10,455 research outputs found
A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps
In this paper we prove a necessary condition of the optimal control problem
for a class of general mean-field forward-backward stochastic systems with
jumps in the case where the diffusion coefficients depend on control, the
control set does not need to be convex, the coefficients of jump terms are
independent of control as well as the coefficients of mean-field backward
stochastic differential equations depend on the joint law of . Two
new adjoint equations are brought in as well as several new generic estimates
of their solutions are investigated for analysing the higher terms, especially,
those involving the expectation which come from the derivatives of the
coefficients with respect to the measure. Utilizing these subtle estimates, the
second-order expansion of the cost functional, which is the key point to
analyse the necessary condition, is obtained, and whereafter the stochastic
maximum principle.Comment: 32 page
Majorana Edge States in Interacting Two-chain Ladders of Fermions
In this work we study interacting spinless fermions on a two-chain ladder
with inter-chain pair tunneling while single-particle tunneling is suppressed
at low energy. The model embodies a symmetry associated with the
fermion parity on each chain. We find that when the system is driven to the
strong-coupling phase by the pair tunneling, Majorana excitations appear on the
boundary. Such Majorana edge states correspond to two-fold degeneracy of ground
states distinguished by different fermion parity on each chain, thus
representing a generalization of one-dimensional topological superconductors.
We also characterize the stability of the ground state degeneracy against local
perturbations. Lattice fermion models realizing such effective field theory are
discussed.Comment: 6 pages, 1 figur
Progenitor delay-time distribution of short gamma-ray bursts: Constraints from observations
Context. The progenitors of short gamma-ray bursts (SGRBs) have not yet been
well identified. The most popular model is the merger of compact object
binaries (NS-NS/NS-BH). However, other progenitor models cannot be ruled out.
The delay-time distribution of SGRB progenitors, which is an important property
to constrain progenitor models, is still poorly understood. Aims. We aim to
better constrain the luminosity function of SGRBs and the delay-time
distribution of their progenitors with newly discovered SGRBs. Methods. We
present a low-contamination sample of 16 Swift SGRBs that is better defined by
a duration shorter than 0.8 s. By using this robust sample and by combining a
self-consistent star formation model with various models for the distribution
of time delays, the redshift distribution of SGRBs is calculated and then
compared to the observational data. Results. We find that the power-law delay
distribution model is disfavored and that only the lognormal delay distribution
model with the typical delay tau >= 3 Gyr is consistent with the data.
Comparing Swift SGRBs with T90 > 0.8 s to our robust sample (T90 < 0.8 s), we
find a significant difference in the time delays between these two samples.
Conclusions. Our results show that the progenitors of SGRBs are dominated by
relatively long-lived systems (tau >= 3 Gyr), which contrasts the results found
for Type Ia supernovae. We therefore conclude that primordial NS-NS systems are
not favored as the dominant SGRB progenitors. Alternatively, dynamically formed
NS-NS/BH and primordial NS-BH systems with average delays longer than 5 Gyr may
contribute a significant fraction to the overall SGRB progenitors.Comment: 8 pages, 6 figures, Astron. Astrophys. in pres
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