Persistence of entanglement in thermal states of spin systems

We study and compare the persistence of bipartite entanglement (BE) and multipartite entanglement (ME) in one-dimensional and two-dimensional spin XY models in an external transverse magnetic field under the effect of thermal excitations. We compare the threshold temperature at which the entanglement vanishes in both types of entanglement. We use the entanglement of formation as a measure of the BE and the geometric measure to evaluate the ME of the system. We have found that in both dimensions in the anisotropic and partially anisotropic spin systems at zero temperatures, all types of entanglement decay as the magnetic field increases but are sustained with very small magnitudes at high field values. Also we found that for the same systems, the threshold temperatures of the nearest neighbour (nn) BEs are higher than both of the next-to-nearest neighbour BEs and MEs and the three of them increase monotonically with the magnetic field strength. Thus, as the temperature increases, the ME and the far parts BE of the system become more fragile to thermal excitations compared to the nn BE. For the isotropic system, all types of entanglement and threshold temperatures vanish at the same exact small value of the magnetic field. We emphasise the major role played by both the properties of the ground state of the system and the energy gap in controlling the characteristics of the entanglement and threshold temperatures. In addition, we have shown how an inserted magnetic impurity can be used to preserve all types of entanglement and enhance their threshold temperatures. Furthermore, we found that the quantum effects in the spin systems can be maintained at high temperatures, as the different types of entanglements in the spin lattices are sustained at high temperatures by applying sufficiently high magnetic fields.Comment: 20 pages, 17 figure

Entanglement in a Time-Dependent Coupled XY Spin Chain in an External Magnetic Field

We consider an infinite one dimensional anisotropic XY spin chain with a nearest neighbor time-dependent Heisenberg coupling J(t) between the spins in presence of a time-dependent magnetic field h(t). We discuss a general solution for the system and present an exact solution for particular choice of J and h of practical interest. We investigate the dynamics of entanglement for different degrees of anisotropy of the system and at both zero and finite temperatures. We find that the time evolution of entanglement in the system show non-ergodic and critical behavior at zero and finite temperatures and different degrees of anisotropy. The asymptotic behavior of entanglement at the infinite time limit at zero temperature and constant J and h depends only the parameter lambda=J/h rather than the individual values of J and h for all degrees of anisotropy but changes for nonzero temperature. Furthermore, the asymptotic behavior is very sensitive to the initial values of J and h and for particular choices we may create finite asymptotic entanglement regardless of the final values of J and h. The persistence of quantum effects in the system as it evolves and as the temperature is raised is studied by monitoring the entanglement. We find that the quantum effects dominates within certain regions of the kT-lambda space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persists in the vicinity of both its critical phase transition point and zero temperature as it evolves in time. Moreover, the interplay between the different system parameters to tune and control the entanglement evolution is explored.Comment: 33 pages, 17 figures; v3: Grammar errors and typos corrected, Figure 17(b) update

Entanglement dynamics of one-dimensional driven spin systems in time-varying magnetic fields

We study the dynamics of entanglement for a one-dimensional spin chain with a nearest neighbor time dependent Heisenberg coupling J(t) between the spins in presence of a time dependent external magnetic field h(t) at zero and finite temperatures. We consider different forms of time dependence for the coupling and magnetic field; exponential, hyperbolic and periodic. We examined the system size effect on the entanglement asymptotic value. It was found that for a small system size the entanglement starts to fluctuate within a short period of time after applying the time dependent coupling. The period of time increases as the system size increases and disappears completely as the size goes to infinity. We also found that when J(t) is periodic the entanglement shows a periodic behavior with the same period, which disappears upon applying periodic magnetic field with the same frequency. Solving the particular case where J(t) and h(t) are proportional exactly, we showed that the asymptotic value of entanglement depends only on the initial conditions regardless of the form of J(t) and h(t) applied at t > 0.Comment: 22 pages and 8 figure

Impurity effect on entanglement in an XY two-dimensional spin lattice

AbstractWe consider a finite two dimensional XY spin model. The model consists of a set of seven localized spin- 12 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction in presence of an external magnetic field. We study the effect of a single impurity spin coupled to its nearest neighbor through an exchange interaction J′ on the pairwise entanglement between the different spins in the lattice. We found that when the spin is located at a border site the entanglement between the impurity and its nearest neighbors increases monotonically with J′ reaching a saturation value that depends on the magnetic field strength h. On the other hand the entanglement with the next nearest spins shows a critical behavior where the entanglement increases and then decreases rapidly until it vanishes. The critical coupling value at which the entanglement vanishes increases as h increases. Studying the entanglement between two spins excluding the impurity show that while the entanglement between two spins coupled to the impurity reach a saturation value as J′ increases, it vanishes for spins not coupled to the impurity. Furthermore studying the effect of a central impurity show that the entanglement between nearest neighbor and next nearest neighbor spins reaches an asymptotic value as J′ increases. Interestingly it was demonstrated that the impurity can be used as a switch to control the entanglement between different spins in the lattice turning it on and off

Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

We study the time evolution of entanglement of two spins in anisotropically coupled quantum dot interacting with the unpolarized nuclear spins environment. We assume that the exchange coupling strength in the z-direction $J_z$ is different from the lateral one $J_l$. We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference $J=\| J_l-J_z\|$ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behavior controlled by the competition between the exchange interaction $J$ and the external magnetic field. The entanglement shows a quasi-symmetric behavior above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for isotropically coupled quantum dot.Comment: 24 pages and 7 figures. v3: major change

Investigation of high bandwith biodevices for transcutaneous wireless telemetry

PhD ThesisBIODEVICE implants for telemetry are increasingly applied today in various areas applications. There are many examples such as; telemedicine, biotelemetry, health care, treatments for chronic diseases, epilepsy and blindness, all of which are using a wireless infrastructure environment. They use microelectronics technology for diagnostics or monitoring signals such as Electroencephalography or Electromyography. Conceptually the biodevices are defined as one of these technologies combined with transcutaneous wireless implant telemetry (TWIT). A wireless inductive coupling link is a common way for transferring the RF power and data, to communicate between a reader and a battery-less implant. Demand for higher data rate for the acquisition data returned from the body is increasing, and requires an efficient modulator to achieve high transfer rate and low power consumption. In such applications, Quadrature Phase Shift Keying (QPSK) modulation has advantages over other schemes, and double the symbol rate with respect to Binary Phase Shift Keying (BPSK) over the same spectrum band. In contrast to analogue modulators for generating QPSK signals, where the circuit complexity and power dissipation are unsuitable for medical purposes, a digital approach has advantages. Eventually a simple design can be achieved by mixing the hardware and software to minimize size and power consumption for implantable telemetry applications. This work proposes a new approach to digital modulator techniques, applied to transcutaneous implantable telemetry applications; inherently increasing the data rate and simplifying the hardware design. A novel design for a QPSK VHDL modulator to convey a high data rate is demonstrated. Essentially, CPLD/FPGA technology is used to generate hardware from VHDL code, and implement the device which performs the modulation. This improves the data transmission rate between the reader and biodevice. This type of modulator provides digital synthesis and the flexibility to reconfigure and upgrade with the two most often languages used being VHDL and Verilog (IEEE Standard) being used as hardware structure description languages. The second objective of this thesis is to improve the wireless coupling power (WCP). An efficient power amplifier was developed and a new algorithm developed for auto-power control design at the reader unit, which monitors the implant device and keeps the device working within the safety regulation power limits (SAR). The proposed system design has also been modeled and simulated with MATLAB/Simulink to validate the modulator and examine the performance of the proposed modulator in relation to its specifications.Higher Education Ministry in Liby

The effect of violence during mass uprisings on the duration of the democratization process and inclusiveness in elections

The democratization process of countries all over the world after mass uprisings differs greatly. Some countries are confronted with extreme violence, while others remain peaceful. This thesis examines whether the amount of violence during mass uprisings leads to a longer democratization process and less inclusive elections in terms of voter base. It looks at the revolutions of 1989 in Eastern Europe which brought down the Communist bloc. The repercussions of the presence or lack of violence during the mass uprisings on the behavior of the population in each country is visible until this very day – with Romania and Bulgaria still struggling from subtle, but deep-rooted internal conflicts and discomfort with the concept of democracy, and Hungary, Poland, the Czech Republic and Slovakia’s significant progress in the democratization process and gradual increase of substantially embracing democratic values

Fault-tolerant fpga for mission-critical applications.

One of the devices that play a great role in electronic circuits design, specifically safety-critical design applications, is Field programmable Gate Arrays (FPGAs). This is because of its high performance, re-configurability and low development cost. FPGAs are used in many applications such as data processing, networks, automotive, space and industrial applications. Negative impacts on the reliability of such applications result from moving to smaller feature sizes in the latest FPGA architectures. This increases the need for fault-tolerant techniques to improve reliability and extend system lifetime of FPGA-based applications. In this thesis, two fault-tolerant techniques for FPGA-based applications are proposed with a built-in fault detection region. A low cost fault detection scheme is proposed for detecting faults using the fault detection region used in both schemes. The fault detection scheme primarily detects open faults in the programmable interconnect resources in the FPGAs. In addition, Stuck-At faults and Single Event Upsets (SEUs) fault can be detected. For fault recovery, each scheme has its own fault recovery approach. The first approach uses a spare module and a 2-to-1 multiplexer to recover from any fault detected. On the other hand, the second approach recovers from any fault detected using the property of Partial Reconfiguration (PR) in the FPGAs. It relies on identifying a Partially Reconfigurable block (P_b) in the FPGA that is used in the recovery process after the first faulty module is identified in the system. This technique uses only one location to recover from faults in any of the FPGA’s modules and the FPGA interconnects. Simulation results show that both techniques can detect and recover from open faults. In addition, Stuck-At faults and Single Event Upsets (SEUs) fault can also be detected. Finally, both techniques require low area overhead