1,606 research outputs found
Statistical Mechanics of the Self-Gravitating Gas: I. Thermodynamic Limit and Phase Diagram
We provide a complete picture to the selfgravitating non-relativistic gas at
thermal equilibrium using Monte Carlo simulations, analytic mean field methods
(MF) and low density expansions. The system is shown to possess an infinite
volume limit in the grand canonical (GCE), canonical (CE) and microcanonical
(MCE) ensembles when(N, V) --> infinity, keeping N/ V^{1/3} fixed. We compute
the equation of state (we do not assume it as is customary), as well as the
energy, free energy, entropy, chemical potential, specific heats, compressibi-
lities and speed of sound;we analyze their properties, signs and singularities.
All physical quantities turn out to depend on a single variable eta = G m^2 N/
[V^{1/3} T] that is kept fixed in the N--> infinity and V --> infinity limit.
The system is in a gaseous phase for eta < eta_T and collapses into a dense
objet for eta > \eta_T in the CE with the pressure becoming large and negative.
At eta simeq eta_T the isothermal compressibility diverges. Our Monte Carlo
simulations yield eta_T simeq 1.515. PV/[NT] = f(eta) and all physical magni-
tudes exhibit a square root branch point at eta = eta_C > eta_T. The MF for
spherical symmetry yields eta_C = 1.561764.. while Monte Carlo on a cube yields
eta_C simeq 1.540.The function f(eta) has a second Riemann sheet which is only
physically realized in the MCE.In the MCE, the collapse phase transition takes
place in this second sheet near eta_MC = 1.26 and the pressure and temperature
are larger in the collapsed phase than in the gas phase.Both collapse phase
transitions (CE and MCE) are of zeroth order since the Gibbs free energy jumps
at the transitions. f(eta), obeys in MF a first order non-linear differential
equation of first kind Abel's type.The MF gives an extremely accurate picture
in agreement with Monte Carlo both in the CE and MCE.Comment: Latex, 51 pages, 15 .ps figures, to appear in Nucl. Phys.
Gamma-ray emission expected from Kepler's SNR
Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova
remnants (SNRs) is used to investigate the properties of Kepler's SNR and, in
particular, to predict the gamma-ray spectrum expected from this SNR.
Observations of the nonthermal radio and X-ray emission spectra as well as
theoretical constraints for the total supernova (SN) explosion energy E_sn are
used to constrain the astronomical and particle acceleration parameters of the
system. Under the assumption that Kepler's SN is a type Ia SN we determine for
any given explosion energy E_sn and source distance d the mass density of the
ambient interstellar medium (ISM) from a fit to the observed SNR size and
expansion speed. This makes it possible to make predictions for the expected
gamma-ray flux. Exploring the expected distance range we find that for a
typical explosion energy E_sn=10^51 erg the expected energy flux of TeV
gamma-rays varies from 2x10^{-11} to 10^{-13} erg/(cm^2 s) when the distance
changes from d=3.4 kpc to 7 kpc. In all cases the gamma-ray emission is
dominated by \pi^0-decay gamma-rays due to nuclear CRs. Therefore Kepler's SNR
represents a very promising target for instruments like H.E.S.S., CANGAROO and
GLAST. A non-detection of gamma-rays would mean that the actual source distance
is larger than 7 kpc.Comment: 6 pages, 4 figures. Accepted for publication in Astronomy and
Astrophysics, minor typos correcte
New evidence for strong nonthermal effects in Tycho's supernova remnant
For the case of Tycho's supernova remnant (SNR) we present the relation
between the blast wave and contact discontinuity radii calculated within the
nonlinear kinetic theory of cosmic ray (CR) acceleration in SNRs. It is
demonstrated that these radii are confirmed by recently published Chandra
measurements which show that the observed contact discontinuity radius is so
close to the shock radius that it can only be explained by efficient CR
acceleration which in turn makes the medium more compressible. Together with
the recently determined new value erg of the SN
explosion energy this also confirms our previous conclusion that a TeV
gamma-ray flux of erg/(cms) is to be expected from
Tycho's SNR. Chandra measurements and the HEGRA upper limit of the TeV
gamma-ray flux together limit the source distance to kpc.Comment: 5 pages, 4 figures. Accepted for publication in Astrophysics and
Space Science, Proc. of "The Multi-Messenger Approach to High-Energy
Gamma-ray Sources (Third Workshop on the Nature of Unidentified High-Energy
Sources)", Barcelona, July 4-7, 200
Statistical Mechanics of the Self-gravitating gas with two or more kinds of Particles
We study the statistical mechanics of the self-gravitating gas at thermal
equilibrium with two kinds of particles. We start from the partition function
