arXiv subjects
Publications and source records attributed to Ayumu Sugita.
Gnutzmann and Zyczkowski have proposed the Renyi-Wehrl entropy as a generalization of the Wehrl entropy, and conjectured that its minimum is obtained for coherent states. We prove this conjecture for the Renyi index q=2,3,... in the cases of compact semisimple Lie groups. A general formula for the minimum value is given.
We investigate the $O(a)$ improved quark action on anisotropic lattice as a potential framework for the heavy quark, which may enable precision computation of hadronic matrix elements of heavy-light mesons. The relativity relations of heavy-light mesons as well as of heavy quarkonium are examined on a quenched lattice with spatial lattice cutoff $a_σ^{-1} \simeq$ 1.6 GeV and the anisotropy $ξ=4$. We find that the bare anisotropy parameter tuned for the massless quark describes both the heavy-heavy and heavy-light mesons within 2% accuracy for the quark mass $a_σm_Q < 0.8$, which covers the charm quark mass. This bare anisotropy parameter also successfully describes the heavy-light mesons in the quark mass region $a_σm_Q \leq 1.2$ within the same accuracy. Beyond this region, the discretization effects seem to grow gradually. The anisotropic lattice is expected to extend by a factor $ξ$ the quark mass region in which the parameters in the action tuned for the massless limit are applicable for heavy-light systems with well controlled systematic errors.
Semiclassical trace formulas are examined using phase space path integrals. Our main concern in this paper is the Maslov index of the periodic orbit, which seems not fully understood in previous works. We show that the calculation of the Maslov index is reduced to a classification of connections on a vector bundle over $S^{1}$ with structure group $Sp(2n,R)$. We derive a formula for the index of the n-repetition, and show that a Bohr-Sommerfeld type quantization condition including quadratic fluctuation around the orbit is derived using this formula.
Maslov indices in periodic-orbit theory are investigated using phase space path integral. Based on the observation that the Maslov index is the multi-valued function of the monodromy matrix, we introduce a generalized monodromy matrix in the universal covering space of the symplectic group and show that this index is uniquely determined in this space. The stability of the orbit is shown to determine the parity of the index, and a formula for the index of the n-repetition of the orbit is derived.
We propose the second moment of the Husimi distribution as a measure of complexity of quantum states. The inverse of this quantity represents the effective volume in phase space occupied by the Husimi distribution, and has a good correspondence with chaoticity of classical system. Its properties are similar to the classical entropy proposed by Wehrl, but it is much easier to calculate numerically. We calculate this quantity in the quartic oscillator model, and show that it works well as a measure of chaoticity of quantum states.