International Journal of Modern Physics B

We develop a magneto-transport theory for the nonlocal response of a two-dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near ν=1/2 in the presence of a periodic density modulation. We introduce a new generic model of a deformed Composite Fermion–Fermi Surface (CF–FS). Our model permits us to explain recent surface acoustic wave observations of anisotropic anomalies¹ in sound velocity and attenuation, such as appearance of peaks and anisotropy, which originate from contributions to the conductivity tensor due to regions of the CF–FS which are flattened by the applied modulation. The calculated magnetic field and wave vector dependence of the CF conductivity, velocity shift and attenuation agree with experiments.

We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the "bare" system onto the linear response of a "dressed" system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.

We present a simple and efficient method for calculating transmission coefficient of two-dimensional quantum wire structures in the presence of magnetic field. The time evolution of a wave packet is first obtained by solving the time dependent Schrödinger equation. Transmission coefficient is then extracted from the wave function by an intergal transform. This method is easier to implement than traditional time-independent methods such as mode matching method and it can be used to study the time evolution of wave functions for systems with arbitrary shape.

We calculate the quantum-mechanical transmission of electrons in a T-shaped opened quantum waveguide (TOQW) subjected to an inhomogeneous magnetic field perpendicular to the TOQW plane with the use of the mode-matching technique. An electron incident through one branch of the waveguide can travel into the other two channels in the quantum ballistic regime. We find that transmission coefficients in two channels exhibit quite difference from each other and depend sensitively on geometric parameters and magnetic configurations. Sharp peaks with unity amplitude and deep dips are observed in transmission spectrum as a function of the Fermi energy of the incident electrons at some high fields. We also study the variation of transmission with magnetic field and find that the transmission exhibits various patterns such as step drop, deep dips, wide valley, large oscillations, or without any structure, sensitively depending on the incident electron energy and magnetic confinement configurations. It is expected that by applying inhomogeneous magnetic fields to the TOQW with appropriate magnetic configuration one may provide an available way to control transmission property of the TOQW to match practical requirements in devices.

We consider a mesoscopic Josephson junction in a circular superconducting ring which encloses a magneto static flux. It is shown that with the junction being initially prepared in its lowest energy level the state of the junction can evolve in a quantum superposition of two coherent states, and squeezing can exist in such system.

It can be shown that the bosonic degree of freedom of the tightly bound on-site electron pairs could be separated as Schwinger bosons. This is implemented by projecting the whole Hilbert space into the Hilbert subspace spanned by states of two kinds of Schwinger bosons (to be called binon and vacanon) subject to a constraint that these two kinds of bosonic quasiparticles cannot occupy the same site. We argue that a binon is actually a kind of quantum fluctuations of electron pairs, and a vacanon corresponds to a vacant state. These two bosonic quasiparticles may be responsible for the Bose–Einstein condensation (BEC) of the system associated with electron pairs. These concepts are also applied to the attractive Hubbard model with strong coupling, showing that it is quite useful. The relevance of the present arguments to the existing theories associated with the BEC of electron pairs is briefly commented.

Mapping of a Bose system of interacting particles onto an effective Bose system having an upper cutoff momentum is derived by integrating out momenta between infinity and p₀ where p₀ is small compared to the inverse de Broglie wavelength λ^-1 of the particles. The mapping, within the ∊-expansion scheme, is a general result independent of any argument specific to the critical region. The cross-over behaviour of pressure and density is worked out in the normal phase as well as in the condensed phase. The results are manifestly independent of the cutoff p₀ as expected on physical grounds.