Proof of the generalized Lieb-Wehrl conjecture for integer indices larger than one

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.Comment: 8 pages, typos fixed, published versio

On the Density of Coprime m-tuples over Holomorphy Rings

Let $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we compute the density of coprime $m$-tuples of elements of $H$. As a side result, we obtain that whenever the complement of $\mathcal S$ is finite, the computation of the density can be reduced to the computation of the $L$-polynomial of the function field. In the rational function field case, classical results for the density of coprime $m$-tuples of polynomials are obtained as corollaries.Comment: To appear in International Journal of Number Theor

Geometrical Pumping in Quantum Transport: Quantum Master Equation Approach

For an open quantum system, we investigate the pumped current induced by a slow modulation of control parameters on the basis of the quantum master equation and full counting statistics. We find that the average and the cumulant generating function of the pumped quantity are characterized by the geometrical Berry-phase-like quantities in the parameter space, which is associated with the generator of the master equation. From our formulation, we can discuss the geometrical pumping under the control of the chemical potentials and temperatures of reservoirs. We demonstrate the formulation by spinless electrons in coupled quantum dots. We show that the geometrical pumping is prohibited for the case of non-interacting electrons if we modulate only temperatures and chemical potentials of reservoirs, while the geometrical pumping occurs in the presence of an interaction between electrons

Role of an intermediate state in homogeneous nucleation

We explore the role of an intermediate state (phase) in homogeneous nucleation phenomenon by examining the decay process through a doubly-humped potential barrier. As a generic model we use the fourth- and sixth-order Landau potentials and analyze the Fokker-Planck equation for the one-dimensional thermal diffusion in the system characterized by a triple-well potential. In the low temperature case we apply the WKB method to the decay process and obtain the decay rate which is accurate for a wide range of depth and curvature of the middle well. In the case of a deep middle well, it reduces to a doubly-humped-barrier counterpart of the Kramers escape rate: the barrier height and the curvature of an initial well in the Kramers rate are replaced by the arithmetic mean of higher(or outer) and lower(or inner) partial barriers and the geometric mean of curvatures of the initial and intermediate wells, respectively. It seems to be a universal formula. In the case of a shallow-enough middle well, Kramers escape rate is alternatively evaluated within the standard framework of the mean-first-passage time problem, which certainly supports the WKB result. The criteria whether or not the existence of an intermediate state can enhance the decay rate are revealed.Comment: 9pages, 11figure

Diffusion in the Markovian limit of the spatio-temporal colored noise

We explore the diffusion process in the non-Markovian spatio-temporal noise.%the escape rate problem in the non-Markovian spatio-temporal random noise. There is a non-trivial short memory regime, i.e., the Markovian limit characterized by a scaling relation between the spatial and temporal correlation lengths. In this regime, a Fokker-Planck equation is derived by expanding the trajectory around the systematic motion and the non-Markovian nature amounts to the systematic reduction of the potential. For a system with the potential barrier, this fact leads to the renormalization of both the barrier height and collisional prefactor in the Kramers escape rate, with the resultant rate showing a maximum at some scaling limit.Comment: 4pages,2figure

Detection of Macroscopic Entanglement by Correlation of Local Observables

We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in arbitrary quantum states that are (effectively) homogeneous. Using this property, we also propose an index of macroscopic entanglement.Comment: Although the index q was proposed for mixed states, it is also applicable to pure states, on which we fix minor bugs (that will be reported in PRL as erratum). The conclusions of the paper remain unchanged. (4 pages, no figures.

Macroscopic entanglement of many-magnon states

We study macroscopic entanglement of various pure states of a one-dimensional N-spin system with N>>1. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge whether such superposition is hidden in a general state, we use an essentially unique index p: A pure state is macroscopically entangled if p=2, whereas it may be entangled but not macroscopically if p<2. This index is directly related to the stability of the state. We calculate the index p for various states in which magnons are excited with various densities and wavenumbers. We find macroscopically entangled states (p=2) as well as states with p=1. The former states are unstable in the sense that they are unstable against some local measurements. On the other hand, the latter states are stable in the senses that they are stable against local measurements and that their decoherence rates never exceed O(N) in any weak classical noises. For comparison, we also calculate the von Neumann entropy S(N) of a subsystem composed of N/2 spins as a measure of bipartite entanglement. We find that S(N) of some states with p=1 is of the same order of magnitude as the maximum value N/2. On the other hand, S(N) of the macroscopically entangled states with p=2 is as small as O(log N)<< N/2. Therefore, larger S(N) does not mean more instability. We also point out that these results are analogous to those for interacting many bosons. Furthermore, the origin of the huge entanglement, as measured either by p or S(N), is discussed to be due to the spatial propagation of magnons.Comment: 30 pages, 5 figures. The manuscript has been shortened and typos have been fixed. Data points of figures have been made larger in order to make them clearly visibl

Simplified expression of shielded MR head response for double-layerperpendicular medium

科研費報告書収録論文(課題番号:09355012・基盤研究(A)(2)・H9～H11/研究代表者:中村, 慶久/垂直ハード磁気ディスク装置を用いる超大容量ストレージシステムの研究

Effective Sampling in the Configurational Space by the Multicanonical-Multioverlap Algorithm

We propose a new generalized-ensemble algorithm, which we refer to as the multicanonical-multioverlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the multi-dimensional, energy-overlap space and explores widely in the configurational space including specific configurations, where the overlap of a configuration with respect to a reference state is a measure for structural similarity. We apply the multicanonical-multioverlap molecular dynamics method to a penta peptide, Met-enkephalin, in vacuum as a test system. We also apply the multicanonical and multioverlap molecular dynamics methods to this system for the purpose of comparisons. We see that the multicanonical-multioverlap molecular dynamics method realizes effective sampling in the configurational space including specific configurations more than the other two methods. From the results of the multicanonical-multioverlap molecular dynamics simulation, furthermore, we obtain a new local-minimum state of the Met-enkephalin system.Comment: 15 pages, (Revtex4), 9 figure