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The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can exponentially grow with time under the same conditions as for the massless case. The proofs are based on estimates of exactly given mass-induced corrections to the massless case., 25 pages, 1 figure

The behavior of energy is studied for the real scalar field satisfying d'Alembert equation in a finite space interval 0t→+∞E(t) < lim sup t→+∞E(t)=+∞) is also possible. For the Neumann boundary condition, E may decay to zero as the time tends to infinity. If a is periodic, the solution is determined by a homeomorphism [Formula: see text] of the circle related to a. The behavior of E depends essentially on the number theoretical characteristics of the rotation number of [Formula: see text].

We consider a quantum particle in a periodic structure submitted to a constant external electromotive force. The periodic background is given by a smooth potential plus singular point interactions and has the property that the gaps between its bands are growing with the band index. We prove that the spectrum is pure point—i.e., trajectories of wave packets lie in compact sets in Hilbert space—if the Bloch frequency is nonresonant with the frequency of the system and satisfies a Diophantine-type estimate, or if it is resonant. Furthermore, we show that the KAM method employed in the nonresonant case produces uniform bounds on the growth of energy for driven systems.

Consider a small sample coupled to a finite number of leads andassume that the total (continuous) system is at thermal equilibrium inthe remote past. We construct a non-equilibrium steady state (NESS) byadiabatically turning on an electrical bias between the leads. The mainmathematical challenge is to show that certain adiabatic wave operatorsexist and to identify their strong limit when the adiabatic parameter tendsto zero. Our NESS is different from, though closely related with the NESSprovided by the Jakic–Pillet–Ruelle approach. Thus we partly settle aquestion asked by Caroli et al. (J. Phys. C Solid State Phys. 4(8):916–929, 1971) regarding the (non)equivalence between the partitioned andpartition-free approaches. Consider a small sample coupled to a finite number of leads andassume that the total (continuous) system is at thermal equilibrium inthe remote past. We construct a non-equilibrium steady state (NESS) byadiabatically turning on an electrical bias between the leads. The mainmathematical challenge is to show that certain adiabatic wave operatorsexist and to identify their strong limit when the adiabatic parameter tendsto zero. Our NESS is different from, though closely related with the NESSprovided by the Jakic–Pillet–Ruelle approach. Thus we partly settle aquestion asked by Caroli et al. (J. Phys. C Solid State Phys. 4(8):916–929, 1971) regarding the (non)equivalence between the partitioned andpartition-free approaches.

International audience; The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant magnetic field is asymptotic, in norm-resolvent sense, to an effective Hamiltonian which has the form of a multi-particle Schr ̈dinger operator with interactions given by one-dimensional δ-potentials. We study this effective Hamiltonian in the case of the H2 -molecule and establish existence of the ground state. We also show that the inter-nuclear equilibrium distance tends to 0 as the field-strength tends to infinity.

International audience; In the first part of the paper, we introduce the Hamiltonian $-\Delta-Z/\sqrt{x^2+y^2}$, Z>0, as a selfadjoint operator in $L^2(R^2)$. A general central point interaction combined with the two-dimensional Coulomb-like potential is constructed and properties of the resulting one-parameter family of Hamiltonians is studied in detail. The construction is also reformulated in the momentum representation and a relation between the coordinate and the momentum representation is derived. In the second part of the paper we prove that the two-dimensional Coulomb-like Hamiltonian can be derived as a norm resolvent limit of the Hamiltonian of a Hydrogen atom in a planar slab as the width of the slab tends to zero.

We consider a hydrogen atom or ion confined within a straight infinite tube. Modelled by an appropriate nonrelativistic Schrodinger operator with Dirichlet boundary conditions, basic properties of the discrete and continuous spectrum of the system are investigated by rigorous methods. This includes the behaviour of energies and ionization potentials when the size of the confining region is changing. For the particular case of cylindrical tubes, classical symmetries are analysed in terms of geometrical mechanics and the results employed for a systematic construction of corresponding symmetry operators in the quantum regime.

It is known that there is at least one bound state in a curved quantum waveguide provided it is sufficiently thin. In this paper we investigate the critical thickness of two-dimensional waveguides above which the discrete spectrum becomes void. We have found an expression for it in the case of a small bending angle. In the general case, its asymptotic behaviour with respect to the bending angle is shown to be governed by local smoothness properties of the boundary. Uniqueness of the critical thickness is also discussed.

27 pages; We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 00, p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and \epsilon is small enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where \sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was discussed earlier in the literature by Howland.

