling dominates when the trap length is about half of the particle number
times the scattering length.Comment: 15 pages (RevTeX4), 11 figures (LaTeX), submitted to Phys. Rev. A.
Second version includes an explicit comparison to N=3, a restructured
manuscript, and updated figure
Electronic properties of ordered and disordered linear clusters of atoms and molecules
The electronic properties of one-dimensional clusters of N atoms or molecules
have been studied. The model used is similar to the Kronig-Penney model with
the potential offered by each ion being approximated by an attractive delta
function. The energy eigenvalues, the eigenstates and the density of states are
calculated exactly for a linear cluster of N atoms or molecules. The dependence
of these quantities on the various parameters of the problem show interesting
behavior. Effects of random distribution of the positions of the atoms and
random distribution of the strengths of the potential have also been studied.
The results obtained in this paper can have direct applications for linear
chain of atoms produced on metal surfaces or artificially created chain of
atoms by using scanning tunneling microscope or in studying molecular
conduction of electrons across one-dimensional barriers.Comment: A shorter version of this paper to be published in Physica
Positive specific heat of the quantum corrected dilaton black hole
Path integral quantization of dilaton gravity in two dimensions is applied to
the CGHS model to the first nontrivial order in matter loops. Our approach is
background independent as geometry is integrated out exactly. The result is an
effective shift of the Killing norm: the apparent horizon becomes smaller. The
Hawking temperature which is constant to leading order receives a quantum
correction. As a consequence, the specific heat becomes positive and
proportional to the square of the black hole mass.Comment: 18 pages, JHEP style, 1 eps figure, v2: extended the discussion,
added new formulas for mass change, added three new references (in particular
[35]
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
In this article, we analyze the third of three papers, in which Einstein
presented his quantum theory of the ideal gas of 1924-1925. Although it failed
to attract the attention of Einstein's contemporaries and although also today
very few commentators refer to it, we argue for its significance in the context
of Einstein's quantum researches. It contains an attempt to extend and exhaust
the characterization of the monatomic ideal gas without appealing to
combinatorics. Its ambiguities illustrate Einstein's confusion with his initial
success in extending Bose's results and in realizing the consequences of what
later became to be called Bose-Einstein statistics. We discuss Einstein's
motivation for writing a non-combinatorial paper, partly in response to
criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments
are based on Einstein's belief in the complete analogy between the
thermodynamics of light quanta and of material particles and invoke
considerations of adiabatic transformations as well as of dimensional analysis.
These techniques were well-known to Einstein from earlier work on Wien's
displacement law, Planck's radiation theory, and the specific heat of solids.
We also investigate the possible role of Ehrenfest in the gestation of the
theory.Comment: 57 pp
Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation
On the basis of recent investigations, a newly developed analytical procedure
is used for constructing a wide class of localized solutions of the controlled
three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the
dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is
decomposed into a two-dimensional (2D) linear Schr\"{o}dinger equation and a
one-dimensional (1D) nonlinear Schr\"{o}dinger equation, constrained by a
variational condition for the controlling potential. Then, the above class of
localized solutions are constructed as the product of the solutions of the
transverse and longitudinal equations. On the basis of these exact 3D
analytical solutions, a stability analysis is carried out, focusing our
attention on the physical conditions for having collapsing or non-collapsing
solutions.Comment: 21 pages, 14 figure
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