Third Cumulant of the total Transmission of diffuse Waves

The probability distribution of the total transmission is studied for waves multiple scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulant of this distribution is presented. Within a diagrammatic approach a theory is developed which relates the third cumulant normalized to the average, $\langle \langle T_a^3 \rangle \rangle$, to the normalized second cumulant $\langle \langle T_a^2 \rangle \rangle$. For a broad Gaussian beam profile it is found that $\langle \langle T_a^3 \rangle \rangle= \frac{16}{5} \langle \langle T_a^2 \rangle \rangle^2$. This is in good agreement with data of optical experiments.Comment: 16 pages revtex, 8 separate postscript figure

Does the Third Law of Thermodynamics hold in the Quantum Regime?

The first in a long series of papers by John T. Lewis, G. W. Ford and the present author, considered the problem of the most general coupling of a quantum particle to a linear passive heat bath, in the course of which they derived an exact formula for the free energy of an oscillator coupled to a heat bath in thermal equilibrium at temperature T. This formula, and its later extension to three dimensions to incorporate a magnetic field, has proved to be invaluable in analyzing problems in quantum thermodynamics. Here, we address the question raised in our title viz. Nernst's third law of thermodynamics

The regularized BRST Jacobian of pure Yang-Mills theory

The Jacobian for infinitesimal BRST transformations of path integrals for pure Yang-Mills theory, viewed as a matrix \unity +\Delta J in the space of Yang-Mills fields and (anti)ghosts, contains off-diagonal terms. Naively, the trace of $\Delta J$ vanishes, being proportional to the trace of the structure constants. However, the consistent regulator \cR, constructed from a general method, also contains off-diagonal terms. An explicit computation demonstrates that the regularized Jacobian Tr\ \Delta J\exp -\cR /M^2 for $M^2\rightarrow \infty$ is the variation of a local counterterm, which we give. This is a direct proof at the level of path integrals that there is no BRST anomaly.Comment: 12 pages, latex, CERN-TH.6541/92, KUL-TF-92/2

Inherent Structures in models for fragile and strong glass

An analysis of the dynamics is performed, of exactly solvable models for fragile and strong glasses, exploiting the partitioning of the free energy landscape in inherent structures. The results are compared with the exact solution of the dynamics, by employing the formulation of an effective temperature used in literature. Also a new formulation is introduced, based upon general statistical considerations, that performs better. Though the considered models are conceptually simple there is no limit in which the inherent structure approach is exact.Comment: 19 pages, 4 figure

Deviations from the Gaussian distribution of mesoscopic conductance fluctuations

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive.Comment: 9 pages, Revtex, with eps figures,to appear in Phys Rev

Simultaneous measurement of two non-commuting quantum variables: Solution of a dynamical model

The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin-$\frac{1}{2}$ system simultaneously interacting with two magnets, which act as measuring apparatuses of two different spin components. We work out the dynamics of this process and determine the final state of the measuring apparatuses, from which we can find the probabilities of the four possible outcomes of the measurements. The measurement is found to be non-ideal, as (i) the joint statistics do not coincide with the one obtained by separately measuring each spin component, and (ii) the density matrix of the spin does not collapse in either of the measured observables. However, we give an operational interpretation of the process as a generalised quantum measurement, and show that it is fully informative: The expected value of the measured spin components can be found with arbitrary precision for sufficiently many runs of the experiment.Comment: 24 pages, 9 figures; close to published versio

"Optical conductance fluctuations: diagrammatic analysis in Landauer approach and non-universal effects"

The optical conductance of a multiple scattering medium is the total transmitted light of a diffuse incoming beam. This quantity, very analogous to the electronic conductance, exhibits universal conductance fluctuations. We perform a detailed diagrammatic analysis of these fluctuations. With a Kadanoff-Baym technique all the leading diagrams are systematically generated. A cancellation of the short distance divergencies occurs, that yields a well behaved theory. The analytical form of the fluctuations is calculated and applied to optical systems. Absorption and internal reflections reduce the fluctuations significantly.Comment: 25 pages Revtex 3.0, 18 seperate postscript figure

Inherent Structure Entropy of Supercooled Liquids

We present a quantitative description of the thermodynamics in a supercooled binary Lennard Jones liquid via the evaluation of the degeneracy of the inherent structures, i.e. of the number of potential energy basins in configuration space. We find that for supercooled states, the contribution of the inherent structures to the free energy of the liquid almost completely decouples from the vibrational contribution. An important byproduct of the presented analysis is the determination of the Kauzmann temperature for the studied system. The resulting quantitative picture of the thermodynamics of the inherent structures offers new suggestions for the description of equilibrium and out-of-equilibrium slow-dynamics in liquids below the Mode-Coupling temperature.Comment: 11 pages of Latex, 3 figure

Graded Majorana spinors

In many mathematical and physical contexts spinors are treated as Grassmann odd valued fields. We show that it is possible to extend the classification of reality conditions on such spinors by a new type of Majorana condition. In order to define this graded Majorana condition we make use of pseudo-conjugation, a rather unfamiliar extension of complex conjugation to supernumbers. Like the symplectic Majorana condition, the graded Majorana condition may be imposed, for example, in spacetimes in which the standard Majorana condition is inconsistent. However, in contrast to the symplectic condition, which requires duplicating the number of spinor fields, the graded condition can be imposed on a single Dirac spinor. We illustrate how graded Majorana spinors can be applied to supersymmetry by constructing a globally supersymmetric field theory in three-dimensional Euclidean space, an example of a spacetime where standard Majorana spinors do not exist.Comment: 16 pages, version to appear in J. Phys. A; AFK previously published under the name A. F. Schunc

Maximal atmospheric neutrino mixing and the small ratio of muon to tau mass

We discuss the problem of the small ratio of muon mass to tau mass in a class of seesaw models where maximal atmospheric neutrino mixing is enforced through a $\mu$--$\tau$ interchange symmetry. We introduce into those models an additional symmetry $T$ such that $m_\mu = 0$ in the case of exact $T$ invariance. The symmetry $T$ may be softly broken in the Higgs potential, and one thus achieves $m_\mu \ll m_\tau$ in a technically natural way. We speculate on a wider applicability of this mechanism.Comment: 10 pages, plain LaTeX, no figures, minor changes, final version for J. Phys.