395 research outputs found
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, 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 of absolutely summable lattice potentials to the optimal class
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 case, it is
proved to occur for both short and long range potentials for Gaussian
distributions, and for potentials of class 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
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