Hamiltonian structure for dispersive and dissipative dynamical systems

We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary fields, in the universal form of a so-called canonical heat bath. After integrating out the heat bath the original dissipative evolution is exactly reproduced. Furthermore, we show that the dynamics associated to a minimal Hamiltonian are essentially unique, up to a natural class of isomorphisms. Using this formalism, we obtain closed form expressions for the energy density, energy flux, momentum density, and stress tensor involving the auxiliary fields, from which we derive an approximate, ``Brillouin-type,'' formula for the time averaged energy density and stress tensor associated to an almost mono-chromatic wave.Comment: 68 pages, 1 figure; introduction revised, typos correcte

Random Dirac operators with time-reversal symmetry

Quasi-one-dimensional stochastic Dirac operators with an odd number of channels, time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and Goldsheid-Margulis to the analysis of random products of matrices in the group SO$^*(2L)$, and then a version of Kotani theory for these operators. Absence of singular spectrum can be shown by adapting an argument of Jaksic-Last if the potential contains random Dirac peaks with absolutely continuous distribution.Comment: parts of introduction made more precise, corrections as follow-up on referee report

Exactly solvable model of quantum diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wavenumber contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. On the other hand, an analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling.Comment: Submitted to J. Stat. Phy

Measurement and modelling of anomalous polarity pulses in a multi-electrode diamond detector

In multi-electrode detectors, the motion of excess carriers generated by ionizing radiation induces charge pulses at the electrodes, whose intensities and polarities depend on the geometrical, electrostatic and carriers transport properties of the device. The resulting charge sharing effects may lead to bipolar currents, pulse height defects and anomalous polarity signals affecting the response of the device to ionizing radiation. This latter effect has recently attracted attention in commonly used detector materials, but different interpretations have been suggested, depending on the material, the geometry of the device and the nature of the ionizing radiation. In this letter, we report on the investigation in the formation of anomalous polarity pulses in a multi-electrode diamond detector with buried graphitic electrodes. In particular, we propose a purely electrostatic model based on the Shockley-Ramo-Gunn theory, providing a satisfactory description of anomalous pulses observed in charge collection efficiency maps measured by means of Ion Beam Induced Charge (IBIC) microscopy, and suitable for a general application in multi-electrode devices and detectors.Comment: 8 pages, 4 figure

Obstructive jaundice secondary to pancreatic head adenocarcinoma in a young teenage boy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Pancreatic adenocarcinoma is extremely rare in childhood. We report a case of metastatic pancreatic adenocarcinoma in a 13-year-old boy, revealed by jaundice.</p> <p>Case presentation</p> <p>A 13-year-old Moroccan boy was admitted with obstructive jaundice to the children's Hospital of Rabat, Department of Pediatric Oncology. Laboratory study results showed a high level of total and conjugated bilirubin. Computerized tomography of the abdomen showed a dilatation of the intra-hepatic and extra-hepatic bile ducts with a tissular heterogeneous tumor of the head of the pancreas and five hepatic lesions. Biopsy of a liver lesion was performed, and a histopathological examination of the sample confirmed the diagnosis of metastatic ductal adenocarcinoma of the pancreas. Our patient underwent a palliative biliary derivation. After that, chemotherapy was administered (5-fluorouracil and epirubicin), however no significant response to treatment was noted and our patient died six months after diagnosis.</p> <p>Conclusion</p> <p>Malignant pancreatic tumors, especially ductal carcinomas, are exceedingly rare in the pediatric age group and their clinical features and treatment usually go unappreciated by most pediatric oncologists and surgeons.</p

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure

Normal transport properties for a classical particle coupled to a non-Ohmic bath

We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a stationary state, because the oscillators cannot effectively absorb the energy of high speed particles. We nonetheless show that the system has at all positive temperatures a well-defined low-field mobility over macroscopic time scales of order exp(-c/F). The mobility is independent of F at low fields, and related to the zero-field diffusion constant D through the Einstein relation. The system therefore exhibits normal transport even though the bath obviously has a discrete frequency spectrum (it is simply monochromatic) and is therefore highly non-Ohmic. Such features are usually associated with anomalous transport properties

Quantum friction

The Brownian motion of a light quantum particle in a heavy classical gas is theoretically described and a new expression for the friction coefficient is obtained for arbitrary temperature. At zero temperature it equals to the de Broglie momentum of the mean free path divided by the mean free path. Alternatively, the corresponding mobility of the quantum particle in the classical gas is equal to the square of the mean free path divided by the Planck constant. The Brownian motion of a quantum particle in a quantum environment is also discussed.Comment: The paper is dedicated to the 85th anniversary of N.N. Tyutyulko

Approach to equilibrium for a class of random quantum models of infinite range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalization allows a neat extension from the class $l_1$ of absolutely summable lattice potentials to the optimal class $l_2$ of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom $l_1$ case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class $l_2$ in the Bernoulli case. Open problems are discussed.Comment: 10 pages, no figures. This last version, to appear in J. Stat. Phys., corrects some minor errors and includes additional references and comments on the relation to experiment