Quenched Invariance Principles for Random Walks with Random Conductances

We prove an almost sure invariance principle for a random walker among i.i.d. conductances in ℤ ^d , d≥2. We assume conductances are bounded from above but we do not require that they are bounded from below.     

Single electron charging effects in semiconductor quantum dots

We have studied charging effects in a lateral split-gate quantum dot defined by metal gates in the two dimensional electron gas (2 DEG) of a GaAs/AlGaAs heterostructure. The gate structure allows an independent control of the conductances of the two tunnel barriers separating the quantum dot from the two 2 DEG leads, and enables us to vary the number of electrons that are localized in the dot. We have measured Coulomb oscillations in the conductance and the Coulomb staircase in current-voltage characteristics and studied their dependence on the conductances of the tunnel barriers. We show experimentally that at zero magnetic field charging effects start to affect the transport properties when both barrier conductances are smaller than the first quantized conductance value of a point contact at 2e ²/h. The experiments are described by a simple model in terms of electrochemical potentials, which includes both the discreteness of the electron charge and the quantum energy states due to confinement.     

Magnetization of disordered ballistic quantum billards

We study the magnetic response of mesoscopic quantum dots in the ballistic regime where the mean free path l_e is larger that the size L of the sample, yet smaller than L(K_FL)^d?1. In this regime, disorder plays an important role. Employing a semiclassical picture we calculate the contribution of long tranjectories which are strongly affected by static disorder and which differ sharply from those of clean systems. In the case of a magnetic field, they give rise to a large linear paramagnetic susceptibility (which is disorder independent), whose magnitude is in agreement with recent experimental results. In the case of a Aharonov-Bohm flux, the susceptibility is disorder dependent and is proportional to the mean free path as in the diffusive regime. We also discuss the corresponding non-linear susceptibilities.     

Molecular physics and chemistry applications of quantum Monte Carlo

We discuss recent work with the diffusion quantum Monte Carlo (QMC) method in its application to molecular systems. The formal correspondence of the imaginary-time Schrödinger equation to a diffusion equation allows one to calculate quantum mechanical expectation values as Monte Carlo averages over an ensemble of random walks. We report work on atomic and molecular total energies, as well as properties including electron affinities, binding energies, reaction barriers, and moments of the electronic charge distribution. A brief discussion is given on how standard QMC must be modified for calculating properties. Calculated energies and properties are presented for a number of molecular systems, including He, F, F^?, H₂, N, and N₂. Recent progress in extending the basic QMC approach to the calculation of “analytic” (as opposed to finite-difference) derivatives of the energy is presented, together with an H₂ potential-energy curve obtained using analytic derivatives.     

Current progress on heat conduction in one-dimensional gas channels

We give a brief review of the past development of model studies on one-dimensional heat conduction. Particularly, we describe recent achievements on the study of heat conduction in one-dimensional gas models including the hard-point gas model and billiard gas channel. For a one-dimensional gas of elastically colliding particles of unequal masses, heat conduction is anomalous due to momentum conservation, and the divergence exponent of heat conductivity is estimated as α≈0.33 in k ∼ L ^α . Moreover, in billiard gas models, it is found that exponent instability is not necessary for normal heat conduction. The connection between heat conductivity and diffusion is investigated. Some new progress is reported. A recently proposed model with a quantized degree of freedom to study the heat transport in quasi-one dimensional systems is illustrated in which three distinct temperature regimes of heat conductivity are manifested. The establishment of local thermal equilibrium (LTE) in homogeneous and heterogeneous systems is also discussed. Finally, we give a summary with an outlook for further study about the problem of heat conduction.     

Universal Schwinger cocycles of current algebras in (D+1)-dimensions: Geometry and physics

We discuss the universal version of the Schwinger terms of current algebra (we call it the universal Schwinger cocycle) forp=3 (herep denotes the class of the Schatten idealI _p , which is related to the (D+1) space-time dimensions byp=(D+1)/2) in detail, and give a conjecture of the general form of the cocycle for anyp. We also discuss the infinite charge renormalizations, the highest weight vector and state vectors forp=3. Last, we give brief comments on the problems caused by the difficulties to construct the measure of infinite-dimensional Grassmann manifolds.     

Low-Energy Universality in Atomic and Nuclear Physics

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this progress report, we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.     

