The transport properties of a quantum dot that is weakly coupled to leads are investigated by using the exact quantum states of a finite number of interacting electrons. It is shown that in addition to the Coulomb blockade, spin selection rules strongly influence the low temperature transport, and lead to experimentally observable effects. Transition probabilities between states that correspond to successive electron numbers vanish if the total spins differ by | ∆S |> 1/2. In non-linear transport, this can lead to negative differential conductances. The linear conductance peaks are suppressed if transitions between successive ground states are forbidden.

The pair localization length L2 of two interacting electrons in one-dimensional disordered systems is studied numerically. Using two direct approaches, we find L2 ∝ L α 1 , where L1 is the one-electron localization length and α ≈ 1.65. This demonstrates the enhancement effect proposed by Shepelyansky, but the value of α differs from previous estimates (α = 2) in the disorder range considered. We explain this discrepancy using a scaling picture recently introduced by Imry and taking into account a more accurate distribution than previously assumed for the overlap of one-electron wavefunctions.PACS numbers: 71.30, 72.15.R Very recently, Shepelyansky [1] considered the problem of two interacting electrons in a random potential, defined by the Schrödinger equation, U characterizes the on-site interaction and V i is a random potential distributed uniformly in the interval [−W, W ]. The indices n 1 and n 2 denote the positions of the first and the second electron, respectively. Shepelyansky proposed that, as a consequence of the interaction U , certain eigenstates extend over a range L 2 much larger than the one-particle localization length L 1 ∝ W −2 . A key quantity in the derivation of this spectacular result in one dimension is the matrix representation U of the Hubbard interaction in the disorder diagonal basis of localized oneelectron eigenstates. With R n,i the amplitude at site n of the one-particle eigenstate with energy E i we have U ij,lm = U Q ij,lm with Q ij,lm = n R n,i R n,j R n,l R n,m .(The Q ij,lm vanish unless all four eigenstates are roughly localized within the same box of size L 1 . Assuming that R n,i ∝ a n / √ L 1 inside the box, with a n a random number of order unity, and neglecting correlations among the a n at different sites n, one finds Q ≈ 1/L 3/2 1 for a typical nonvanishing matrix element. In [1], this estimate was adopted and used to reduce the original problem to a certain band matrix model, eventually giving L 2 ∝ L 2 1 . Later, Imry [2] employed the Thouless scaling block picture to reinforce, interpret and generalize this result. The key step in this approach involves the pair conductance g 2 = (U Q/δ 2 ) 2 , where δ 2 is the two-particle level spacing in a block of size L 1 and Q is evaluated between adjacent blocks. Using Q ≈ 1/L 3/2 1 as before, Imry finds that g 2 ≈ 1 on the scale L 2 ∝ L 2 1 , in agreement with Shepelyansky. As a second important result both approaches predict that the effect does not depend on the sign of U .In this letter, we confirm the enhancement effect by studying both the original model (1) for finite size samples and an infinite "bag model" with medium-range interaction. However, we find L 2 ∝ L α 1 with α ≈ 1.65 instead of α = 2 in both cases. Moreover, the sign of U is not entirely irrelevant. We suggest that the small value for α is due to a very peculiar distribution of the Q ij,lm .

The electronic environment causes decoherence and dissipation of the collective surface plasmon excitation in metallic nanoparticles. We show that the coupling to the electronic environment influences the width and the position of the surface plasmon resonance. A redshift with respect to the classical Mie frequency appears in addition to the one caused by the spill out of the electronic density outside the nanoparticle. We characterize the spill-out effect by means of a semiclassical expansion and obtain its dependence on temperature and the size of the nanoparticle. We demonstrate that both, the spill-out and the environment-induced shift are necessary to explain the experimentally observed frequencies and confirm our findings by time-dependent local density approximation calculations of the resonance frequency. The size and temperature dependence of the environmental influence results in a qualitative agreement with pump-probe spectroscopic measurements of the differential light transmission.

We determine the lifetime of the surface plasmon in metallic nanoparticles under various conditions, concentrating on the Landau damping, which is the dominant mechanism for intermediate-size particles. Besides the main contribution to the lifetime, which smoothly increases with the size of the particle, our semiclassical evaluation yields an additional oscillating component. For the case of noble metal particles embedded in a dielectric medium, it is crucial to consider the details of the electronic confinement; we show that in this case the lifetime is determined by the shape of the self-consistent potential near the surface. Strong enough perturbations may lead to the second collective excitation of the electronic system. We study its lifetime, which is limited by two decay channels: Landau damping and ionization. We determine the size dependence of both contributions and show that the second collective excitation remains as a well-defined resonance.

We study the linewidth of the surface plasmon resonance in the optical absorption spectrum of metallic nanoparticles, when the decay into electron-hole pairs is the dominant channel. Within a semiclassical approach, we find that the electron-hole density-density correlation oscillates as a function of the size of the particles, leading to oscillations of the linewidth. This result is confirmed numerically for alkali and noble metal particles. While the linewidth can increase strongly, the oscillations persist when the particles are embedded in a matrix.

