On the tau-functions of the Degasperis-Procesi equation

The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and pfaffians, and the $\tau$-functions of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and Theoretical, to be publishe

Small-Recoil Approximation

In this review we discuss a technique to compute and to sum a class of Feynman diagrams, and some of its applications. These are diagrams containing one or more energetic particles that suffer very little recoil in their interactions. When recoil is completely neglected, a decomposition formula can be proven. This formula is a generalization of the well-known eikonal formula, to non-abelian interactions. It expresses the amplitude as a sum of products of irreducible amplitudes, with each irreducible amplitude being the amplitude to emit one, or several mutually interacting, quasi-particles. For abelian interaction a quasi-particle is nothing but the original boson, so this decomposition formula reduces to the eikonal formula. In non-abelian situations each quasi-particle can be made up of many bosons, though always with a total quantum number identical to that of a single boson. This decomposition enables certain amplitudes of all orders to be summed up into an exponential form, and it allows subleading contributions of a certain kind, which is difficult to reach in the usual way, to be computed. For bosonic emissions from a heavy source with many constituents, a quasi-particle amplitude turns out to be an amplitude in which all bosons are emitted from the same constituent. For high-energy parton-parton scattering in the near-forward direction, the quasi-particle turns out to be the Reggeon, and this formalism shows clearly why gluons reggeize but photons do not. The ablility to compute subleading terms in this formalism allows the BFKL-Pomeron amplitude to be extrapolated to asymptotic energies, in a unitary way preserving the Froissart bound. We also consider recoil corrections for abelian interactions in order to accommodate the Landau-Pomeranchuk-Migdal effect.Comment: 21 pages with 4 figure

Nuclear spin qubits in a trapped-ion quantum computer

Physical systems must fulfill a number of conditions to qualify as useful quantum bits (qubits) for quantum information processing, including ease of manipulation, long decoherence times, and high fidelity readout operations. Since these conditions are hard to satisfy with a single system, it may be necessary to combine different degrees of freedom. Here we discuss a possible system, based on electronic and nuclear spin degrees of freedom in trapped ions. The nuclear spin yields long decoherence times, while the electronic spin, in a magnetic field gradient, provides efficient manipulation, and the optical transitions of the ions assure a selective and efficient initialization and readout.Comment: 7 page

Achieving precise mechanical control in intrinsically noisy systems

How can precise control be realized in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way of achieving precise control in signal-dependent noisy environments. When the control signal has Poisson or supra-Poisson noise, precise control is not possible. If, however, the control signal has sub-Poisson noise, then precise control is possible. For this case, the precise control solution is not a function, but a rapidly varying random process that must be averaged with respect to a governing probability density functional. Our theoretical approach is applied to the control of straight-trajectory arm movement. Sub-Poisson noise in the control signal is shown to be capable of leading to precise control. Intriguingly, the control signal for this system has a natural counterpart, namely the bursting pulses of neurons-trains of Dirac-delta functions-in biological systems to achieve precise control performance

Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity

We present a quantum electrodynamical model involving nitrogen-vacancy centers coupled to a whispering-gallery mode cavity. Two schemes are considered to create W state and Bell state, respectively. One of the schemes makes use of the Raman transition with the cavity field virtually excited; The other enables the Bell state preparation and quantum information transfer by virtue of dark state evolution and adiabatic passage, which is tolerant to ambient noise and experimental parameter fluctuations. We justify our schemes by considering the experimental feasibility and challenge using currently available technology.Comment: 8 pages and 5 figure

The development of local government financial vehicles in China: A case study of Jiaxing Chengtou

Financial intermediaries have been widely used in urban development. Since the global financial crisis, it has been an urgent task to understand their operation and implications for financial risks. This paper examines emerging local government financial vehicles (LGFVs) in China. We review their history, current status and underlying financial mechanisms. Confronting the global financial crisis, China has taken a stimulus plan to invest four-trillion Yuan in urban development to stimulate the economy. The plan has been largely fulfilled by the LGFVs. This paper investigates the case of Jiaxing City Construction Investment Corporation (Jiaxing Chengtou), which plays a role of LGFVs. We find that it mainly uses bank loans and bonds to finance land and infrastructure development. To borrow from the capital market, Jiaxing Chengtou collateralizes allocated state-owned land and enhances credits by build and transfer protocols with the city government. However, the enterprise did not manage to pay back its loans, which has led to further borrowing. Due to the central government’s control, Jiaxing Chengtou has been nominally detached from the municipal government since 2012, but it maintains a financial role. It has been re-packaged with other LGFVs to access foreign bond markets. The paper reveals how LGFVs act as financial conduits to connect local governments with the financial market in China

Log-Harnack Inequality for Stochastic Differential Equations in Hilbert Spaces and its Consequences

A logarithmic type Harnack inequality is established for the semigroup of solutions to a stochastic differential equation in Hilbert spaces with non-additive noise. As applications, the strong Feller property as well as the entropy-cost inequality for the semigroup are derived with respect to the corresponding distance (cost function)