David E. Logan

Quantum localization and energy flow in many‐dimensional Fermi resonant systems

The quantum mechanics of energy flow in many‐dimensional Fermi resonant systems has several connections to the theory of Anderson localization in disordered solids. We argue that in high dimensional and highly quantum mechanical systems the energy flow can be modeled as coherent transport on a locally but weakly correlated random energy surface. This model exhibits a sharp but continuous transition from local to global energy flow characterized by critical exponents. Dephasing smears the transition and an interesting nonmonotonic dependence of energy flow rate on environmental coupling is predicted to occur near the transition.

The non-coincidence effect in the raman spectra of polar liquids

Abstract A theory is presented for the first moments of the infrared, isotropic Raman and anisotropic Raman spectra of symmetric polar modes in dipolar isotopic binary mixtures. Particular attention is given to the Raman non-coincidence effect. The thermodynamic state dependences of first moment differences are investigated, together with the influence of the static dielectric constant on the non-coincidence effect. The theory is compared with experiments on specific systems, with which it is found to be in good agreement.

On the isotropic Raman spectra of isotopic binary mixtures

A theory is developed for the isotropic Raman spectrum of nondegenerate modes in polyatomic binary mixtures. Particular emphasis is attached to isotopic binary mixtures and the problem of dipolar resonant transfer. The thermodynamic state dependences of spectral features are investigated in some detail. Attention is focused on quantities which are experimentally accessible by isotopic dilution experiments, in particular the frequency shift of the spectrum consequent upon isotopic dilution, and also the resultant changes in spectral second moments. The theory is compared with some existing experiments on specific systems, and a number of predictions are made which are capable of being tested experimentally.

The Raman noncoincidence effect in dipolar binary mixtures

Abstract A molecular theory is given for the thermodynamic state dependence of the Raman noncoincidence effect, arising from transition dipolar resonant transfer in dipolar binary liquid mixtures. Predictions of the theory are discussed, and some suggestions for possible experiments are made.

Quantum phase transition in quantum dot trimers

We investigate a system of three tunnel-coupled semiconductor quantum dots in a triangular geometry, one of which is connected to a metallic lead, in the regime where each dot is essentially singly occupied. Both ferro- and antiferromagnetic spin-1/2 Kondo regimes, separated by a quantum phase transition, are shown to arise on tuning the interdot tunnel couplings and should be accessible experimentally. Even in the ferromagnetically-coupled local moment phase, the Kondo effect emerges in the vicinity of the transition at finite temperatures. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of the problem.

A local moment approach to the Anderson model

A theory is developed for the single-particle spectra of the symmetric Anderson model, in which local moments are introduced explicitly from the outset. Dynamical coupling of single-particle processes to low-energy spin-flip excitations leads, within the framework of a two-self-energy description, to a theory in which both low- and high-energy spectral features are simultaneously captured, while correctly preserving Fermi liquid behaviour at low energies. The atomic limit, non-interacting limit and strong-coupling behaviour of the spectrum are each recovered. For strong coupling in particular, both the exponential asymptotics of the Kondo resonance and concomitant many-body broadening of the Hubbard satellite bands are shown to arise naturally within the present approach.

The density of states of a spatially disordered tight-binding model

The authors give an exact analysis of the configurationally averaged Green functions for a random tight-binding model characterised by quenched liquid-like disorder, using a graph-theoretical method originally applied by Wertheim to a problem in classical dielectric theory. The structural characteristics of the system are incorporated fully. They derive a formally exact self-consistency equation for the averaged diagonal Green function G(z), from which follows the density of states. A systematic derivation and critical discussion of various approximate theories for G(z) is given. They also show that extension to include site-diagonal disorder is straightforward for single-site theories. Finally, an illustrative calculation of the density of states is carried out for the low-density domain.

Zero-bias conductance in carbon nanotube quantum dots.

We present numerical renormalization group calculations for the zero-bias conductance of quantum dots made from semiconducting carbon nanotubes. These explain and reproduce the thermal evolution of the conductance for different groups of orbitals, as the dot-lead tunnel coupling is varied and the system evolves from correlated Kondo behavior to more weakly correlated regimes. For integer fillings N=1, 2, 3 of an SU(4) model, we find universal scaling behavior of the conductance that is distinct from the standard SU(2) universal conductance, and concurs quantitatively with experiment. Our results also agree qualitatively with experimental differential conductance maps.

Local moment formation and Kondo screening in impurity trimers.

We study theoretically a triangular cluster of three magnetic impurities, hybridizing locally with conduction electrons of a metallic host. Such a cluster is the simplest to exhibit frustration, an important generic feature of many complex molecular systems in which different interactions compete. Here, low-energy doublet states of the trimer are favored by effective exchange interactions produced by strong electronic repulsion in localized impurity orbitals. Parity symmetry protects a level crossing of such states on tuning microscopic parameters, while an avoided crossing arises in the general distorted case. Upon coupling to a metallic host, the behavior is shown to be immensely rich because collective quantum many-body effects now also compete. In particular, impurity degrees of freedom are totally screened at low temperatures in a Kondo-screened Fermi liquid phase, while degenerate ground states persist in a local moment phase. Local frustration drives the quantum phase transition between the two, which may be first order or of Kosterlitz-Thouless type, depending on symmetries. Unusual mechanisms for local moment formation and Kondo screening are found due to the orbital structure of the impurity trimer. Our results are of relevance for triple quantum dot devices. The problem is studied by a combination of analytical arguments and the numerical renormalization group.

On the dielectric theory of fluids: II. Gases in non-uniform fields

In this, the third paper of a series, we develop a rigorous theory of the static dielectric constant, e, of non-polar fluids within the Quadrupole Approximation, whereby the effects of induced molecular quadrupoles are incorporated into the theory. The molecular quadrupoles are induced in response to the gradients of both the externally applied field and the fields due to the molecular dipoles and quadrupoles. Two hitherto distinct approaches to the problem of the electrostatic constitutive relationship are considered. The first is a grand canonical fluctuation formalism, formulated in terms of the local field and field gradient introduced in paper I of the series. The second, or direct approach to the problem is based on treating the externally applied field (field gradient) as the driving field (field gradient) in the microscopic linear response equations. By starting from non-local integral equations relating the macroscopic dipole (quadrupole) polarization, P(Q), to the external field and field gradie...