Dynamical formation of stable irregular transients in discontinuous map systems

Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so far. In this paper, we investigate the dynamical formation of stable irregular transients in coupled discontinuous map systems. Interestingly, it is found that the transient dynamics has a hidden pattern in the phase space: it repeatedly approaches a basin boundary and then jumps from the bundary to a remote region in the phase space. This pattern can be clearly visualized by measuring the distance sequences between the trajectory and the basin boundary. The dynamical formation of stable chaos originates from the intersection points of the discontinuous boundaries and their images. We carry out numerical experiments to verify this mechanism.Comment: 5 pages, 5 figure

Complexing Agents on Carbon Content and Lithium Storage Capacity of LiFePO 4

Olivine-structured LiFePO4 faces its intrinsic challenges in terms of poor electrical conductivity and lithium-ion diffusion capability for application to lithium-ion batteries. Cost-effective sol-gel approach is advantageous to in situ synthesize carbon-coated LiFePO4 (LiFePO4/C) which can not only improve electronic conductivity but also constrain particle size to nanometer scale. In this study, the key parameter is focused on the choice and amount of chelating agents in this synthesis route. It was found that stability of complexing compounds has significant impacts on the carbon contents and electrochemical properties of the products. At the favorable choice of precursors, composition, and synthesis conditions, nanocrystalline LiFePO4/C materials with appropriate amount of carbon coating were successfully obtained. A reversible capacity of 162 mAh/g was achieved at 0.2C rate, in addition to good discharge rate capability

Rate-Distortion-Based Physical Layer Secrecy with Applications to Multimode Fiber

Optical networks are vulnerable to physical layer attacks; wiretappers can improperly receive messages intended for legitimate recipients. Our work considers an aspect of this security problem within the domain of multimode fiber (MMF) transmission. MMF transmission can be modeled via a broadcast channel in which both the legitimate receiver's and wiretapper's channels are multiple-input-multiple-output complex Gaussian channels. Source-channel coding analyses based on the use of distortion as the metric for secrecy are developed. Alice has a source sequence to be encoded and transmitted over this broadcast channel so that the legitimate user Bob can reliably decode while forcing the distortion of wiretapper, or eavesdropper, Eve's estimate as high as possible. Tradeoffs between transmission rate and distortion under two extreme scenarios are examined: the best case where Eve has only her channel output and the worst case where she also knows the past realization of the source. It is shown that under the best case, an operationally separate source-channel coding scheme guarantees maximum distortion at the same rate as needed for reliable transmission. Theoretical bounds are given, and particularized for MMF. Numerical results showing the rate distortion tradeoff are presented and compared with corresponding results for the perfect secrecy case.Comment: 30 pages, 5 figures, accepted to IEEE Transactions on Communication

Magnetic Phase Transitions in One-dimensional Strongly Attractive Three-Component Ultracold Fermions

We investigate the nature of trions, pairing and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the groundstate energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.Comment: 4 pages, 3 figures, minor revisions to text, replacement figure, refs added and update

Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.Comment: 8 pages, 6 figures, additional text and reference

Universal behavior of giant electroresistance in epitaxial La0.67Ca0.33MnO3 thin films

We report a giant resistance drop induced by dc electrical currents in La0.67Ca0.33MnO3 epitaxial thin films. Resistance of the patterned thin films decreases exponentially with increasing current and a maximum drop shows at the temperature of resistance peak Tp. Variation of resistance with current densities can be scaled below and above Tp, respectively. This work can be useful for the future applications of electroresistance.Comment: 13 pages, 4 figure