41,746 research outputs found
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
Analytical Potential Energy Function for the Ground State X^{1} Sigma^+ of LaCl
The equilibrium geometry, harmonic frequency and dissociation energy of
lanthanum monochloride have been calculated at B3LYP, MP2, QCISD(T) levels with
energy-consistent relativistic effective core potentials. The possible
electronic state and reasonable dissociation limit for the ground state are
determined based on atomic and molecular reaction statics. Potential energy
curve scans for the ground state X^{1} Sigma^+ have been carried out with B3LYP
and QCISD(T) methods due to their better performance in bond energy
calculations. We find the potential energy calculated with QCISD(T) method is
about 0.5 eV larger than dissociation energy when the diatomic distance is as
large as 0.8 nm. The problem that single-reference ab initio methods don't meet
dissociation limit during calculations of lanthanide heavy-metal elements is
analyzed. We propose the calculation scheme to derive analytical Murrell-Sorbie
potential energy function and Dunham expansion at equilibrium position.
Spectroscopic constants got by standard Dunham treatment are in good agreement
with results of rotational analyses on spectroscopic experiments. The
analytical function is of much realistic importance since it is possible to be
applied to predict fine transitional structure and study reaction dynamic
process.Comment: 10 pages, 1 figure, 3 table
Asynchronous Distributed ADMM for Large-Scale Optimization- Part I: Algorithm and Convergence Analysis
Aiming at solving large-scale learning problems, this paper studies
distributed optimization methods based on the alternating direction method of
multipliers (ADMM). By formulating the learning problem as a consensus problem,
the ADMM can be used to solve the consensus problem in a fully parallel fashion
over a computer network with a star topology. However, traditional synchronized
computation does not scale well with the problem size, as the speed of the
algorithm is limited by the slowest workers. This is particularly true in a
heterogeneous network where the computing nodes experience different
computation and communication delays. In this paper, we propose an asynchronous
distributed ADMM (AD-AMM) which can effectively improve the time efficiency of
distributed optimization. Our main interest lies in analyzing the convergence
conditions of the AD-ADMM, under the popular partially asynchronous model,
which is defined based on a maximum tolerable delay of the network.
Specifically, by considering general and possibly non-convex cost functions, we
show that the AD-ADMM is guaranteed to converge to the set of
Karush-Kuhn-Tucker (KKT) points as long as the algorithm parameters are chosen
appropriately according to the network delay. We further illustrate that the
asynchrony of the ADMM has to be handled with care, as slightly modifying the
implementation of the AD-ADMM can jeopardize the algorithm convergence, even
under a standard convex setting.Comment: 37 page
- …