Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann
نویسندگان
چکیده
O. Waldmann [1] has shown that some spin systems, which fulfill the condition of a weakly homogeneous coupling matrix, have a spectrum whose minimal energies Emin(S), or maximal energies Emax(S), are rather poorly approximated by a quadratic dependence on the total spin quantum number. We comment on this observation and provide the new argument that, under certain conditions, the approximating parabolas appear as natural bounds of the spectrum generated by spin coherent states. In our article [2] we demonstrated that the spectrum of interacting spin systems, with Hamiltonians of the following form H ∼ ≡ ∑
منابع مشابه
Bounding and approximating parabolas for the spectrum of Heisenberg spin systems
– We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only assumption adopted is that the mean coupling strength of any spin w. r. t. its neighbours is constant for all N spins. The coefficients of the bounding parabolas...
متن کاملError bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion
On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.
متن کاملRadically Questioning the Principle of the Least Restrictive Alternative: A Reply to Nir Eyal; Comment on “Nudging by Shaming, Shaming by Nudging”
In his insightful editorial, Nir Eyal explores the connections between nudging and shaming. One upshot of his argument is that we should question the principle of the least restrictive alternative in public health and health policy. In this commentary, I maintain that Eyal’s argument undermines only a rather implausible version of the principle of the least restrictive alternative and I sketch ...
متن کاملThe Structure of Bhattacharyya Matrix in Natural Exponential Family and Its Role in Approximating the Variance of a Statistics
In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001