In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(…
This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current …
We continue our study of colligative properties of solutions initiated in math-ph/0407034. We focus on the situations where, in a system of linear size $L$, the concentration and the chemical potential scale like $c=ξ/L$ and $h=b/L$, respectively. We find that there exists a critical value $\xit$ s…
The goal of this note is to give an elementary and very short solution to equations of motion for the Kovalevskaya top. For this we use some results from original papers by Kovalevskay, Kötter and Weber and also the authors Lax representation (see math-ph/0111024)…
In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or arXiv:1002.0999v1 [math-ph]) we introduced a modified Fourier-Cattaneo law and derived a non-autonomous telegraph-type heat conduction equation which has desirable self-similar solution. Now we present a detailed in-depth analysis of…
Let H be a self-adjoint operator such that exp(-aH) is of trace class for some a<1. Let V be a symmetric operator, Kato bounded relative to H. We show that log Tr[exp(-H+xV)] is a real analytic function of x in a hood of x=0. We show that the Gibbs states of H+xV form a real analytic Banach manifold…
Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q does not provide an "exact" description…
A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper, we derived a new moment system of PBMFT by using the moment closure technique in kinetic theory under the assumption tha…
We experimentally demonstrate that a squeezed probe optical field can improve the sensitivity of the magnetic field measurements based on nonlinear magneto-optical rotation (NMOR) with an amplitude-modulated pump when compared to a coherent probe field under identical conditions. To realize an all-a…
Conventional noise analysis in atomic-ensemble sensing assumes a continuous-medium approximation, thereby treating the atomic system as a deterministic dielectric. Here, we demonstrate that this assumption breaks down due to the discrete, particulate nature of the ensemble, giving rise to an intrins…