Akika Nakamichi

Coupled spin models for magnetic variation of planets and stars

Geomagnetism is characterized by intermittent polarity reversals and rapid fluctuations. We have recently proposed a coupled macro-spin model to describe these dynamics based on the idea that the whole dynamo mechanism is described by the coherent interactions of many local elements. In this paper, we further develop this idea and construct the minimal model for magnetic variations. This simple model naturally yields many of the observed features of geomagnetism: its time evolution, the power spectrum, the frequency distribution of stable polarity periods etc. This model is characterized by two coexisting phases of spins: i.e. the cluster phase which determines the global dipole magnetic moment, and the expanded phase which gives random perpetual perturbations that yield the intermittent polarity flip of the dipole moment. This model can also describe the synchronization of the spin oscillations. This corresponds to the case of our Sun and the model well describes the quasi-regular cycles of the solar magnetism. Furthermore, by analysing the relevant terms of magnetohydrodynamic equations based on our model, we have obtained a scaling relation for the magnetism for planets, satellites and the Sun. Comparing it with various observations, we can estimate the relevant scale of the macro-spins.

Is galaxy distribution non-extensive and non-Gaussian?

Self-gravitating systems in the Universe are generally thought to be non-extensive, and often show long-tails in various distribution functions. In principle, these non-Boltzmann properties are naturally expected from the peculiar property of gravity, long-range and unshielded. Therefore, the ordinary Boltzmann statistical mechanics would not be applicable for these self-gravitating systems in its naive form. In order to step further, we quantitatively investigate the above two properties, non-extensivity and long-tails, by explicitly introducing various models of statistical mechanics. We use the data of CfA II South redshift survey and apply the count-in-cell method. We study four statistical mechanics: (1) Boltzmann statistical mechanics, (2) Fractal statistical mechanics, (3) Renyi-entropy-based (REB) statistical mechanics, and (4) Tsallis statistical mechanics, and use Akaike information criteria (AIC) for the fair comparison. We found that both Renyi-entropy-based statistical model and Tsallis statistical model are far better than the other two models. Therefore, the long-tail in the distribution function turns out to be essential.

Universal non-Gaussian velocity distribution in violent gravitational processes.

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.

Local virial relation for self-gravitating system.

We demonstrate that the quasi-equilibrium state in a self-gravitating N-body system after cold collapse is uniquely characterized by the local virial relation using numerical simulations. Conversely, assuming the constant local virial ratio and Jeans equation for a spherically steady-state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Specifically, the local virial relation always provides a solution which has a power-law density profile in both the asymptotic regions r --> 0 and infinity. This type of solution is commonly observed in many numerical simulations. Only the anisotropic velocity dispersion controls this asymptotic behavior of density profile.

Quantum Measurement Driven by Spontaneous Symmetry Breaking

Quantum mechanics cannot be applied within a closed system. Inevitable measurement process in quantum mechanics is usually treated separately from the basic principles of the framework and requires outside observer of the system. In this paper, we propose that the quantum measurement process is actually a physical process associated with the ubiquitous mechanism of spontaneous symmetry breaking. Based on this proposal, we construct a quantum measurement model in which the mixed state evolves into a pure state as the dynamical pro-coherence process. Furthermore, the classically distinguishable pointer parameter emerges as the c-number order parameter in the formalism of closed time-path quantum field theory. We also discuss the precision of the measurement and the possible deduction of the Born probability postulate.

Local virial relation and velocity anisotropy for collisionless self-gravitating systems

The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. The other is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes is examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index n ∼ 5 with a flat boundary condition at the center are compatible with the numerical results, except for the outer region. Using the analytic solutions based on the static and spherical Jeans equation, we show that this incompatibility in the outer region implies the important effect of anisotropy of velocity dispersion. Furthermore, the velocity anisotropy is essential in explaining various numerical results under the condition of the local virial relation.The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. Another is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes are examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index

CO ( J = 1-0) Observation of the cD Galaxy of AWM 7: Constraints on the Evaporation of Molecular Gas

n \sim 5

Renormalization group approach in Newtonian cosmology

with a flat boundary condition at the center are compatible with the numerical results, except for the outer region. Using the analytic solutions based on the static and spherical Jeans equation, we show that this incompatibility in the outer region implies the important effect of anisotropy of velocity dispersion. Furthermore, the velocity anisotropy is essential in explaining various numerical results under the condition of the local virial relation.

Physics of quantum measurement and its interdisciplinary applications

We have searched for molecular gas in the cD galaxy of a poor cluster of galaxies, AWM 7, using the Nobeyama 45 m telescope. We did not detect CO emission in the galaxy. Our limit of molecular gas in the inner 7.5 kpc is MH 2 10~ 3, where / is the ratio of the heat conduction rate to that of Spitzer. However, this contradicts recent X-ray observations showing / < 10~5. Thus, the non-detection of CO cannot be explained by evaporation, and most of the cooled gas predicted by a cooling flow model may not change into molecular gas in the cD galaxy. Moreover, we estimate the evaporation time of molecular clouds brought to a cD galaxy through the capture of gas-rich galaxies and find that these clouds should not be evaporated if / < 10~ 3 - 10~ 4. Therefore, the non-detection of CO in a cD galaxy could constrain the total mass of the molecular clouds brought into it.

Acquired scaling relations in dark matter turbulence

We apply the renormalization group (RG) method to examine the observable scaling properties in Newtonian cosmology. The original scaling properties of the equations of motion in our model are modified for averaged observables on constant time slices. In the RG flow diagram, we find three robust fixed points: Einstein\char21{}de Sitter, Milne, and quiescent fixed points. Their stability (or instability) property does not change under the effect of fluctuations. Inspired by the inflationary scenario in the early Universe, we set the Einstein\char21{}de Sitter fixed point with small fluctuations as the boundary condition at the horizon scale. Solving the RG equations under this boundary condition toward the smaller scales, we find a generic behavior of observables such that the density parameter