in the canonical ensemble which we express as a functional integral over the
densities of the two kinds of particles for a large number of particles. The
system is shown to possess an infinite volume limit when (N_1,N_2,V)->infty,
keeping N_1/V^{1/3} and N_2/V^{1/3} fixed. The saddle point approximation
becomes here exact for (N_1,N_2,V)->infty.It provides a nonlinear differential
equation on the particle densities. For the spherically symmetric case, we
compute the densities as functions of two dimensionless physical parameters:
eta_1=G m_1^2 N_1/[V^{1/3} T] and eta_2=G m_2^2 N_2/[V^{1/3} T] (where G is
Newton's constant, m_1 and m_2 the masses of the two kinds of particles and T
the temperature). According to the values of eta_1 and eta_2 the system can be
either in a gaseous phase or in a highly condensed phase.The gaseous phase is
stable for eta_1 and eta_2 between the origin and their collapse values. The
gas is inhomogeneous and the mass M(R) inside a sphere of radius R scales with
R as M(R) propto R^d suggesting a fractal structure. The value of d depends in
general on eta_1 and eta_2 except on the critical line for the canonical ensem-
ble where it takes the universal value d simeq 1.6 for all values of N_1/N_2.
The equation of state is computed.It is found to be locally a perfect gas
equation of state. Thermodynamic functions are computed as functions of eta_1
and eta_2. They exhibit a square root Riemann sheet with the branch points on
the critical canonical line. This treatment is further generalized to the
self-gravitating gas with n-types of particles.Comment: LaTex, 29 pages, 11 .ps figures, expanded version to appear in Phys.
Rev.
Polarization Correlations of 1S0 Proton Pairs as Tests of Bell and Wigner Inequalities
In an experiment designed to overcome the loophole of observer dependent
reality and satisfying the counterfactuality condition, we measured
polarization correlations of 1S0 proton pairs produced in 12C(d,2He) and
1H(d,He) reactions in one setting. The results of these measurements are used
to test the Bell and Wigner inequalties against the predictions of quantum
mechanics.Comment: 8 pages, 4 figure
The Cluster Expansion for the Self-Gravitating gas and the Thermodynamic Limit
We develop the cluster expansion and the Mayer expansion for the
self-gravitating thermal gas and prove the existence and stability of the
thermodynamic limit N, V to infty with N/V^{1/3} fixed. The essential
(dimensionless) variable is here eta = [G m^2 N]/[V^{1/3} T] (which is kept
fixed in the thermodynamic limit). We succeed in this way to obtain the
expansion of the grand canonical partition function in powers of the fugacity.
The corresponding cluster coefficients behave in the thermodynamic limit as
[eta/N]^{j-1} c_j where c_j are pure numbers. They are expressed as integrals
associated to tree cluster diagrams. A bilinear recurrence relation for the
coefficients c_j is obtained from the mean field equations in the Abel form. In
this way the large j behaviour of the c_j is calculated. This large j behaviour
provides the position of the nearest singularity which corresponds to the
critical point (collapse) of the self-gravitating gas in the grand canonical
ensemble. Finally, we discuss why other attempts to define a thermodynamic
limit for the self-gravitating gas fail.Comment: LaTex 12 pages, 1 figure .p
The Point of Origin of the Radio Radiation from the Unresolved Cores of Radio-Loud Quasars
Locating the exact point of origin of the core radiation in active galactic
nuclei (AGN) would represent important progress in our understanding of
physical processes in the central engine of these objects. However, due to our
inability to resolve the region containing both the central compact object and
the jet base, this has so far been difficult. Here, using an analysis in which
the lack of resolution does not play a significant role, we demonstrate that it
may be impossible even in most radio loud sources for more than a small
percentage of the core radiation at radio wavelengths to come from the jet
base. We find for 3C279 that percent of the core flux at 15 GHz must
come from a separate, reasonably stable, region that is not part of the jet
base, and that then likely radiates at least quasi-isotropically and is
centered on the black hole. The long-term stability of this component also
suggests that it may originate in a region that extends over many Schwarzschild
radii.Comment: 7 pages with 3 figures, accepted for publication in Astrophysics and
Space Scienc
Evaluation of treatments for claw horn lesions in dairy cows in a randomized controlled trial
