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Displaying 181 –
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318
In this paper, for the second initial boundary value problem for Schrödinger systems, we obtain a performance of generalized solutions in a neighborhood of conical points on the boundary of the base of infinite cylinders. The main result are asymptotic formulas for generalized solutions in case the associated spectrum problem has more than one eigenvalue in the strip considered.
We consider a multi-polaron model obtained by coupling the many-body Schrödinger equation for N interacting electrons with the energy functional of a mean-field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitute a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background....
We characterize the dynamics of the finite time blow-up solutions with minimal mass for the focusing mass-critical Hartree equation with H¹(ℝ⁴) data and L²(ℝ⁴) data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we analyze the mass concentration phenomenon of such blow-up solutions.
We present the semi-conductor Boltzmann equation,
which is time-reversible, and indicate that it can be formally derived
by considering the large time and small perturbing potential limit
in the Von-Neumann equation (time-reversible). We then rigorously compute
the corresponding asymptotics in the case of the Von-Neumann equation on
the Torus. We show that the limiting equation we obtain does not coincide
with the physically realistic model. The former is indeed
an equation of Boltzmann type, yet...
This article reflects in its content the talk the author gave at the XVII Congresso dellUnione Matematica Italiana, held in Milano, 8-13 September 2003. We review about some recent results on the problem of deriving the Gross-Pitaevskii equation in dimension one from the dynamics of a quantum system with a large number of identical bosons. We explain the motivations for some peculiar choices (shape of the interaction potential, scaling, initial datum). Open problems are pointed out and difficulties...
A relativistic calculation of the Lamb shift, using the classical field created by the Dirac transition currents, is proposed.
In this paper, we prove propagation estimates for a massive Dirac equation in flat
spacetime. This allows us to construct the asymptotic velocity operator and to
analyse its spectrum. Eventually, using this new information, we are able to obtain
complete scattering results; that is to say we prove the existence and the asymptotic
completeness of the Dollard modified wave operators.
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