Electronic structure and excitations on clean and nanostructured metal surfaces

We present a brief overview of recent studies and new theoretical results for electron-phonon interaction in the $\overline{Y}$ surface states on FCC(110) noble metal surfaces as well as in surface and quantum-well states of thin films. We discuss the oscillations of electron-phonon coupling parameter λ and the respective contribution to the lifetime broadening of these states. We analyse the effect of spin-orbit splitting of surface states on an electron-electron contribution to lifetimes of excited electrons (holes). Oscillations of the electron-electron contribution and quadratic dependence of the linewidth on energy is discussed for ultrathin Pb(111) films.     

Liquid water: A very complex fluid

Although H₂O has been the topic of considerable research since the beginning of the century, the peculiar physical properties are still not well understood. First we discuss some of the anomalies of this ‘complex fluid’. Then we describe a qualitative interpretation in terms of percolation concepts. Finally, we discuss recent experiments and simulations relating to the hyothesis that, in addition to the known critical point in water, there exists a ‘second’ critical point at low temperatures. In particular, we discuss very recent measurements of the compression-induced melting and decompression-induced melting lines of high-pressure forms of ice. We show how knowledge of these lines enables one to obtain an approximation for the Gibbs potential G(P, T) and the equation of state V(P,T) for water, both of which are consistent with the possible continuity of liquid water and the amorphous forms of solid water.     

Update on the status of hadronic squeezed correlations at RHIC energies

In high energy heavy ion collisions a hot and dense medium is formed, where the hadronic masses may be shifted from their asymptotic values. If this mass modification occurs, squeezed back-to-back correlations (BBC) of particle-antiparticle pairs are predicted to appear, both in the femionic (fBBC) and in the bosonic (bBBC) sectors. Although they have unlimited intensity even for finite-size expanding systems, these hadronic squeezed correlations are very sensitive to their time emission distribution. Here we discuss results in case this time emission is parameterized by a Lévy-type distribution, showing that it reduces the signal even more dramatically than a Lorentzian distribution, which already reduces the intensity of the effect by orders of magnitude, as compared to the sudden emission. However, we show that the signal could still survive if the duration of the process is short, and if the effect is searched for lighter mesons, such as kaons. We compare some of our results to recent PHENIX preliminary data on squeezed correlations of K ⁺ K ⁻ pairs.     

Does the local structure play a role in high temperature superconductivity?

Many highT_csystems exhibit structural distortions or anomalies, some of which correlate withT_c. We present our results for three such systems and discuss them in the context of providing any evidence for coupling of the lattice to the superconducting pairs. We then propose a modulation type of experiment that should provide unambiguous results if a significant lattice-pair coupling does exist.     

Infrared singularities in one-dimensional fermi systems

We study the infrared problem in one-dimensional Fermi systems with general interactions including backward scattering. The singular structure of the ground state energy which is a function of two coupling parametersu andv is determined exactly. For attractiveu-coupling one has power law singularities inv with a characteristic singular exponentk varying continuously withu. This behavior is reminiscent of a phase transition of continuous order and is obtained here by exploiting the analogy of the 1-d Fermi system and a 2-d classical plasma with a long range logarithmic Coulomb potential and a short range cut off. We also discuss other recent approaches to the problem.Supported in part by the Army Research Office, Durham, N.C., while the author was a summer visitor at Stanford University.     

On the linear dependence of 13C spin polarization parameters

The Jahn-Teller (J-T) effect in systems of four-fold symmetry is well known to differ from that in all other point groups with respect to the nature of the J-T active normal modes of vibration. The present report addresses some previously unnoticed features which are of intrinsic importance in recognizing and understanding the unique manifestations of quadrate symmetry in both the static and dynamic Jahn-Teller effects. We first consider the nature of the static J-T potential surfaces when coupling to and strains in two modes, b ₁ and b ₂, are included in the hamiltonian.

The second part of this paper is devoted to an examination of the dynamic J-T effect in four-fold systems. Utilizing both perturbation theory and numerical solution to the Schrödinger equation, we examine the spin-hamiltonian parameters for a metalloporphyrin ³ E_u triplet state and discuss some dynamical processes, including reorientation of the system between minima, spin-lattice relaxation, and the dependences of these phenomena on the nature and magnitude of the off-diagonal terms in the hamiltonian. There emerge from this analysis several signal differences between the Jahn-Teller effect for a doubly degenerate state in four-fold systems and in the more usual cubic or tetrahedral situation.     

solitons in quantum Hall systems

We present here an elementary pedagogical introduction to CP_N solitons in quantum Hall systems. We begin with a brief introduction to both CP_N models and to quantum Hall (QH) physics. We then focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact CP_N fields for N = 1 and N = 3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding CP_N field equations. We conclude with a brief summary of our own recent work in this area, done with Sankalpa Ghosh. Received 17 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: doug0700@mail.jnu.ac.in     

A Noncommutative Approach to Ordinary Differential Equations

We adapt ideas coming from Quantum Mechanics to develop a non-commutative strategy for the analysis of some systems of ordinary differential equations. We show that the solution of such a system can be described by an unbounded, self-adjoint and densely defined operator H which we call, in analogy with Quantum Mechanics, the Hamiltonian of the system.We discuss the role of H in the analysis of the integrals of motion of the system. Finally, we apply this approach to several examples.     

