Point interaction Hamiltonians in bounded domains
نویسندگان
چکیده
منابع مشابه
Point Interaction Hamiltonians in Bounded Domains
Making use of recent techniques in the theory of selfadjoint extensions of symmetric operators, we characterize the class of point interaction Hamiltonians in a 3-D bounded domain with regular boundary. In the particular case of one point interaction acting in the center of a ball, we obtain an explicit representation of the point spectrum of the operator togheter with the corresponding related...
متن کاملLeaky Quantum Graphs: Approximations by Point Interaction Hamiltonians
We prove an approximation result showing how operators of the type −∆ − γδ(x − Γ) in L2(R2), where Γ is a graph, can be modeled in the strong resolvent sense by point-interaction Hamiltonians with an appropriate arrangement of the δ potentials. The result is illustrated on finding the spectral properties in cases when Γ is a ring or a star. Furthermore, we use this method to indicate that scatt...
متن کاملSwarming in bounded domains
The Vicsek model is a prototype for the emergence of collective motion. In free space, it is characterized by a swarm of particles all moving in the same direction. Since this dynamic does not include attraction among particles, the swarm, while aligning in velocity space, has no spatial coherence. Adding specular reflection at the boundaries generates global spatial coherence of the swarms whi...
متن کاملBounded Domains and Unbounded Domains
First, notions of inside components and outside components are introduced for any subset of n-dimensional Euclid space. Next, notions of the bounded domain and the unbounded domain are defined using the above components. If the dimension is larger than 1, and if a subset is bounded, a unbounded domain of the subset coincides with an outside component (which is unique) of the subset. For a spher...
متن کاملFixed-Point Hamiltonians in Quantum Mechanics
The basis of the renormalization group invariance of quantum mechanics is given through the concept of fixed-point Hamiltonians. We apply this concept to formulate renormalized Hamiltonians in quantum mechanics, for systems described by interactions that originally contain point-like singularities (as the Dirac-delta and/or its derivatives). The proposed scheme relies on a renormalized form of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2770672