International Journal of Theoretical Physics - In this work, we give an analytical derivation of the reduced density matrix between two qubits in a cavity field, which is described by the quantum... 相似文献
Journal of Thermal Analysis and Calorimetry - In O2/N2 and O2/CO2 atmospheres with oxygen concentrations of 21%, 30%, and 50%, combustion characteristics index, apparent activation energy, and... 相似文献
We consider the following system with critical exponent in : where , and . Using finite dimensional reduction method, we prove the existence of multi-bump solutions. Their bumps can be placed on arbitrarily many or even infinitely many lattice points in . Since or , we introduce two new norms to avoid singularity. 相似文献
In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L2(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space Hσ (ℝ) (σ ⩾ 0) and reduces to L2(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).