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1.
C.-A. Pillet 《Communications in Mathematical Physics》1991,140(2):241-274
We develop a scheme based on pseudo-differential operators to analyze the propagation of excitations in inhomogeneous extended systems. This method is used in a very specific situation, however we think that it has some generality and should apply to various other problems of current interest. We study the well known two-dimensionalsymmetric model of solidification introduced by Langer and Turski. Assuming the existence of Ivantsov-like steady-state solutions, we calculate their excitation spectrum. We show that there are no unstable propagating modes if the Gibbs-Thomson effect is taken into account. This proves that the growth of needle-crystals is stable with respect to side-branching. 相似文献
2.
3.
L.?Bruneau V.?Jak?i?Email author Y.?Last C.-A.?Pillet 《Communications in Mathematical Physics》2015,338(1):347-366
In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample \({\mathcal{S}}\) connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer–Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of \({\mathcal{S}}\). In this spirit, we define Landauer–Büttiker crystalline currents by extending the Landauer–Büttiker formula to a setup where the sample \({\mathcal{S}}\) is replaced by a periodic structure whose unit cell is \({\mathcal{S}}\). We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics. 相似文献
4.
Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks
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Vojkan Jakšić Vahagn Nersesyan Claude‐Alain Pillet Armen Shirikyan 《纯数学与应用数学通讯》2015,68(12):2108-2143
We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc. 相似文献
5.
T. P. Gaidei A. I. Kokorin N. Pillet V. N. Sadov M. E. Strukova S. M. Filatov E. S. Khaustova N. T. Yaroshenko 《Russian Journal of Applied Chemistry》2010,83(6):1130-1138
Data of activity of rhodium catalysts prepared on different carriers in reactions of nitrous oxide decomposition is presented;
this data gave the possibility to choose the most promising carrier for the elaboration of the catalyst of nitrous oxide decomposition
and to use it in high energy plants such as micro rocket engines of space shuttles management systems. 相似文献
6.
Drag C Laburthe Tolra B T'Jampens B Comparat D Allegrini M Crubellier A Pillet P 《Physical review letters》2000,85(7):1408-1411
In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the s-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel f = 4, m(f) = 4. We analyzed the intensities of the lines associated with the Cs2 0(-)(g) state dissociating to the 6s(1/2)+6p(3/2) asymptote. This yields a value of the Cs triplet state scattering length, a(T) = -530a(0), while consistency requirements impose a value of the multipole ground state molecular coefficient, C6 = 6510 a.u. 相似文献
7.
Claude-Alain Pillet 《Communications in Mathematical Physics》1986,105(2):259-280
Absence of bound states and asymptotic completeness are proven for a quantum particle in a time dependent random (Markovian) short range potential. Systems with confining potentials are also considered and unboundedness of the energy in time is shown. 相似文献
8.
This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.] where we have proven the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes in thermally driven quantum open systems. In this note we extend the derivation of the Green-Kubo formula to heat and charge fluxes and discuss some other generalizations of the model and results of [V. Jakšić Y. Ogata and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.]. 相似文献
9.
We consider a model describing finitely many free Fermi gas reservoirs coupled by local interactions and prove the Green–Kubo
formulas and the Onsager reciprocity relations for heat and charge fluxes generated by temperature and chemical potential
differentials.
Submitted: September 2, 2006. Accepted: November 21, 2006. 相似文献
10.
We investigate the dynamics of anN-level system linearly coupled to a field of mass-less bosons at positive temperature. Using complex deformation techniques, we develop time-dependent perturbation theory and study spectral properties of the total Hamiltonian. We also calculate the lifetime of resonances to second order in the coupling. 相似文献