Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality （QEI）, in which the energy ...Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality （QEI）, in which the energy density is averaged over time, or space, or over space and time. By now temporal QEIs have been established for various quantum fields, but less work has been done for the spacetime quantum energy inequality. In this paper we deal with the free Rarita-Schwinger field and present a quantum inequality bound on the energy density averaged over space and time. Comparison with the QEI for the Rarita-Schwinger field shows that the lower bound is the same with the QEI. At the same time, we find the quantum inequality for the Rarita-Schwinger field is weaker than those for the scalar and Dirac fields. This fact gives further support to the conjecture that the more freedom the field has, the more easily the field displays negative energy density and the weaker the quantum inequality becomes.展开更多
The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set S...The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H(Sing(u)) 0, with is = dimensionM. Here is Hausdorff measure with respect to parabolic metric ρ(x,t),(y,s)=max{|x-y|, }.展开更多
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent informat...In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the Holevo quantity, and average entropy inequalities. These results shed new light on quantum information inequalities.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10375023 and 10125521, the Program for New Century Excellent Talents under Grant No. 04-0784, the Key Project of the Ministry of Education under Grant No. 205110, and the 973 State Key Basic Research and Development Program of China under Grant No. G2000077400
文摘Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality （QEI）, in which the energy density is averaged over time, or space, or over space and time. By now temporal QEIs have been established for various quantum fields, but less work has been done for the spacetime quantum energy inequality. In this paper we deal with the free Rarita-Schwinger field and present a quantum inequality bound on the energy density averaged over space and time. Comparison with the QEI for the Rarita-Schwinger field shows that the lower bound is the same with the QEI. At the same time, we find the quantum inequality for the Rarita-Schwinger field is weaker than those for the scalar and Dirac fields. This fact gives further support to the conjecture that the more freedom the field has, the more easily the field displays negative energy density and the weaker the quantum inequality becomes.
基金the National Natural Science Foundation of China (No.10071013).
文摘The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H(Sing(u)) 0, with is = dimensionM. Here is Hausdorff measure with respect to parabolic metric ρ(x,t),(y,s)=max{|x-y|, }.
基金Supported by National Natural Science Foundation of China under Grant Nos.11301124,11171301the Doctoral Programs Foundation of Ministry of Education of China under Grant No.J20130061
文摘In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the Holevo quantity, and average entropy inequalities. These results shed new light on quantum information inequalities.
