The paper deals with the nonequilibrium two-lead Anderson model, considered as an adequate description for transport through a d-c biased quantum dot. Using a self-consistent equation-ofmotion method generalized out of equilibrium, we calculate a fourth-order decoherence rate γ (4) induced by a bias voltage V . This decoherence rate provides a cut-off to the infrared divergences of the self-energy showing up in the Kondo regime. At low temperature, the Kondo peak in the density of states is split into two peaks pinned at the chemical potential of the two leads. The height of these peaks is controlled by γ (4) . The voltage dependence of the differential conductance exhibits a zero-bias peak followed by a broad Coulomb peak at large V , reflecting charge fluctuations inside the dot. The low-bias differential conductance is found to be a universal function of the normalized bias voltage V /TK, where TK is the Kondo temperature. The universal scaling with a single energy scale TK at low bias voltages is also observed for the renormalized decoherence rate γ (4) /TK . We discuss the effect of γ (4) on the crossover from strong to weak coupling regime when either the temperature or the bias voltage is increased.

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The graph isomorphism problem (GI) plays a central role in the theory of computational complexity and has importance in physics and chemistry as well \cite{kobler93,fortin96}. No polynomial-time algorithm for solving GI is known. We investigate classical and quantum physics-based polynomial-time algorithms for solving the graph isomorphism problem in which the graph structure is reflected in the behavior of a dynamical system. We show that a classical dynamical algorithm proposed by Gudkov and Nussinov \cite{gudkov02} as well as its simplest quantum generalization fail to distinguish pairs of non-isomorphic strongly regular graphs. However, by combining the algorithm of Gudkov and Nussinov with a construction proposed by Rudolph \cite{rudolph02} in which one examines a graph describing the dynamics of two particles on the original graph, we find an algorithm that successfully distinguishes all pairs of non-isomorphic strongly regular graphs that we tested with up to 29 vertices.

We solve the Schrödinger equation for two electrons plus one hole by writing it in the electronexciton basis. The main advantage of this basis is to eliminate the exciton contribution from the trion energy in a natural way. The interacting electron-exciton system is treated using the recently developed composite boson many-body formalism which allows an exact handling of electron exchange. We numerically solve the resulting electron-exciton Schrödinger equation, with the exciton levels restricted to the lowest 1s, 2s and 3s states, and we derive the trion ground state energy as a function of the electron-to-hole mass ratio. While our results are in reasonable agreement with those obtained through the best variational methods using free carrier basis, this electron-exciton basis is mostly suitable to easily reach the bound and unbound trion excited states. Through their wave functions, we here calculate the optical absorption spectrum in the presence of hot carriers for 2D quantum wells. We find large peaks located at the exciton levels, which are attributed to electron-exciton (unbound) scattering states, and small peaks identified with trion bound states.

We study the spin-valley Kondo effect of a silicon quantum dot occupied by N electrons, with N up to four. We show that the Kondo resonance appears in the N = 1, 2, 3 Coulomb blockade regimes, but not in the N = 4 one, in contrast to the spin-1/2 Kondo effect, which only occurs at N = odd. Assuming large orbital level spacings, the energy states of the dot can be simply characterized by fourfold spin-valley degrees of freedom. The density of states (DOS) is obtained as a function of temperature and applied magnetic field using a finite-U equation-of-motion approach. The structure in the DOS can be detected in transport experiments. The Kondo resonance is split by the Zeeman splitting and valley splitting for double-and triple-electron Si dots, in a similar fashion to single-electron ones. The peak structure and splitting patterns are much richer for the spin-valley Kondo effect than for the pure spin Kondo effect.

Motivated by recent experimental results, we use a factorization approach to study the threebody B → D ( * ) K − K 0 decay modes. Two mechanisms are proposed for kaon pair production: current-produced (from vacuum) and transition (from B meson).is governed solely by the current-produced mechanism. As the kaon pair can be produced only by the vector current, the matrix element can be extracted from e + e − → KK processes via isospin relations. The decay rates obtained this way are in good agreement with experiment. Both current-produced and transition processes contribute to B − → D ( * )0 K − K 0 decays. By using QCD counting rules and the measured B − → D ( * )0 K − K 0 decay rates, the measured decay spectra can be understood.

The charge transport of a serially coupled quantum dots (SCQD) connected to the metallic electrodes is theoretically investigated in the Coulomb blockade regime. A closed-form expression for the tunneling current of SCQD in the weak interdot hopping limit is obtained by solving an extended two-site Hubbard model via the Green's function method. We use this expression to investigate spin current rectification, negative differential conductance, and coherent tunneling in the nonlinear response regime. The current rectification arising from the space symmetry breaking of SCQD is suppressed by increasing temperature. The calculation of SCQD is extended to the case of multiple parallel SCQDs for studying the charge ratchet effect and SCQD with multiple levels. In the linear response regime, the functionalities of spin filter and low-temperature current filter are demonstrated to coexist in this system. It is further demonstrated that two-electron spin singlet and triplet states can be readily resolved from the measurement of Seebeck coefficient rather than that of electrical conductance.