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7 papers · 1 filter
Repeated Quantum Interactions and Unitary Random Walks
Stéphane Attal, Ameur Dhahri
Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize thos…
Variational methods in relativistic quantum mechanics
Maria J. Esteban, Mathieu Lewin, Eric séré
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are f…
Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance
José Alfredo Cañizo
Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discret…
Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems
Jean Dolbeault, Patricio Felmer, Michael Loss +1
We prove a Lieb-Thirring type inequality for potentials such that the associated Schrödinger operator has a pure discrete spectrum made of an unbounded sequence of eigenvalues. Thi…
Binding energy for hydrogen-like atoms in the Nelson model without cutoffs
Christian Hainzl, Masao Hirokawa, Herbert Spohn
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge , , fixed at the origin an…
An analytical proof of Hardy-like inequalities related to the Dirac operator
J. Dolbeault, M. J. Esteban, M. Loss +1
We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral inf…