2,337,640 research outputs found
Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems
We consider the statistical mechanics of a general relativistic
one-dimensional self-gravitating system. The system consists of -particles
coupled to lineal gravity and can be considered as a model of
relativistically interacting sheets of uniform mass. The partition function and
one-particle distitrubion functions are computed to leading order in
where is the speed of light; as results for the
non-relativistic one-dimensional self-gravitating system are recovered. We find
that relativistic effects generally cause both position and momentum
distribution functions to become more sharply peaked, and that the temperature
of a relativistic gas is smaller than its non-relativistic counterpart at the
same fixed energy. We consider the large-N limit of our results and compare
this to the non-relativistic case.Comment: latex, 60 pages, 22 figure
A Schroedinger link between non-equilibrium thermodynamics and Fisher information
It is known that equilibrium thermodynamics can be deduced from a constrained
Fisher information extemizing process. We show here that, more generally, both
non-equilibrium and equilibrium thermodynamics can be obtained from such a
Fisher treatment. Equilibrium thermodynamics corresponds to the ground state
solution, and non-equilibrium thermodynamics corresponds to excited state
solutions, of a Schroedinger wave equation (SWE). That equation appears as an
output of the constrained variational process that extremizes Fisher
information. Both equilibrium- and non-equilibrium situations can thereby be
tackled by one formalism that clearly exhibits the fact that thermodynamics and
quantum mechanics can both be expressed in terms of a formal SWE, out of a
common informational basis.Comment: 12 pages, no figure
Choice of Consistent Family, and Quantum Incompatibility
In consistent history quantum theory, a description of the time development
of a quantum system requires choosing a framework or consistent family, and
then calculating probabilities for the different histories which it contains.
It is argued that the framework is chosen by the physicist constructing a
description of a quantum system on the basis of questions he wishes to address,
in a manner analogous to choosing a coarse graining of the phase space in
classical statistical mechanics. The choice of framework is not determined by
some law of nature, though it is limited by quantum incompatibility, a concept
which is discussed using a two-dimensional Hilbert space (spin half particle).
Thus certain questions of physical interest can only be addressed using
frameworks in which they make (quantum mechanical) sense. The physicist's
choice does not influence reality, nor does the presence of choices render the
theory subjective. On the contrary, predictions of the theory can, in
principle, be verified by experimental measurements. These considerations are
used to address various criticisms and possible misunderstandings of the
consistent history approach, including its predictive power, whether it
requires a new logic, whether it can be interpreted realistically, the nature
of ``quasiclassicality'', and the possibility of ``contrary'' inferences.Comment: Minor revisions to bring into conformity with published version.
Revtex 29 pages including 1 page with figure
Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity
We develop the canonical formalism for a system of bodies in lineal
gravity and obtain exact solutions to the equations of motion for N=2. The
determining equation of the Hamiltonian is derived in the form of a
transcendental equation, which leads to the exact Hamiltonian to infinite order
of the gravitational coupling constant. In the equal mass case explicit
expressions of the trajectories of the particles are given as the functions of
the proper time, which show characteristic features of the motion depending on
the strength of gravity (mass) and the magnitude and sign of the cosmological
constant. As expected, we find that a positive cosmological constant has a
repulsive effect on the motion, while a negative one has an attractive effect.
