On a lattice, as the momentum space is compact, the kinetic energy is bounded not only from below but also from above. It is shown that this, somehow removes the distinction between repulsive and attractive forces. In particular, it is seen that a region with attractive force would appear forbidden for states with energies higher than a certain value, while repulsive forces could develop bound-states. An explicit transformation is introduced which transforms the spectrum of a system corresponding to a repulsive force, to that of a similar system corresponding to an attractive force. Explicit numerical examples are presented for discrete energies of bound-states of a particle experiencing repulsive force by a piecewise constant potential. Finally, the parameters of a specific one dimensional translationally invariant system on continuum are tuned so that the energy of the system resembles the kinetic energy of a system on a one dimensional lattice. In particular, it is shown that the parameters could be tuned so that while the width of the first energy band and its position are kept finite, the energy gap between the first energy band and the next energy band go to infinity, so that effectively only the first energy band is relevant.
A Comparative Interpretation of the Thermodynamic Functions of a Relativistic Bound State problem proposed with an Attractive or a Repulsive Surface Effect
Casimir-Lifshitz interaction between ZnO and SiO2 nanorods in bromobenzene: retardation effects turn the interaction repulsive at intermediate separations
A unified theory of strong coupling Bose polarons: From repulsive polarons to non-Gaussian many-body bound states
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）
我们提出了两个新的模型，排斥Casimir相互作用之间的正微扰。一个例子依赖于介电响应的非局部性，一个依赖于（吸引）模式之间的干扰。这样的例子在一维无质量理论中是不可能实现的，因为它们被Lambrecht，Jaekel和Lambreaud [Phys.Lett. A 225（1997）]到非局部扰动和负扰动
