Non-probabilistic solutions of imprecisely defined fractional-order diffusion equationsChakraverty, S.; Tapaswini, Smita
doi: 10.1088/1674-1056/23/12/120202pmid: N/A
The fractional diffusion equation is one of the most important partial differential equations (PDEs) to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 < 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases.
A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equationLv, Zhong-Quan; Zhang, Lu-Ming; Wang, Yu-Shun
doi: 10.1088/1674-1056/23/12/120203pmid: N/A
In this paper, we derive a new method for a nonlinear Schrödinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ‖ · ‖2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.
Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum opticsZhan, De-Hui; Fan, Hong-Yi
doi: 10.1088/1674-1056/23/12/120301pmid: N/A
We derive some new generating function formulae of the two-variable Hermite polynomials, such as Hn,2m (x), H2n,2m (x,y), and H2n+l,2m+k (x,y). We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.
Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation methodEshghi, M.; Ikhdair, S. M.
doi: 10.1088/1674-1056/23/12/120304pmid: N/A
A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S(r) and a vector V(r) Mie-type potential in the radial coordinates, as well as a tensor potential U(r) in the form of Coulomb potential. In the pseudospin (p-spin) symmetry setting = Cps and = V(r), an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spinorbit coupling number . Special attention is devoted to the case = 0 for which p-spin symmetry is exact. The Laplace transform approach (LTA) is used in our calculations. Some numerical results are obtained and compared with those of other methods.
Preparation of optimal entropy squeezing state of atomic qubit inside the cavity via two-photon process and manipulation of atomic qubit outside the cavityZhou, Bing-Ju; Peng, Zhao-Hui; Jia, Chun-Xia; Jiang, Chun-Lei; Liu, Xiao-Juan
doi: 10.1088/1674-1056/23/12/120305pmid: N/A
Considering two atomic qubits initially in Bell states, we send one qubit into a vacuum cavity with two-photon resonance and leave the other one outside. Using quantum information entropy squeezing theory, the time evolutions of the entropy squeezing factor of the atomic qubit inside the cavity are discussed for two cases, i.e., before and after rotation and measurement of the atomic qubit outside the cavity. It is shown that the atomic qubit inside the cavity has no entropy squeezing phenomenon and is always in a decoherent state before the operating atomic qubit outside the cavity. However, the periodical entropy squeezing phenomenon emerges and the optimal entropy squeezing state can be prepared for the atomic qubit inside the cavity by adjusting the rotation angle, choosing the interaction time between the atomic qubit and the cavity, controlling the probability amplitudes of subsystem states. Its physical essence is cutting the entanglement between the atomic qubit and its environment, causing the atomic qubit inside the cavity to change from the initial decoherent state into maximum coherent superposition state, which is a possible way of recovering the coherence of a single atomic qubit in the noise environment.
Generating genuine multipartite entanglement via X Y-interaction and via projective measurementsAli, Mazhar
doi: 10.1088/1674-1056/23/12/120307pmid: N/A
We have studied the generation of multipartite entangled states for the superconducting phase qubits. The experiments performed in this direction have the capacity to generate several specific multipartite entangled states for three and four qubits. Our studies are also important as we have used a computable measure of genuine multipartite entanglement whereas all previous studies analyzed certain probability amplitudes. As a comparison, we have reviewed the generation of multipartite entangled states via von Neumann projective measurements.