Integrable dispersionless KdV hierarchy with sources

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge

Separation of variables for soliton equations via their binary constrained flows

Binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows. For their separation of variables only N pairs of canonical separated variables can be introduced via their Lax matrices by using the normal method. A new method to introduce the other N pairs of canonical separated variables and additional separated equations is proposed. The Jacobi inversion problems for binary constrained flows are established. Finally, the factorization of soliton equations by two commuting binary constrained flows and the separability of binary constrained flows enable us to construct the Jacobi inversion problems for some soliton hierarchies.Comment: 39 pages, Amste

Single-particle subband structure of Quantum Cables

We proposed a model of Quantum Cable in analogy to the recently synthesized coaxial nanocable structure [Suenaga et al. Science, 278, 653 (1997); Zhang et al. ibid, 281, 973 (1998)], and studied its single-electron subband structure. Our results show that the subband spectrum of Quantum Cable is different from either double-quantum-wire (DQW) structure in two-dimensional electron gas (2DEG) or single quantum cylinder. Besides the double degeneracy of subbands arisen from the non-abelian mirrow reflection symmetry, interesting quasicrossings (accidental degeneracies), anticrossings and bundlings of Quantum Cable energy subbands are observed for some structure parameters. In the extreme limit (barrier width tends to infinity), the normal degeneracy of subbands different from the DQW structure is independent on the other structure parameters.Comment: 12 pages, 9 figure

Quantum Cable as transport spectroscopy of 1D DOS of cylindrical quantum wires

We considered the proposed Quantum Cable as a kind of transport spectroscopy of one-dimensional (1D) density of states (DOS) of cylindrical quantum wires. By simultaneously detecting the direct current through the cylindrical quantum wire and the leaked tunneling current into the neighboring wire at desired temperatures, one can obtain detailed information about 1D DOS and subband structure of cylindrical quantum wires.Comment: 7 pages, 4 figures, late

On the Toda Lattice Equation with Self-Consistent Sources

The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.Comment: 20 page

Electron transport in interacting hybrid mesoscopic systems

A unified theory for the current through a nanoscale region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific circumstances. In such a formulation, the requirement of gauge invariance for the current is satisfied automatically. Moreover, one can judge unambiguously what quantities can be measured in the transport experiment

The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page

The generalized Kupershmidt deformation for constructing new integrable systems from integrable bi-Hamiltonian systems

Based on the Kupershmidt deformation for any integrable bi-Hamiltonian systems presented in [4], we propose the generalized Kupershmidt deformation to construct new systems from integrable bi-Hamiltonian systems, which provides a nonholonomic perturbation of the bi-Hamiltonian systems. The generalized Kupershmidt deformation is conjectured to preserve integrability. The conjecture is verified in a few representative cases: KdV equation, Boussinesq equation, Jaulent-Miodek equation and Camassa-Holm equation. For these specific cases, we present a general procedure to convert the generalized Kupershmidt deformation into the integrable Rosochatius deformation of soliton equation with self-consistent sources, then to transform it into a $t$-type bi-Hamiltonian system. By using this generalized Kupershmidt deformation some new integrable systems are derived. In fact, this generalized Kupershmidt deformation also provides a new method to construct the integrable Rosochatius deformation of soliton equation with self-consistent sources.Comment: 21 pages, to appear in Journal of Mathematical Physic