Molecular structure of nuclei

Cluster structures of nuclei are discussed, with emphasis on nuclear clustering in unstable nuclei. The subjects we discuss are alpha condensed states, clustering in Be and B isotopes, and clustering in ³²Mg and ³⁰Ne. The subject of alpha cluster condensation comes from the clustering nature of dilute nuclear matter. We discuss that recent heavy-ion central collision experiments give us nice evidence of the clustering in dilute nuclear matter. We then present a new prediction of the existence of the “alpha cluster condensed states” in the self-conjugate 4n nuclei around the breakup threshold energy into n alpha-particles. As for the clustering in neutron-rich Be, we discuss the comparison between the antisymmetrized molecular-dynamics results and the recent experimental data, which shows that the clustering feature manifests itself very clearly in neutron-rich Be isotopes both in the ground and excited states. Clustering in Be isotopes near neutron dripline is intimately related to the breaking of the neutron magic number N = 8. We report our recent study about the possible relationship between the clustering and the breaking of the neutron magic number N = 20 in ³²Mg and ³⁰Ne. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: horiuchi@ruby.scphys.kyoto-u.ac.jp     

Decay of correlations. IV. Necessary and sufficient conditions for a rapid decay of correlations

We considerN-particle systems whose probability distributions obey the master equation. For these systems, we derive the necessary and sufficient conditions under which the reducedn-particle (n) probabilities also obey master equations and under which the Ursell functions decay to their equilibrium values faster than the probability distributions. These conditions impose restrictions on the form of the transition rate matrix and thus on the form of its eigenfunctions. We first consider systems in which the eigenfunctions of theN-particle transition rate matrix are completely factorized and demonstrate that for such systems, the reduced probabilities obey master equations and the Ursell functions decay rapidly if certain additional conditions are imposed. As an example of such a system, we discuss a random walk ofN pairwise interacting walkers. We then demonstrate that for systems whoseN-particle transition matrix can be written as a sum of one-particle, two-particle, etc. contributions, and for which the reduced probabilities obey master equations, the reduced master equations become, in the thermodynamic limit, those for independent particles, which have been discussed by us previously. As an example of suchN-particle systems, we discuss the relaxation of a gas of interacting harmonic oscillators.Supported in part (grants to D.B. and K.E.S.) by the Advanced Research Projects Agency of the Department of Defense as monitored by the U.S. Office of Naval Research under Contract N00014-69-A-0200-6018, and in part (grant to I.O.) by the National Science Foundation.     

Macroscopic behavior of systems with an axial dynamic preferred direction

We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new cross-coupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called [^(l)]\hat l vector in superfluid ³He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.     

A Non-Commutative Approach to Ordinary Differential Equations

We adapt ideas coming from Quantum Mechanics to develop a non-commutative strategy for the analysis of some systems of ordinary differential equations. We show that the solution of such a system can be described by an unbounded, self-adjoint and densely defined operator H which we call, in analogy with Quantum Mechanics, the Hamiltonian of the system. We discuss the role of H in the analysis of the integrals of motion of the system. Finally, we apply this approach to several examples. Pacs Numbers: 02.30.Hq, 03.65.-w, 03.65.Db     

Coulomb blockade in single tunnel-junctions: Quantum mechanical effects of the electromagnetic environment

We discuss the interaction of a tunneling electron with its equilibrium electromagnetic environment. The environment of an isolated tunnel junction is modeled by a set of harmonic oscillators that are suddenly displaced when an electron tunnels across the junction. We treat these displaced oscillators quantum mechanically, predicting behavior that is very different than that predicted by a semiclassical treatment. In particular, the shape of the zero-bias anomaly caused by the Coulomb blockade (a single-electron charging effect), is found to be strongly dependent on the impedance,Z (), of the leads connected to the junction. Comparison with three recent experiments demonstrates that the quantum mechanical treatment of this model correctly describes the essential physics in these systems.