Lameness is one of the most significant endemic disease problems facing the dairy industry. Claw horn lesions (principally sole hemorrhage, sole ulcer, and white line disease) are some of the most prevalent conditions. Despite the fact that thousands of animals are treated for these conditions every year, experimental evidence is limited on the most effective treatment protocols. A randomized, positively controlled clinical trial was conducted to test the recovery of newly lame cows with claw horn lesions. Animals on 5 farms were locomotion scored every 2 wk. Cows were eligible for recruitment if they had 2 nonlame scores followed by a lame score and had a claw horn lesion on a single claw of a single foot. Following a therapeutic trim, enrolled cows were randomly allocated to 1 of 4 treatments: treatment 1—no further treatment (positive control; TRM), treatment 2—trim plus a block on the sound claw (TB), treatment 3—trim plus a 3-d course of the nonsteroidal anti-inflammatory drug (NSAID) ketoprofen (TN), treatment 4—trim plus a block plus ketoprofen (TBN). The primary outcome measure was locomotion score 35 d after treatment, by an observer blind to treatment group. Descriptive statistics suggested that treatment groups were balanced at the time of enrollment, that is, randomization was successful. Based on a sound locomotion score (score 0) 35 d after treatment, the number of cures was 11 of 45 (24.4%) for TRM, 14 of 39 (35.9%) for TB, 12 of 42 (28.6%) for TN, and 23 of 41 (56.1%) for TBN. The difference between TBN and TRM was significant. To test for confounding imbalances between treatment groups, logistic regression models were built with 2 outcomes, either sound (score 0) or nonlame (score 0 or 1) 35 d after treatment. Compared with TRM, animals that received TBN were significantly more likely to cure to a sound outcome. Farm, treatment season, lesion diagnosis, limb affected, treatment operator, and stage of lactation were included in the final models. Our work suggests that lameness cure is maximized with NSAID treatment in addition to the common practices of therapeutic trimming and elevation of the diseased claw using a block when cows are newly and predominantly mildly lame
Superconductor coupled to two Luttinger liquids as an entangler for electron spins
We consider an s-wave superconductor (SC) which is tunnel-coupled to two
spatially separated Luttinger liquid (LL) leads. We demonstrate that such a
setup acts as an entangler, i.e. it creates spin-singlets of two electrons
which are spatially separated, thereby providing a source of electronic
Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage,
which is smaller than the energy gap in the SC, a stationary current of
spin-entangled electrons can flow from the SC to the LL leads due to Andreev
tunneling events. We discuss two competing transport channels for Cooper pairs
to tunnel from the SC into the LL leads. On the one hand, the coherent
tunneling of two electrons into the same LL lead is shown to be suppressed by
strong LL correlations compared to single-electron tunneling into a LL. On the
other hand, the tunneling of two spin-entangled electrons into different leads
is suppressed by the initial spatial separation of the two electrons coming
from the same Cooper pair. We show that the latter suppression depends
crucially on the effective dimensionality of the SC. We identify a regime of
experimental interest in which the separation of two spin-entangled electrons
is favored. We determine the decay of the singlet state of two electrons
injected into different leads caused by the LL correlations. Although the
electron is not a proper quasiparticle of the LL, the spin information can
still be transported via the spin density fluctuations produced by the injected
spin-entangled electrons.Comment: 15 pages, 2 figure
Dynamic generation of maximally entangled photon multiplets by adiabatic passage
The adiabatic passage scheme for quantum state synthesis, in which atomic
Zeeman coherences are mapped to photon states in an optical cavity, is extended
to the general case of two degenerate cavity modes with orthogonal
polarization. Analytical calculations of the dressed-state structure and Monte
Carlo wave-function simulations of the system dynamics show that, for a
suitably chosen cavity detuning, it is possible to generate states of photon
multiplets that are maximally entangled in polarization. These states display
nonclassical correlations of the type described by Greenberger, Horne, and
Zeilinger (GHZ). An experimental scheme to realize a GHZ measurement using
coincidence detection of the photons escaping from the cavity is proposed. The
correlations are found to originate in the dynamics of the adiabatic passage
and persist even if cavity decay and GHZ state synthesis compete on the same
time scale. Beyond entangled field states, it is also possible to generate
entanglement between photons and the atom by using a different atomic
transition and initial Zeeman state.Comment: 22 pages (RevTeX), including 23 postscript figures. To be published
in Physical Review
- …