We consider two particles with a local interaction U in a random potential at a scale L1 (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define the symmetry breaking parameter µ ∝ U −2 associated to the statistical invariance under change of basis. We show that the Wigner-Dyson rigidity of the energy levels is maintained up to an energy Eµ. We find that Eµ ∝ 1/ √ µ when Γ (the inverse lifetime of the states of the preferential basis) is smaller than ∆2 (the level spacing), and Eµ ∝ 1/µ when Γ > ∆2. This implies that the two-particle localization length L2 first increases as |U | before eventually behaving as U 2 .PACS numbers: 72.15, 73.20For a single particle diffusing in a disordered system of size L smaller than the one particle localization length L 1 , there are two characteristic energies: the Thouless energy E c =hD/L 2 and the level spacing, D and d are the band width, the diffusion constant and the system dimension, respectively). If one writes the distribution of energy levels as a Gibbs factor of a fictituous Coulomb gas, the corresponding pairwise interaction for levels with separation ǫ < E c coincides [1] with the logarithmic repulsion characteristic of the matrix ensembles which are statistically invariant under change of basis, e. g. the Gaussian Orthogonal Ensemble (GOE). For ǫ > E c , the level repulsion vanishes more or less quickly, depending on the system dimension. The dimensionless conductance g 1 is given by E c /∆ 1 . This ratio is the single relevant parameter in the scaling theory of localization. In quasi-one dimension, the size where g 1 ≈ 1 defines L 1 . In three dimensions, the mobility edge is characterized by g 1 ≈ g c where g c is of order 1.We shall generalize those concepts to two particles with a local (repulsive or attractive) interaction. This two interacting particle (TIP) problem has received a particular attention since Shepelyansky [2] pointed out that certain TIP states may extend over a scale L 2 much larger than L 1 . Shepelyansky's original reasoning consists in mapping the problem for L ≫ L 1 onto a random band matrix model with a superimposed diagonal matrix (SBRM-model). Imry [3] used later the Thouless scaling block picture to arrive at precisely the same results as Shepelyansky. The smearing due to the interaction of the energy levels within L 1 was estimated using Fermi's golden rule, yielding L 2 ∝ U 2 . This delocalization effect has been confirmed by transfer matrix studies [4,5], and unambiguously illustrated from numerical studies [6] of rings threaded by an AB-flux. However, in one dimension, for system sizes which can be numerically investigated, one obtains To understand those contradictory results, we study the TIP energy level statistics at a scale L 1 in order to identify the energy which plays the role of E c in this case, and to determine its dependence on U . For the original TIP-problem, we assume a tight-binding model1 sites p where the random potential is ...

A systematic theory of the conductance measurements of noninvasive (weak probe) scanning gate microscopy is presented that provides an interpretation of what precisely is being measured. A scattering approach is used to derive explicit expressions for the first-and second-order conductance changes due to the perturbation by the tip potential in terms of the scattering states of the unperturbed structure. In the case of a quantum point contact, the first-order correction dominates at the conductance steps and vanishes on the plateaux where the second-order term dominates. Both corrections are nonlocal for a generic structure. Only in special cases, such as that of a centrally symmetric quantum point contact in the conductance quantization regime, can the second-order correction be unambiguously related with the local current density. In the case of an abrupt quantum point contact, we are able to obtain analytic expressions for the scattering eigenfunctions and thus evaluate the resulting conductance corrections.

The full spectrum of two interacting electrons in a disordered mesoscopic one{dimensional ring threaded by a magnetic ux is calculated numerically. For ring sizes far exceeding the one{particle localization length L1 we nd several h=2e{periodic states whose eigenfunctions exhibit a pairing e ect. This represents the rst direct observation of interaction{assisted coherent pair propagation, the pair being delocalized on the scale of the whole ring.PACS numbers: 72.15, 73.20 For more than three decades Anderson localization has been a subject of intensive research (for a review see 1]). Among the rst results in this eld was the fact that noninteracting electrons in one dimension (1d) are always localized and that their wave{functions decay exponentially on the scale of the localization length L 1 . Very recently, Shepelyansky 2] and later Imry 3] considered two interacting electrons in a 1d random potential. Both authors suggest that in a regime of not too strong disorder correlated electron pair states may extend over a distance L 2 / L 2 1 much larger than L 1 . This completely novel e ect could very well have a fundamental impact on our understanding of the localization problem and other related areas. However, the methods employed in 2,3], though powerful and suggestive, are partly approximate and partly qualitative. Shepelyansky's original reasoning relied on certain assumptions of a statistical nature, allowing him to map the problem onto a random band matrix model. A numerical study of this model together with additional evidence from a variety of other models formed the basis for his claim. Imry, on the other hand, invoked the Thouless scaling block picture to arrive at precisely the same results as Shepelyansky. Moreover, Imry's approach seems to be very suitable to generalize the e ect to higher dimensions.The key quantity in 2,3] was the distribution of interaction matrix elements in the disorder{diagonal basis. This distribution de nes the statistical properties of the band matrix model and provides the interblock coupling in the scaling approach. In a recent study 4] employing the transfer matrix technique we investigated numerically both nite and in nite systems starting from rst principles. In this work, the principal e ect was con rmed, but the two{particle localization length L 2 was found to scale with a smaller exponent, L 2 / L 1:65 1 , in the parameter range investigated. This modi cation could be attributed to particular properties of the above{mentioned distribution which had not been taken into account in 2,3].In the present paper, we demonstrate the existence of h=2e{periodic states in the spectrum of a disordered mesoscopic ring with two interacting electrons by direct diagonalization. Inspection of the two{electron eigenfunctions reveals that this period halving is indeed due to a pairing e ect: Both electrons propagate coherently around the ring, staying within a distance of a few L 1 from each other. This is the rst direct observation of interaction{assisted coherent pair propagation ...