Abstract:
Einstein's field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a self-consistency condition. In this work, the Deutsch equation is formulated as an eigenvalue problem. The disappearance of entanglement between two qubits in an Einstein-Podolsky-Rosen (EPR) state near a CTC is demonstrated. The method is utilized to analyze the discontinuous evolution of two chronology respecting (CR) qubits near a CTC.

Abstract:
We study time dependence of exchange symmetry properties of Bell states when two qubits interact with local baths having identical parameters. In case of classical noise, we consider a decoherence Hamiltonian which is invariant under swapping the first and second qubits. We find that as the system evolves in time, two of the three symmetric Bell states preserve their qubit exchange symmetry with unit probability, whereas the symmetry of the remaining state survives with a maximum probability of 0.5 at the asymptotic limit. Next, we examine the exchange symmetry properties of the same states under local, quantum mechanical noise which is modeled by two identical spin baths. Results turn out to be very similar to the classical case. We identify decoherence as the main mechanism leading to breaking of qubit exchange symmetry.

Abstract:
We studied the effects of nonmagnetic impurities on high-temperature superconductors by solving the Bogoliubov-de Gennes equations on a two-dimensional lattice via exact diagonalization technique in a fully self-consistent way. We found that s-wave order parameter is almost unaffected by impurities at low concentrations while $d_{x^2-y^2}$-wave order parameter exhibits a strong linear decrease with impurity concentration. We evaluated the critical impurity concentration $n_i^c$ at which superconductivity ceases to be 0.1 which is in good agreement with experimental values. We also investigated how the orthorhombic nature of the crystal structure affects the suppression of superconductivity and found that anisotropy induces an additional s-wave component. Our results support $d_{x^2-y^2}$-wave symmetry for tetragonal and $s+d_{x^2-y^2}$-wave symmetry for orthorhombic structure.

Abstract:
We study the localization property of a two-dimensional noninteracting electron gas in the presence of randomly distributed short-range scatterers. We evaluate the participation number of the eigenstates obtained by exact diagonalization technique. At low impurity concentrations we obtain self-averaged values showing that all states, except those exactly at the Landau level, are localized with finite localization length. We conclude that there is no universal localization exponent and at least at low impurity concentrations localization length does not diverge.

Abstract:
We introduce an exactly solvable model to study decoherence of a central spin interacting with a spin bath where the coupling is mediated by phonons which we assume to be in a coherent state or thermal distribution. For the coherent state case, we find that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times. If the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important role in decoherence with increasing temperature. We also discuss possible effects of the temperature on spin bath contribution to decoherence.

Abstract:
A method, analogous to supersymmetry transformation in quantum mechanics, is developed for a particle in the lowest Landau level moving in an arbitrary potential. The method is applied to two-dimensional potentials formed by Dirac delta scattering centers. In the periodic case, the problem is solved exactly for rational values of the magnetic flux (in units of flux quantum) per unit cell. The spectrum is found to be self-similar, resembling the Hofstadter butterfly.

Abstract:
We study pairing correlations in ultrasmall superconductor in the nanoscopic limit by means of a toy model where electrons are confined in a single, multiply degenerate energy level. We solve the model exactly to investigate the temperature and magnetic field dependence of number parity effect (dependence of ground state energy on evenness or oddness of the number of electrons). We find a different parity effect parameter to critical temperature ratio (=~ 4 rather than 3.5) which turns out to be consistent with exact solution of the BCS gap equation for our model. This suggest the equivalence between the parity effect parameter and the superconducting gap. We also find that magnetic field is suppressed as temperature increases.

Abstract:
We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator does not depend on the state to be transferred. We show that perfect state transfer over an arbitrary distance can be achieved only if the walk is driven by an identity or a flip coin operator. Other biased coin operators and Hadamard coin allow perfect state transfer over finite distances only. Furthermore, we show that quantum walks ending with a perfect state transfer are periodic.

Abstract:
We have analytically calculated the quantum discord for a system composed of spin-$j$ and spin-1/2 subsystems possessing SU(2) symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in our case amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have also compared their quantum discord with entanglement. Although the system under consideration is separable nearly all throughout of its parameter space as $j$ increases, we have seen that discord content remains significantly large. Investigation of quantum discord in SU(2) invariant states may find application in quantum computation protocols that utilize quantum discord as a resource since they arise in many real physical systems.

Abstract:
We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii equation within the semi-classical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for finite number of particles at low temperature indicating a phase transition for weakly interacting systems.