43,931 research outputs found
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
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
-functions of the DP equation are obtained from the pseudo 3-reduction of
the 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)
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