Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory

Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the fundamental Bose-Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativistic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic postulates, Mach's principle and cosmology, are discussed. For estimate the values of the generated masses of the otherwise massless particles such as the photon, we propose few simple models which take into account small vacuum fluctuations. It turns out that the photon's mass can be naturally expressed in terms of the elementary electrical charge and the extensive length parameter of the nonlinearity. Finally, we outline the topological properties of the logarithmic theory and corresponding solitonic solutions.Comment: Dedicated to memory of V. L. Ginzburg (1916-2009). Updates: (v2) chapter on BEC/fluid/gravity correspondence; (v3) comments on BEC-vacuum thermodynamics, induced relativity postulates, Mach's principle, Weyl curvature hypothesis, BEC-vacuum cosmology and origin of fundamental scalar field; (v4) appendix with quantum-informational arguments towards LogSE; (v5 [pub]) refs about superfluid vacuu

Non-Hermitian Hamiltonians and stability of pure states

We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the degree and type of such an instability are controlled by the environment-induced anti-Hermitian parts of Hamiltonians. Using the quantum-statistical approach for non-Hermitian Hamiltonians and related non-linear master equation, we derive the equations that are necessary to study the stability properties of any model described by a non-Hermitian Hamiltonian. It turns out that the instability of pure states is not preassigned in the evolution equation but arises as the emergent phenomenon in its solutions. In order to illustrate the general formalism and different types of instability that may occur, we perform the local stability analysis of some exactly solvable two-state models, which can be used in the theories of open quantum-optical and spin systems.Comment: 7 pages, 2 composite figures. Updates: v2: changed title, minor corrections (published version