A New Approach to the Quantum Mechanical Stability

Jean Bellissard

Akitomo Tachibana

Abstract A new concept of the “stability” of the quantum mechanical state is presented. This concept is closely related to the hydrodynamical theory of quantum mechanics. For charged particles, the “stability” against the application of the external electromagnetic field is examined. Under a nonlinear interaction, a new type of the solitonlike phenomenon is shown as a novel, illustrative example of the “stable” state. An extension for the relativistic treatment is also examined.

Yakir Aharonov

Gil Elgressy, Lawrence Paul Horwitz

In this paper, an underlying perturbed Ricci flow construction is made within the metric operator space, originating from the Heisenberg dynamical equations, to formulate a method which appears to provide a new geometric approach for the geometric formulation of the quantum mechanical dynamics. A quantum mechanical notion of stability and local instability is introduced within the quantum mechanical theory, based on the quantum mechanical dynamical equations governing the evolution of the tensor metric operator. The stability analysis is conducted in the topology of little Ho¨lder spaces of metrics which the tensor metric operator acts on. Finally, a theorem is introduced in an attempt to characterize the stability properties of the quantum mechanical system such that it brings the quantum mechanical dynamics into the analysis.

Spyros Efthimiades

Igor Ferrier-Barbut

A new class of quantum mechanical liquids is stabilized by an elegant mechanism that allows them to exist despite being orders of magnitude thinner than air.