A New Optimal Stepsize For Approximate Dynamic Programming

Approximate dynamic programming (ADP) has proven itself in a wide range of applications spanning large-scale transportation problems, health care, revenue management, and energy systems. The design of effective ADP algorithms has many dimensions, but one crucial factor is the stepsize rule used to update a value function approximation. Many operations research applications are computationally intensive, and it is important to obtain good results quickly. Furthermore, the most popular stepsize formulas use tunable parameters and can produce very poor results if tuned improperly. We derive a new stepsize rule that optimizes the prediction error in order to improve the short-term performance of an ADP algorithm. With only one, relatively insensitive tunable parameter, the new rule adapts to the level of noise in the problem and produces faster convergence in numerical experiments.Comment: Matlab files are included with the paper sourc

Neutron diffraction, magnetization and ESR studies of pseudocubic Nd(0.75)Ba(0.25)MnO3 and its unusual critical behavior above Tc

Results of structural neutron diffraction study, magnetization and ESR measure-ments are presented for insulating Nd0.75Ba0.25MnO3, Tc = 129 K. The crystal structure is refined in the range 4.2-300 K. The compound is found to exhibit the Jahn-Teller (JT) transition at 250 K. The field cooled (FC) magnetization data are in a reasonable agreement with the predictions for a 3D isotropic ferromagnet above Tc. However, these measurements reveal a difference between the FC and zero FC data in the paramagnetic region. ESR results are also in a correspondence with behavior of a cubic ferromagnet above T* = 143 K. It is shown that an anisotropic exchange coupling of the Mn and Nd magnetic moments can give a substantial contribution in ESR linewidth masking its critical enhan-cement. The different temperature treatments of the sample reveal a temperature hysteresis of the ESR spectra below T* indicating an anomalous response in the paramagnetic region. The study of phase transition in this manganite suggests change in its character from the second to first order at T*. The conventional free energy including the magnetization and magnetic field is not found to describe the first order transition. This suggests that the charge, orbital and JT phonon degrees of freedom, in addition to magnetization, may be the critical variables, the unusual character of the transition being determined by their coupling. Unconventional critical behavior is attributed to orbital liquid metallic phase that coexists with the initial orbital ordered phase below T*.Comment: 18 pages, 5 figures, submitted to Phys. Rev.

Alternative fast quantum logic gates using nonadiabatic Landau-Zener-St\"{u}ckelberg-Majorana transitions

A conventional realization of quantum logic gates and control is based on resonant Rabi oscillations of the occupation probability of the system. This approach has certain limitations and complications, like counter-rotating terms. We study an alternative paradigm for implementing quantum logic gates based on Landau-Zener-St\"{u}ckelberg-Majorana (LZSM) interferometry with non-resonant driving and the alternation of adiabatic evolution and non-adiabatic transitions. Compared to Rabi oscillations, the main differences are a non-resonant driving frequency and a small number of periods in the external driving. We explore the dynamics of a multilevel quantum system under LZSM drives and optimize the parameters for increasing single- and two-qubit gates speed. We define the parameters of the external driving required for implementing some specific gates using the adiabatic-impulse model. The LZSM approach can be applied to a large variety of multi-level quantum systems and external driving, providing a method for implementing quantum logic gates on them.Comment: 15 pages, 12 figure

The Faraday effect and phase transition in the CH 3 NH 3 PbI 3 halide perovskite single crystal

The spin degree of freedom of charge carriers in halide-perovskite semiconductors can be highly useful for information photonics applications. The Faraday effect is known to be the best indicator of paramagnetism of the material and of the spin-light interaction. In this work, the Faraday effect is demonstrated, for the first time, in a hybrid organic-inorganic halide perovskite MAPbI3 (MA+=CH3NH+3). The Faraday rotation and birefringence were measured across the tetragonal-cubic phase transition at 327 K. The Faraday rotation is strongly suppressed below the phase transition temperature due to anisotropy (linear birefringence) of the tetragonal crystal phase. The situation changes drastically above the phase transition temperature, when the crystal becomes optically isotropic. The emerging Faraday rotation obeys the Curie law, demonstrating its population-related paramagnetic nature. This observation opens new prospects for application of these systems and for their investigations using methods of the polarization noise spectroscopy applicable to optically anisotropic materials.Comment: 12 pages, 5 figure

Spin noise of a halide perovskite

We report on first observation of spin noise in a strongly birefringent semiconductor -- halide perovskite single crystal MAPbI$_3$. The observed spin noise resonance is ascribed to free holes with a record spin dephasing time of 4 ns. The spin dynamics is found to be affected by the residual light absorption of the crystal providing renormalization of the Larmor frequency. Extended spin noise spectroscopy with rotating magnetic field allowed us not only to evaluate the $g$-factor anisotropy, but also to distinguish two different spin subsystems tentatively associated to twinning of the crystal.Comment: 14 pages, 11 figure