Search results for "Hamiltonian"
showing 10 items of 662 documents
Negatively Charged Gangliosides Promote Membrane Association of Amphipathic Neurotransmitters
2018
Lipophilic neurotransmitters (NTs) such as dopamine are chemical messengers enabling neurotransmission by adhering onto the extracellular surface of the post-synaptic membrane in a synapse, followed by binding to their receptors. Previous studies have shown that the strength of the NT-membrane association is dependent on the lipid composition of the membrane. Negatively charged lipids such as phosphatidylserine, phosphatidylglycerol, and phosphatidic acid have been indicated to promote NT-membrane binding, however these anionic lipids reside almost exclusively in the intracellular leaflet of the post-synaptic membrane instead of the extracellular leaflet facing the synaptic cleft. Meanwhile…
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
A generalization of Françoise's algorithm for calculating higher order Melnikov functions
2002
Abstract In [J. Differential Equations 146 (2) (1998) 320–335], Francoise gives an algorithm for calculating the first nonvanishing Melnikov function Ml of a small polynomial perturbation of a Hamiltonian vector field and shows that Ml is given by an Abelian integral. This is done under the condition that vanishing of an Abelian integral of any polynomial form ω on the family of cycles implies that the form is algebraically relatively exact. We study here a simple example where Francoise's condition is not verified. We generalize Francoise's algorithm to this case and we show that Ml belongs to the C [ log t,t,1/t] module above the Abelian integrals. We also establish the linear differentia…
Abelian integrals and limit cycles
2006
Abstract The paper deals with generic perturbations from a Hamiltonian planar vector field and more precisely with the number and bifurcation pattern of the limit cycles. In this paper we show that near a 2-saddle cycle, the number of limit cycles produced in unfoldings with one unbroken connection, can exceed the number of zeros of the related Abelian integral, even if the latter represents a stable elementary catastrophe. We however also show that in general, finite codimension of the Abelian integral leads to a finite upper bound on the local cyclicity. In the treatment, we introduce the notion of simple asymptotic scale deformation.
Alien limit cycles near a Hamiltonian 2-saddle cycle
2005
Abstract It is known that perturbations from a Hamiltonian 2-saddle cycle Γ can produce limit cycles that are not covered by the Abelian integral, even when it is generic. These limit cycles are called alien limit cycles. This phenomenon cannot appear in the case that Γ is a periodic orbit, a non-degenerate singularity, or a saddle loop. In this Note, we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. To cite this article: M. Caubergh et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).
ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS
1992
In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator…
Electronic structure of phthalocyanines : Theoretical investigation of the optical properties of phthalocyanine monomers, dimers, and crystals
1990
We present valence effective Hamiltonian (VEH) calculations on the optical absorptions of a series of phthalocyanine compounds: the metal‐free phthalocyanine molecule, a model system for the lithium phthalocyanine molecule, the metal‐free phthalocyanine dimer, and model systems for the lutetium diphthalocyanine and the lithium phthalocyanine crystal. For these compounds, it is found that the major factor influencing the evolution of the optical transitions is not the electronic structure of the metal but rather the geometric structure: phthalocyanine intraring geometry and, in the dimers and crystals, interring separation and staggering angle. The origin of the so‐called Soret or B absorpti…
The vibrational levels of methane obtained from analyses of high-resolution spectra
2006
International audience; Methane and its tetrahedral isotopologues are spherical-top molecules whose high-resolution rovibrational spectra can only be analyzed in detail, thanks to sophisticated symmetry-adapted tensorial models. However, the effective Hamiltonian parameters of such models do not give direct access to the positions of the vibrational sublevels. In this paper, we present a calculation of the vibrational level positions for 12CH4, 13CH4, 12CD4 and 13CD4 performed using the effective Hamiltonian parameters obtained through recent analyses. We also include the results of a re-analysis of the octad system of 12CH4 performed with a higher order of the development which slightly im…
Adiabatic evolution of quantum-mechanical systems
1991
A description of the adiabatic approximation in terms of the time-evolution operator is presented. Corrections to the approximation are studied, and it is seen that these can be obtained in a simple way in the case of a rapidly oscillating Hamiltonian.
Geometric factors in the adiabatic evolution of classical systems
1992
Abstract The adiabatic evolution of the classical time-dependent generalized harmonic oscillator in one dimension is analyzed in detail. In particular, we define the adiabatic approximation, obtain a new derivation of Hannay's angle requiring no averaging principle and point out the existence of a geometric factor accompanying changes in the adiabatic invariant.