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Register a new userA Two Fluid Description of the Quantum Hall Soliton
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We show that the Quantum Hall Soliton constructed in cite{giantbob} is stable under small perturbations. We find that creating quasiparticles actually lowers the energy of the system, and discuss whether this indicates an instability on the time scales relevant to the problem.
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We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced in the previous century. The developed formalism permits to relate the circulation conservation (Tompson theorem) with the invariance of the theory with respect to special diffiomorphisms and establish also the new conservation laws. We discuss also the difference of the Eulerian and Lagrangian description, pointing out the incompleteness of the first. The constructed formalism is also applicable for ideal plasma. We conclude with several remarks on the quantization of the fluid.
We present a systematic study of the response properties of two-band (multi-gap) superconductors with spin-singlet (s-wave) pairing correlations, which are assumed to be caused by both intraband (lambda_{ii}, i=1,2) and interband (lambda_{12}) pairing interactions. In this first of three planned publications we concentrate on the properties of such superconducting systems in global and local thermodynamic equilibrium, the latter including weak perturbations in the stationary long-wavelength limit. The discussion of global thermodynamic equilibrium must include the solution (analytical in the Ginzburg-Landau and the low temperature limit) of the coupled self-consistency equations for the two energy gaps Delta_i(T), i=1,2. These solutions allow to study non-universal behavior of the two relevant BCS-Muhlschlegel parameters, namely the specific heat discontinuity Delta C/C_N and the zero temperature gaps Delta_i(0)/pi k_B T_c, i=1,2. The discussion of a local equilibrium situation includes the calculation of the supercurrent density as a property of the condensate, and the calculation of both the specific heat capacity and the spin susceptibility as properties of the gas of thermal excitations in the spirit of a microscopic two-fluid description. Non-monotonic behavior in the temperature dependences of the gaps and all these local response functions is predicted to occur particularly for very small values of the interband pair-coupling constant lambda_{12}.
Using the Madelung transformation we show that in a quantum Free Electron Laser (QFEL) the beam obeys the equations of a quantum fluid in which the potential is the classical potential plus a quantum potential. The classical limit is shown explicitly.
We investigate a coupled system of a Dirac particle and a pseudoscalar field in the form of a soliton in (1+1) dimensions and find some of its exact solutions numerically. We solve the coupled set of equations self-consistently and non-perturbatively by the use of a numerical method and obtain the bound states of the fermion and the shape of the soliton. That is the shape of the static soliton in this problem is not prescribed and is determined by the equations themselves. This work goes beyond the perturbation theory in which the back reaction of the fermion on soliton is its first order correction. We compare our results to those of an exactly solvable model in which the soliton is prescribed. We show that, as expected, the total energy of our system is lower than the prescribed one. We also compute non-perturbatively the vacuum polarization of the fermion induced by the presence of the soliton and display the results. Moreover, we compute the soliton mass as a function of the boson and fermion masses and find that the results are consistent with Skyrmes phenomenological conjecture. Finally, we show that for fixed values of the parameters, the shape of the soliton obtained from our exact solutions depends slightly on the fermionic state to which it is coupled. However, the exact shape of the soliton is always very close to the isolated kink.
We describe D=4 twistorial membrane in terms of two twistorial three-dimensional world volume fields. We start with the D-dimensional p-brane generalizations of two phase space string formulations: the one with $p+1$ vectorial fourmomenta, and the second with tensorial momenta of $(p+1)$-th rank. Further we consider tensionful membrane case in D=4. By using the membrane generalization of Cartan-Penrose formula we express the fourmomenta by spinorial fields and obtain the intermediate spinor-space-time formulation. Further by expressing the worldvolume dreibein and the membrane space-time coordinate fields in terms of two twistor fields one obtains the purely twistorial formulation. It appears that the action is generated by a geometric three-form on two-twistor space. Finally we comment on higher-dimensional (D>4) twistorial p-brane models and their superextensions.
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