Dual condensates at finite isospin chemical potential

The dual observables as order parameters for center symmetry are tested at finite isospin chemical potential $\mu_I$ in a Polyakov-loop enhanced chiral model of QCD with physical quark masses. As a counterpart of the dressed Polyakov-loop, the first Fourier moment of pion condensate is introduced for $\mu_I>{m_\pi}/{2}$ under the temporal twisted boundary conditions for quarks. We demonstrate that this dual condensate exhibits the similar temperature dependence as the conventional Polyakov-loop. We confirm that its rapid increase with $T$ is driven by the evaporating of pion condensation. On the other hand, the dressed Polyakov-loop shows abnormal thermal behavior, which even decreases with $T$ at low temperatures due to the influence of pion condensate. We thus argue that in QCD the critical temperature extracting from a dual observable may have nothing to do with the quark confinement-deconfinement transition if the quark mass is very small.Comment: 8 pages, 6 figure

On global solution to the Klein-Gordon-Hartree equation below energy space

In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in $\R^3$. By making use of Bourgain's method in conjunction with a precise Strichartz estimate of S.Klainerman and D.Tataru, we establish the $H^s (s<1)$ global well-posedness of the Cauchy problem for the cubic convolution defocusing Klein-Gordon-Hartree equation. Before arriving at the previously discussed conclusion, we obtain global solution for this non-scaling equation with small initial data in $H^{s_0}\times H^{s_0-1}$ where $s_0=\frac\gamma 6$ but not $\frac\gamma2-1$, for this equation that we consider is a subconformal equation in some sense. In doing so a number of nonlinear prior estimates are already established by using Bony's decomposition, flexibility of Klein-Gordon admissible pairs which are slightly different from that of wave equation and a commutator estimate. We establish this commutator estimate by exploiting cancellation property and utilizing Coifman and Meyer multilinear multiplier theorem. As far as we know, it seems that this is the first result on low regularity for this Klein-Gordon-Hartree equation.Comment: 31 page

Transmitter Optimization Techniques for Physical Layer Security

Information security is one of the most critical issues in wireless networks as the signals transmitted through wireless medium are more vulnerable for interception. Although the existing conventional security techniques are proven to be safe, the broadcast nature of wireless communications introduces different challenges in terms of key exchange and distributions. As a result, information theoretic physical layer security has been proposed to complement the conventional security techniques for enhancing security in wireless transmissions. On the other hand, the rapid growth of data rates introduces different challenges on power limited mobile devices in terms of energy requirements. Recently, research work on wireless power transfer claimed that it has been considered as a potential technique to extend the battery lifetime of wireless networks. However, the algorithms developed based on the conventional optimization approaches often require iterative techniques, which poses challenges for real-time processing. To meet the demanding requirements of future ultra-low latency and reliable networks, neural network (NN) based approach can be employed to determine the resource allocations in wireless communications. This thesis developed different transmission strategies for secure transmission in wireless communications. Firstly, transmitter designs are focused in a multiple-input single-output simultaneous wireless information and power transfer system with unknown eavesdroppers. To improve the performance of physical layer security and the harvested energy, artificial noise is incorporated into the network to mask the secret information between the legitimate terminals. Then, different secrecy energy efficiency designs are considered for a MISO underlay cognitive radio network, in the presence of an energy harvesting receiver. In particular, these designs are developed with different channel state information assumptions at the transmitter. Finally, two different power allocation designs are investigated for a cognitive radio network to maximize the secrecy rate of the secondary receiver: conventional convex optimization framework and NN based algorithm