However, some surprising features emerge that are absent for vanishing
cosmological constant. For a certain range of the negative cosmological
constant the motion shows a double maximum behavior as a combined result of an
induced momentum-dependent cosmological potential and the gravitational
attraction between the particles. For a positive cosmological constant, not
only bounded motions but also unbounded ones are realized. The change of the
metric along the movement of the particles is also exactly derived.Comment: 37 pages, Latex, 24 figure
Dynamical N-body Equlibrium in Circular Dilaton Gravity
We obtain a new exact equilibrium solution to the N-body problem in a
one-dimensional relativistic self-gravitating system. It corresponds to an
expanding/contracting spacetime of a circle with N bodies at equal proper
separations from one another around the circle. Our methods are
straightforwardly generalizable to other dilatonic theories of gravity, and
provide a new class of solutions to further the study of (relativistic)
one-dimensional self-gravitating systems.Comment: 4 pages, latex, reference added, minor changes in wordin
Two Step Filament Eruption During 14-15 March 2015
We present here an interesting two-step filament eruption during 14-15 March
2015. The filament was located in NOAA AR 12297 and associated with a halo
Coronal Mass Ejection (CME). We use observations from the Atmospheric Imaging
Assembly (AIA) and Heliospheric Magnetic Imager (HMI) instruments onboard the
Solar Dynamics Observatory (SDO), and from the Solar and Heliospheric
Observatory (SOHO) Large Angle and Spectrometric Coronagraph (LASCO). We also
use H-alpha data from the Global Oscillation Network Group (GONG) telescope and
the Kanzelhoehe Solar Observatory. The filament shows a first step eruption on
14 March 2015 and it stops its rise at a projected altitude ~ 125 Mm on the
solar disk. It remains at this height for ~ 12 hrs. Finally it eruptes on 15
March 2015 and produced a halo CME. We also find jet activity in the active
region during both days, which could help the filament de-stabilization and
eruption. The decay index is calculated to understand this two-step eruption.
The eruption could be due to the presence of successive
instability-stability-instability zones as the filament is rising.Comment: 11 pages, 7 figures, accepted for the publication in Solar Physic
Chaos in an Exact Relativistic 3-body Self-Gravitating System
We consider the problem of three body motion for a relativistic
one-dimensional self-gravitating system. After describing the canonical
decomposition of the action, we find an exact expression for the 3-body
Hamiltonian, implicitly determined in terms of the four coordinate and momentum
degrees of freedom in the system. Non-relativistically these degrees of freedom
can be rewritten in terms of a single particle moving in a two-dimensional
hexagonal well. We find the exact relativistic generalization of this
potential, along with its post-Newtonian approximation. We then specialize to
the equal mass case and numerically solve the equations of motion that follow
from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining
orbits in both the hexagonal and 3-body representations of the system, and plot
the Poincare sections as a function of the relativistic energy parameter . We find two broad categories of periodic and quasi-periodic motions that we
refer to as the annulus and pretzel patterns, as well as a set of chaotic
motions that appear in the region of phase-space between these two types.
Despite the high degree of non-linearity in the relativistic system, we find
that the the global structure of its phase space remains qualitatively the same
as its non-relativisitic counterpart for all values of that we could
study. However the relativistic system has a weaker symmetry and so its
Poincare section develops an asymmetric distortion that increases with
increasing . For the post-Newtonian system we find that it experiences a
KAM breakdown for : above which the near integrable regions
degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon
reques
Comment on ``Consistent Sets Yield Contrary Inferences in Quantum Theory''
In a recent paper Kent has pointed out that in consistent histories quantum
theory it is possible, given initial and final states, to construct two
different consistent families of histories, in each of which there is a
proposition that can be inferred with probability one, and such that the
projectors representing these two propositions are mutually orthogonal. In this
note we stress that, according to the rules of consistent history reasoning two
such propositions are not contrary in the usual logical sense namely, that one
can infer that if one is true then the other is false, and both could be false.
No single consistent family contains both propositions, together with the
initial and final states, and hence the propositions cannot be logically
compared. Consistent histories quantum theory is logically consistent,
consistent with experiment as far as is known, consistent with the usual
quantum predictions for measurements, and applicable to the most general
physical systems. It may not be the only theory with these properties, but in
our opinion, it is the most promising among present possibilities.Comment: 2pages, uses REVTEX 3.
Real-space renormalisation group approach to driven diffusive systems
We introduce a real-space renormalisation group procedure for driven
diffusive systems which predicts both steady state and dynamic properties. We
apply the method to the boundary driven asymmetric simple exclusion process and
recover exact results for the steady state phase diagram, as well as the
crossovers in the relaxation dynamics for each phase.Comment: 10 pages, 5 figure
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