Searcharxiv⌕ Search

arXiv subjects

Ken Kuriyama

Publications and source records attributed to Ken Kuriyama.

8 recordsLinked to original sources
arXiv2017

Lipschitz continuity and monotone decreasingness of the solution to the BCS gap equation for superconductivity

In the preceding work \cite{watanabe3}, it is shown that the solution to the BCS gap equation for superconductivity is continuous with respect to both the temperature and the energy under the restriction that the temperature is very small. Without this restriction, we show in this paper that the solution is continuous with respect to both the temperature and the energy, and that the solution is Lipschitz continuous and monotonically decreasing with respect to the temperature.

math-ph↗
arXiv2016

Smoothness and monotone decreasingness of the solution to the BCS-Bogoliubov gap equation for superconductivity

We show the temperature dependence such as smoothness and monotone decreasingness with respect to the temperature of the solution to the BCS-Bogoliubov gap equation for superconductivity. Here the temperature belongs to the closed interval $[0,\, τ]$ with $τ>0$ nearly equal to half of the transition temperature. We show that the solution is continuous with respect to both the temperature and the energy, and that the solution is Lipschitz continuous and monotone decreasing with respect to the temperature. Moreover, we show that the solution is partially differentiable with respect to the temperature twice and the second-order partial derivative is continuous with respect to both the temperature and the energy, or that the solution is approximated by such a smooth function.

math-ph↗
arXiv2010

A generalized Fannes inequality

We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes inequality.

quant-ph↗
arXiv2005

Generalized Shannon inequalities based on Tsallis relative operator entropy

Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par} are extended in terms of the parameter of the Tsallis relative operator entropy. Moreover the generalized Tsallis relative operator entropy is introduced and then several operator inequalities are derived.

math.FA↗
arXiv2005

A note on operator inequalities of Tsallis relative operator entropy

Tsallis relative operator entropy was defined as a parametric extension of relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of Tsallis relative operator entropy, some operator inequalities related to Tsallis relative operator entropy are shown in the present paper. Our inequalities give the upper and lower bounds of Tsallis relative operator entropy. The operator equality on Tsallis relative operator entropy is also shown by considering the tensor product. This relation generalizes the pseudoadditivity for Tsallis entropy. As a corollary of our operator equality derived from the tensor product manipulation, we show several operator inequalities including the superadditivity and the subadditivity for Tsallis relative operator entropy. Our results are generalizations of the superadditivity and the subadditivity for Tsallis entropy.

math.FA↗
arXiv2005

On trace inequalities and their applications to noncommutative communication theory

Certain trace inequalities related to matrix logarithm are shown. These results enable us to give a partial answer of the open problem conjectured by A.S.Holevo. That is, concavity of the auxiliary function which appears in the random coding exponent as the lower bound of the quantum reliability function for general quantum states is proven in the case of $0\leq s\leq 1$.

quant-ph↗
arXiv2005

An elementary formula for entanglement entropies of fermionic systems

An elementary formula for the von Neumann and Renyi entropies describing quantum correlations in two-fermionic systems having four single particle states is presented. An interesting geometric structure of fermionic entanglement is revealed. A connection with the generalized Pauli principle is established.

quant-ph↗