87 research outputs found

    Generalization of Sato equation and systems of multidimensional nonlinear Partial Differential Equations

    Full text link
    This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE) together with solutions parameterized by the set of arbitrary functions.Comment: 10 page

    On integration of multidimensional generalizations of classical CC- and SS-integrable nonlinear partial differential equations

    Full text link
    We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical CC- and SS-integrable Partial Differential Equations (PDEs). Generalizations of (1+1)-dimensional CC-integrable and (2+1)-dimensional SS-integrable NN-wave equations are derived among examples. Examples of multidimensional second order PDEs are represented as well.Comment: 31 page

    Partial structural restoring of two-qubit transferred state

    Full text link
    We consider the communication line with two-qubit sender and receiver, the later is embedded into the four-qubit extended receiver. Using the optimizing unitary transformation on the extended receiver we restore the structure of the non-diagonal part of an arbitrary initial sender's state at the remote receiver at certain time instant. Obstacles for restoring the diagonal part are discussed. We represent examples of such structural restoring in a communication line of 42 spin-1/2 particles.Comment: 17 pages, 2 figure

    Informational correlation between two parties of a quantum system: short spin-1/2 chains with XY Hamiltonian

    Full text link
    We introduce the informational correlation EABE^{AB} between two interacting quantum subsystems AA and BB of a quantum system as the number of arbitrary parameters φi\varphi_i of a unitary transformation UAU^A (locally performed on the subsystem AA) which may be detected in the subsystem BB by the local measurements. This quantity indicates whether the state of the subsystem BB may be effected by means of the unitary transformation applied to the subsystem AA. Emphasize that EAB≠EBAE^{AB}\neq E^{BA} in general. The informational correlations in systems with tensor product initial states are studied in more details. In particular, it is shown that the informational correlation may be changed by the local unitary transformations of the subsystem BB. However, there is some non-reducible part of EAB(t)E^{AB}(t) which may not be decreased by any unitary transformation of the subsystem BB at a fixed time instant tt. Two examples of the informational correlations between two parties of the four node spin-1/2 chain are studied.Comment: 45 pages, 2 figure

    A variant of the Dressing Method applied to nonintegrable multidimensional nonlinear Partial Differential Equations

    Full text link
    We describe a variant of the dressing method giving alternative representation of multidimensional nonlinear PDE as a system of Integro-Differential Equations (IDEs) for spectral and dressing functions. In particular, it becomes single linear Partial Differential Equation (PDE) with potentials expressed through the field of the nonlinear PDE. The absence of linear overdetermined system associated with nonlinear PDE creates an obstacle to obtain evolution of the spectral data (or dressing functions): evolution is defined by nonlinear IDE (or PDE in particular case). As an example, we consider generalization of the dressing method applicable to integrable (2+1)-dimensional NN-wave and Davey-Stewartson equations. Although represented algorithm does not supply an analytic particular solutions, this approach may have a perspective development.Comment: 14 page

    Construction of particular solutions to nonlinear equations of Mathematical Physics by using matrix algebraic equation

    Full text link
    The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between algebraic matrix equations and PDE. Example of (2+2)-dimensional generalization of Burgers equation is given.Comment: 17 page

    The minimal entanglement of bipartite decompositions as a witness of strong entanglement in a quantum system

    Full text link
    We {characterize the multipartite entanglement in a quantum system by the quantity} which vanishes if only the quantum system may be decomposed into two weakly entangled subsystems, unlike measures of multipartite entanglement introduced before. We refer to this {quantity} as the minimal entanglement of bipartite decompositions (MEBD). Big MEBD means that the system may not be decomposed into two weakly entangled subsystems. MEBD allows one to define, for instance, whether the given quantum system may be a candidate for a quantum register, where the above decomposition is undesirable. A method of lower estimation of MEBD is represented. Examples of big MEBD in spin-1/2 chains governed by the HdzH_{dz} Hamiltonian in the strong external magnetic field are given.Comment: 11 pages, 1 figur

    Partially integrable generalizations of classical integrable models by combination of characteristics method and Hopf-Cole transformation

    Full text link
    We represent an integration algorithm combining the characteristics method and Hopf-Cole transformation. This algorithm allows one to partially integrate a large class of multidimensional systems of nonlinear Partial Differential Equations (PDEs). A specific generalization of the equation describing the dynamics of two-dimensional viscous fluid and a generalization of the Korteweg-de Vries equation are examples of such systems. The richness of available solution space for derived nonlinear PDEs is discussed.Comment: 7 page

    Remote creation of a one-qubit mixed state through a short homogeneous spin-1/2 chain

    Full text link
    We consider a method of remote mixed state creation of a one-qubit subsystem (receiver) in a spin-1/2 chain governed by the nearest-neighbor XYXY-Hamiltonian. Owing to the evolution of the chain along with the variable local unitary transformation of the one- or two-qubit sender, a large variety of receiver states can be created during some time interval starting with a fixed initial state of the whole quantum system. These states form the creatable region of the receiver's state-space. It is remarkable that, having the two-qubit sender, a large creatable region may be covered at a properly fixed time instant t0t_0 using just the variable local unitary transformation of the sender. In this case we have completely local control of the remote state creation. In general, for a given initial state, there are such receiver's states that may not be created using the above tool. These states form the unavailable region. In turn, this unavailable region might be the creatable region of another sender. Thus, in future, we have a way to share the whole receiver's state-space among the creatable regions of several senders. The effectiveness of remote state creation is characterized by the density function of the creatable region.Comment: 30 pages, 5 figure

    Generalized hierarchy of matrix Burgers type and nn-wave equations

    Full text link
    This article concerns the dressing method for solving of multidimensional nonlinear Partial Differential Equations. In particular, we join hierarchy of matrix Burgers type equation with hierarchies of equations integrable by the Inverse Spectral Transform (IST). Example of resonance interaction of wave packets in (3+1)-dimensions is given.Comment: 7 page
    • …
    corecore