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands., Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theor

We analyse the low lying spectrum of a model of excitons in carbon nanotubes. Consider two particles with an attractive Coulomb self-interaction, placed on an infinitely long cylinder. If the cylinder radius becomes small, the low lying spectrum is well described by a one-dimensional effective Hamiltonian which is exactly solvable., final version, accepted for publication in Annales Henri Poincare

We propose three effective Hamiltonians which approximate atoms in very strong homogeneous magnetic fields $B$ modelled by the Pauli Hamiltonian, with fixed total angular momentum with respect to magnetic field axis. All three Hamiltonians describe $N$ electrons and a fixed nucleus where the Coulomb interaction has been replaced by $B$-dependent one-dimensional effective (vector valued) potentials but without magnetic field. Two of them are solvable in at least the one electron case. We briefly sketch how these Hamiltonians can be used to analyse the bottom of the spectrum of such atoms., 43 pages

We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state. Udgivelsesdato: JUN We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.

The linear optical properties of semiconducting carbon nanotubes are dominated by quasi-one-dimensional excitons formed by single electron-hole pairs. Hence, the nonlinear response at high pump levels most likely leads to the formation of exciton complexes involving several electron-hole pairs. Such complexes would threfore play an important role in e.g. lasing applications. We demonstrate here that the biexciton complex is surprisingly stable for nanotubes in a wide diameter range. Theoretical predictions for the signature of such states in pump-probe spectroscopy are presented. Udgivelsesdato: FEB The linear optical properties of semiconducting carbon nanotubes are dominated by quasi-one-dimensional excitons formed by single electron-hole pairs. Hence, the nonlinear response at high pump levels most likely leads to the formation of exciton complexes involving several electron-hole pairs. Such complexes would threfore play an important role in e.g. lasing applications. We demonstrate here that the biexciton complex is surprisingly stable for nanotubes in a wide diameter range. Theoretical predictions for the signature of such states in pump-probe spectroscopy are presented.

Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable. Udgivelsesdato: Maj Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schr\"odinger operators with a sufficiently strongly attractive $\delta$ interaction supported by a periodic curve in $\mathbb{R}^d, d=2,3$., Comment: LaTeX 2e, 10 pages

We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer has the hard-wall boundary. Under the assumption that the surface curvatures vanish at infinity we find sufficient conditions which guarantee the existence of geometrically induced bound states., Comment: 20 pages in LaTeX

We discuss the Noeckel model of an open quantum dot, i.e., a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, there are embedded eigenvalues which turn into resonances if the symmetry is violated, either by applying a magnetic field or by deformation of the well. For a weak symmetry breaking we derive the perturbative expansion of these resonances. We also deduce a sufficient condition under which the discrete spectrum of such a system (without any symmetry) survives the presence of a strong magnetic field. It is satisfied, in particular, if the dot potential is purely attractive., Comment: LaTeX, 15 pages; a revised text to appear in Rep. Math. Phys.; a changed title plus a few minor corrections

We study the quantum dynamics generated by $H^{SW}=-{d^2\over dx^2}+V-x$ with $V$ a real periodic function of weak regularity. We prove that the continuous spectrum of $H^{SW}$ is never empty, and furthermore that for $V$ small enough there are no bound states., Comment: 16 pages

Accompagner un enfant porteur de handicap dans une structure d’accueil de la petite enfance met le professionnel dans une place particuliere, parfois paradoxale. L’accompagnement des accueillants eux-memes dans le cadre d’un groupe de parole met en œuvre une fonction contenante, au benefice egalement des enfants et de leurs parents. A l’ecoute des participants d’un tel groupe, des psychologues cliniciens decrivent les enjeux qui leur semblent lies a cette place particuliere : les processus psychiques en jeu dans l’accueil d’un tout-petit, les representations liees au handicap, aux parents, a la valeur du travail, a celle du savoir.

We propose very elementary tools to locate subsets of the complex energy plane where quantum resonances can only take place. The methods uses positivity of some auxiliary operators.

La prestation de service unique, mise en place par la caf comme mode de reglementation financiere de l’accueil des jeunes enfants dans des structures collectives vient contrecarrer tout ce qui a ete pense, imagine, cree depuis nombre d’annees quant a l’accompagnement des jeunes enfants et de leurs parents dans les premiers temps de separation. La logique comptable peut prendre le dessus au risque de precariser l’accueil des tout-petits. Ce sont les consequances qu’elle entraine sur les enjeux fondamentaux de la relation d’un enfant avec ses parents et les autres adultes qui s’occupent de lui qui sont ici soulevees et questionnees.

