14,703 research outputs found
Possible quantum phase-manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms
The recent realization of mixed-dimensional systems of cold atoms has
attracted much attention from both experimentalists and theorists. Different
effective interactions and novel correlated quantum many-body phases may be
engineered in these systems, with the different phases being tunable via
external parameters. In this article we investigate a two-species Fermi atom
mixture: one species of atom exists in two hyperfine states and is confined to
move in a two-leg ladder, interacting with an on-site interaction, and the
other moves freely in a two dimensional square lattice that contains the
two-leg ladder. The two species of atoms interact via an on-site interaction on
the ladder. In the limit of weak inter-species interactions, the
two-dimensional gas can be integrated out, leading to an effective long-range
mediated interaction in the ladder, generated by to the on-site inter-species
interaction. We show that the form of the mediated interaction can be
controlled by the density of the two-dimensional gas and that it enhances the
charge density wave instability in the two-leg ladder after the renormalization
group transformation. Parameterizing the phase diagram with various
experimentally controllable quantities, we discuss the possible tuning of the
macroscopic quantum many-body phases of the two-leg ladder in this
mixed-dimensional fermionic cold atom system.Comment: 4 pages and 3 figure
Correct-by-synthesis reinforcement learning with temporal logic constraints
We consider a problem on the synthesis of reactive controllers that optimize
some a priori unknown performance criterion while interacting with an
uncontrolled environment such that the system satisfies a given temporal logic
specification. We decouple the problem into two subproblems. First, we extract
a (maximally) permissive strategy for the system, which encodes multiple
(possibly all) ways in which the system can react to the adversarial
environment and satisfy the specifications. Then, we quantify the a priori
unknown performance criterion as a (still unknown) reward function and compute
an optimal strategy for the system within the operating envelope allowed by the
permissive strategy by using the so-called maximin-Q learning algorithm. We
establish both correctness (with respect to the temporal logic specifications)
and optimality (with respect to the a priori unknown performance criterion) of
this two-step technique for a fragment of temporal logic specifications. For
specifications beyond this fragment, correctness can still be preserved, but
the learned strategy may be sub-optimal. We present an algorithm to the overall
problem, and demonstrate its use and computational requirements on a set of
robot motion planning examples.Comment: 8 pages, 3 figures, 2 tables, submitted to IROS 201
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