Oč vlastně jde v teorii Schrodingerových operátorů?
On a class of conservative, highly accurate Galerkin methods for the Schrödinger equation
On a counterexample of Garofalo-Lin for a unique continuation of Schrödinger equation.
On a differential equation approach to quantum field theory : causality property for the solutions of Thirring's model
On blow-up for the Hartree equation
We study the blow-up of solutions to the focusing Hartree equation . We use the strategy derived from the almost finite speed of propagation ideas devised by Bourgain (1999) and virial analysis to deduce that the solution with negative energy (E(u₀) < 0) blows up in either finite or infinite time. We also show a result similar to one of Holmer and Roudenko (2010) for the Schrödinger equations using techniques from scattering theory.
On classical solutions of the relativistic Vlasov-Klein-Gordon system.
On diamagnetism and de Haas-van Alphen effect
On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum
On large amplitude solutions of the Yang-Mills equations in Minkowski space-time
On phase segregation in nonlocal two-particle Hartree systems
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
On representations of Lie algebras of a generalized Tavis-Cummings model.
On some properties of the solution of the differential equation
In the paper it is shown that each solution ot the initial value problem (2), (3) has a finite limit for , and an asymptotic formula for the nontrivial solution tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions , .
On Space-Time Means and Strong Global Solutions of Nonlinear Hyperbolic Equations.
On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field.
On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points
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.
On the binding of polarons in a mean-field quantum crystal
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....
On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴
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.
On the classification of the Lie algebras .
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
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...