We show that under suitable non-trapping conditions on the potential V at energy E the Schrodinger operator H = − h 2 Δ + V exhibits no resonance in a neighbourhood of E for small h . We briefly discuss some critical values of E like thresholds or barrier tops.

Duclos Pierre. Grandeurs faiblesses aspirations de la « political science ». In: Revue française de science politique, 4ᵉ année, n°1, 1954. pp. 156-184.

Duclos Pierre. L'Europe entre la mort et la vie. In: Revue française de science politique, 4ᵉ année, n°3, 1954. pp. 589-609.

Control, adrenalectomized, and cortisol-treated rats were maintained under rigidly controlled conditions, and the adenohypophyses were examined histologically with two staining procedures which differentiate six distinct cell types. Only one cell type demonstrated cytological evidence of increased synthetic activity 32 days after adrenalectomy (the changes were, however, minimal) and decreased synthetic activity following the chronic injection of cortisol. This cell type, which we designate as the corticotroph, would be classed as a chromophobe (no stainable granules) with use of standard histological techniques, but is, in fact, as Herlant's Tetrachrome demonstrates, a distinct acidophilic cell type different from the prolactin cell and the somatotroph. The determination of adenohypophyseal DNA and RNA revealed no evidence of increased protein synthetic activity following bilateral adrenalectomy, but did reveal evidence of decreased protein synthetic activity following the chronic injection of cortisol.

Duclos Pierre. L'État devant la Personne et la Société. In: Revue française de science politique, 2ᵉ année, n°4, 1952. pp. 768-781.

Duclos Pierre. À propos de l'« optique du comportement ». In: Revue française de science politique, 12ᵉ année, n°2, 1962. pp. 399-413.

Duclos Pierre. Le paradoxe du « political scientist ». In: Revue française de science politique, 10ᵉ année, n°1, 1960. pp. 114-129.

Duclos Pierre. Quelques sociétés politiques européennes vues d'outre-Atlantique. In: Revue française de science politique, 5ᵉ année, n°1, 1955. pp. 129-137.

Duclos Pierre. De la démocratie et de ses styles. In: Revue française de science politique, 5ᵉ année, n°3, 1955. pp. 632-640.

Félicie Gimet, born 1835, an anarchist affiliated to the free-masonry, had a leading part in the killing of the rue Haxo on May 26th 1871 at the end of the Commune de Paris. Possessed by a kind of evil spirit she probably did launch the massacre of the " otages " including 24 clerics. Her sentence was commuted by the court-marshall and she was handed over to the supervision of the Sœurs des Prisons. She even converted, captivated by the memory of the Jesuit Father Pierre Olivaint, the most famous of the victims, who made a strong impression on her when he was incercerated at La Roquette. She as received into the Filles Repenties and ended her life (1893) in prayer and penance., Félicie Gimet, née en 1835, anarchiste affiliée à la franc-maçonnerie, joua un rôle prépondérant dans le massacre de la rue Haxo, le 26 mai 1871, à la fin de la Commune de Paris ; en proie à une sorte de possession diabolique, elle a même sans doute déclenché la tuerie des 50 « otages », dont 24 ecclésiastiques. Graciée par le conseil de guerre et confiée à la surveillance des Sœurs des Prisons, elle en vint à se convertir, subjuguée par le souvenir du Père jésuite Pierre Olivaint, la plus célèbre des victimes, éminente personnalité qui l'attirait irrésistiblement tandis qu'il était incarcéré à la Roquette. Admise parmi les Filles repenties, F. Gimet termina sa vie (1893) dans la prière et la mortification., Duclos Pierre. Une pétroleuse convertie : Félicie Gimet et Pierre Olivaint. In: Revue d'histoire de l'Église de France, tome 74, n°192, 1988. pp. 53-62.

We study the spectral properties of multiple well Schrodinger operators on ℝn. We give in particular upper bounds on energy shifts due to tunnel effect and localization properties of wave packets. Our methods are based on Agmon type estimates for resolvents in classically forbidden regions and geometric perturbation theory. Our results are valid also for an infinite number of wells, arbitrary spectral type and in non-semi-classical regimes.

Duclos Pierre. Fédéralisme des doctrinaires et fédéralisme des savants. In: Revue française de science politique, 6ᵉ année, n°4, 1956. pp. 892-905.