41,529 research outputs found
Thermodynamic arrow of time of quantum projective measurements
We investigate a thermodynamic arrow associated with quantum projective
measurements in terms of the Jensen-Shannon divergence between the probability
distribution of energy change caused by the measurements and its time reversal
counterpart. Two physical quantities appear to govern the asymptotic values of
the time asymmetry. For an initial equilibrium ensemble prepared at a high
temperature, the energy fluctuations determine the convergence of the time
asymmetry approaching zero. At low temperatures, finite survival probability of
the ground state limits the time asymmetry to be less than . We
illustrate our results for a concrete system and discuss the fixed point of the
time asymmetry in the limit of infinitely repeated projections.Comment: 6 pages in two columns, 1 figure, to appear in EP
Comparison of free energy estimators and their dependence on dissipated work
The estimate of free energy changes based on Bennett's acceptance ratio
method is examined in several limiting cases and compared with other estimates
based on the Jarzynski equality and on the Crooks relation. While the absolute
amount of dissipated work, defined as the surplus of average work over the free
energy difference, limits the practical applicability of Jarzynski's and
Crooks' methods, the reliability of Bennett's approach is restricted by the
difference of the dissipated works in the forward and the backward process. We
illustrate these points by considering a Gaussian chain and a hairpin chain
which both are extended during the forward and accordingly compressed during
the backward protocol. The reliability of the Crooks relation predominantly
depends on the sample size; for the Jarzynski estimator the slowness of the
work protocol is crucial, and the Bennett method is shown to give precise
estimates irrespective of the pulling speed and sample size as long as the
dissipated works are the same for the forward and the backward process as it is
the case for Gaussian work distributions. With an increasing dissipated work
difference the Bennett estimator also acquires a bias which increases roughly
in proportion to this difference. A substantial simplification of the Bennett
estimator is provided by the 1/2-formula which expresses the free energy
difference by the algebraic average of the Jarzynski estimates for the forward
and the backward processes. It agrees with the Bennett estimate in all cases
when the Jarzynski and the Crooks estimates fail to give reliable results
Effects of Luminosity Functions Induced by Relativistic Beaming on Statistics of Cosmological Gamma-Ray Bursts
We study the effects of the beaming-induced luminosity function on statistics
of observed GRBs, assuming the cosmological scenario. We select and divide the
BATSE 4B data into 588 long bursts (T sec) and 149 short bursts
(T sec), and compare the statistics calculated in each subgroup. The
of the long bursts is $ 0.2901\pm 0.0113$, and that of the
short bursts is $0.4178\pm 0.0239$, which is a Euclidean value. For luminosity
function models, we consider a cylindrical-beam and a conic-beam. We take into
account the spatial distribution of GRB sources as well. A broad luminosity
function is naturally produced when one introduces beaming of GRBs. We
calculate the maximum detectable redshift of GRBs, $z_{\rm max}$. The estimated
$z_{\rm max}$ for the cylindrical-beam case is as high as $\sim 14$ for the
long bursts and $\sim 3$ for the short bursts. The large $z_{\rm max}$ value
for the short bursts is rather surprising in that the for
this subgroup is close to the so-called Euclidean value, 0.5. We calculate the
fraction of bursts whose redshifts are larger than a certain redshift ,
i.e. . When we take and apply the luminosity function
derived for the cylindrical-beam, the expected is
for long bursts. When we increase the opening angle of the conic beam to
, decreases to at . We conclude that the beaming-induced luminosity functions are
compatible with the redshift distribution of observed GRBs and that the
apparent Euclidean value of may not be due to the Euclidean
space distribution but to the luminosity distribution.Comment: Accepted for publication in the Astronomical Journal (vol. 548, Feb.
20 2001
Witten Index and Wall Crossing
We compute the Witten index of one-dimensional gauged linear sigma models
with at least supersymmetry. In the phase where the gauge
group is broken to a finite group, the index is expressed as a certain residue
integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied
through the phase boundaries. The wall crossing formula is expressed as an
integral at infinity of the Coulomb branch. The result is applied to many
examples, including quiver quantum mechanics that is relevant for BPS states in
theories.Comment: 123 pages, v3: the discussion on the smooth transition (Section 4.4)
is improved, more minor corrections made; v2: references added, minor
corrections mad
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