Events, processes, and the time of a killing

The paper proposes a novel solution to the problem of the time of a killing (ToK), which persistently besets theories of act-individuation. The solution proposed claims to expose a crucial wrong-headed assumption in the debate, according to which ToK is essentially a problem of locating some event that corresponds to the killing. The alternative proposal put forward here turns on recognizing a separate category of dynamic occurents, viz. processes. The paper does not aim to mount a comprehensive defense of process ontology, relying instead on extant defenses. The primary aim is rather to put process ontology to work in diagnosing the current state of play over ToK, and indeed in solving it

Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors

We study the response of the transmission eigenvalue spectrum of disordered metallic conductors to an arbitrary external perturbation. For systems without time-reversal symmetry we find an exact non-perturbative solution for the two-point correlation function, which exhibits a new kind of universal behavior characteristic of disordered conductors. Systems with orthogonal and symplectic symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of Oxford), to appear in Phys. Rev. B (Rapid Communication

Correlations and fluctuations of a confined electron gas

The grand potential $\Omega$ and the response $R = - \partial \Omega /\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\mu$ or external parameter $x$. We compute their autocorrelation as a function of $\mu$, $x$ and temperature. The result is related to the short-time dynamics of the corresponding classical system, implying in general the absence of a universal regime. Chaotic, diffusive and integrable motions are investigated, and illustrated numerically. The autocorrelation of the persistent current of a disordered mesoscopic ring is also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.

Mesoscopic mechanism of adiabatic charge transport

We consider adiabatic charge transport through mesoscopic metallic samples caused by a periodically changing external potential. We find that both the amplitude and the sign of the charge transferred through a sample per period are random sample specific quantities. The characteristic magnitude of the charge is determined by the quantum interference.Comment: 4 pages, 2 figure

A Brownian Motion Model of Parametric Correlations in Ballistic Cavities

A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We derive a formula for the power spectrum of the fluctuations of transport observables as a response to an external adiabatic perturbation. Our formula correctly recovers the Lorentzian-squared behaviour obtained by semiclassical approaches for the correlation function of conductance fluctuations.Comment: 19 pages, written in RevTe

Optimal Fluctuations and Tail States of non-Hermitian Operators

A statistical field theory is developed to explore the density of states and spatial profile of `tail states' at the edge of the spectral support of a general class of disordered non-Hermitian operators. These states, which are identified with symmetry broken, instanton field configurations of the theory, are closely related to localized sub-gap states recently identified in disordered superconductors. By focusing separately on the problems of a quantum particle propagating in a random imaginary scalar potential, and a random imaginary vector potential, we discuss the methodology of our approach and the universality of the results. Finally, we address potential physical applications of our findings.Comment: 27 pages AMSLaTeX (with LaTeX2e), 12 eps figures (J. Phys. A, to appear

Manifestation of Quantum Chaos in Electronic Band Structures

We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the {\it ab initio} band structure of silicon and the tight-binding spectrum of the alloy $Al_xGa_{1-x}As$, and show that some of their statistical properties obey the universal predictions of quantum chaos derived from the theory of random matrices. Also, the Bloch momenta are interpreted as external, tunable, parameters, acting on the reduced (unit cell) Hamiltonian, in close analogy to Aharonov-Bohm fluxes threading a torus. They are used in the investigation of the parametric autocorrelator of crystal velocities. We find that our results are in good agreement with the universal curves recently proposed by Simons and coworkers.Comment: 15 pages with 6 Postscript figures included, RevTex-3, CMT-ERM/940

Quantum Mechanics with Random Imaginary Scalar Potential

We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble averaged one-particle Green function from which we obtain the density of complex eigenvalues. Based on the connection between non-Hermitian quantum mechanics and the statistical mechanics of polymer chains, we determine the distribution function of a self-interacting polymer in dimensions $d>4$.Comment: 10 pages, 1 eps figur

Non-universal corrections to the level curvature distribution beyond random matrix theory

The level curvature distribution function is studied beyond the random matrix theory for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the level curvature distribution is calculated using the nonlinear sigma-model. The sign of the correction depends on the presence or absence of the global gauge invariance and is different for perturbations caused by the constant vector-potential and by the random magnetic field. Scaling arguments are discussed that indicate on the qualitative difference in the level statistics in the dirty metal phase for space dimensionalities $d4$.Comment: 4 pages, Late