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We study the nuclear Schiff moments of $^{129}$Xe and $^{199}$Hg induced by the nucleon electric dipole moment using large-scale shell model calculations. For $^{129}$Xe, we find a linear relation between the leading-order contribution and magnetic moment, which would be useful in reducing the theoretical uncertainty. The conventional model space does not contain the $ 0g_{ 9/2 } $ and $ 0h_{ 9/2 } $ orbitals, which are connected to the spin-orbit partners by large matrix elements. Thus, to evaluate the influence of the relevant single-particle orbitals outside the conventional model space, we apply the quasiparticle vacua shell model method. Moreover, the next-to-leading-order contribution arises from parity and time-reversal violation inside the nucleus. We demonstrate that these secondary effects do not induce any significant disturbance to the correlation. Additionally, we report the shell model results for the nuclear Schiff moment coefficients of $^{199}$Hg. Compared to previous studies, the results obtained in this study are rather large, indicating a higher sensitivity to the neutron electric dipole moment.

We report on the operation of co-located ${}^{129}$Xe and ${}^{131}$Xe nuclear spin masers with an external feedback scheme, and discuss the use of ${}^{131}$Xe as a comagnetometer in measurements of the ${}^{129}$Xe spin precession frequency. By applying a correction based on the observed change in the ${}^{131}$Xe frequency, the frequency instability due to magnetic field and cell temperature drifts are eliminated by two orders of magnitude. The frequency precision of 6.2 $\mu$Hz is obtained for a 10$^4$ s averaging time, suggesting the possibility of future improvement to $\approx$ 1 nHz by improving the signal-to-noise ratio of the observation., Comment: 8 pages, 5 figures

The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a nucleon interacts with other nucleons as well as with electrons. Nuclear structure calculations of the CP-odd nuclear Schiff moment are discussed using the shell model and other theoretical approaches. Results of the calculations of atomic electric dipole moments due to the interaction of the nuclear Schiff moment with the electrons and the P and time-reversal (T) symmetry violating tensor-pseudotensor electron-nucleus are elucidated using different relativistic many-body theories. The principles of the measurement of the electric dipole moments of diamagnetic atoms are outlined. Upper limits for the nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained combining the results of atomic experiments and relativistic many-body theories. The coefficients for the different sources of CP violation have been estimated at the elementary particle level for all the diamagnetic atoms of current experimental interest and their implications for physics beyond the standard model is discussed. Possible improvements of the current results of the measurements as well as quantum chromodynamics, nuclear and atomic calculations are suggested., Comment: 46 pages, 19 tables and 16 figures. A review article accepted for EPJA

The magnitude of traction forces exerted by living animal cells on their environment is a monotonically increasing and approximately sigmoidal function of the stiffness of the external medium. This observation is rationalized using active matter theory: adaptation to substrate rigidity results from an interplay between passive elasticity and active contractility., Comment: 4 pages, 2 figures

Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns., Comment: 5 pages, 3 figures

We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the smaller values to larger ones. By using this linear correlation we are able to predict reasonably all eigenvalues of given shell model Hamiltonian without complicated iterations., Comment: 4 pages

In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.

We study the hadron-quark phase transition in a molecular dynamics (MD) of quark degrees of freedom. The hadron state at low density and temperature, and the deconfined quark state at high density and temperature are observed in our model. We investigate the equations of state and draw the phase-diagram at wide baryon density and temperature range. We also discuss the transport property, e.g. viscosity, of $q\bar{q}$ matter. It is found that the ratio of the shear viscosity to the entropy density is less than one for quark matter., Comment: Poster presentation at Quark Matter 2005

In this paper we study energy centroids such as those with fixed spin and isospin, those with fixed irreducible representations for bosons, in the presence of random two-body and/or three-body interactions. Our results show that regularities of energy centroids of fixed spin states reported in earlier works are more robust than expected., Comment: Physical Review C, in press

In this talk we shall show our recent results in understanding the spin$^{\rm parity}$ 0$^+$ ground state (0 g.s.) dominance of many-body systems. We propose a simple approach to predict the spin $I$ g.s. probabilities which does not require the diagonalization of a Hamiltonian with random interactions. Some findings related to the 0 g.s. dominance will also be discussed., Comment: 11 pages and 4 figures

We present our results on properties of ground states for nucleonic systems in the presence of random two-body interactions. In particular we present probability distributions for parity, seniority, spectroscopic (i.e., in the laboratory framework) quadrupole moments and $\alpha$ clustering in the ground states. We find that the probability distribution for the parity of the ground states obtained by a two-body random ensemble simulates that of realistic nuclei: positive parity is dominant in the ground states of even-even nuclei while for odd-odd nuclei and odd-mass nuclei we obtain with almost equal probability ground states with positive and negative parity. In addition we find that for the ground states, assuming pure random interactions, low seniority is not favored, no dominance of positive values of spectroscopic quadrupole deformation, and no sign of $\alpha$-cluster correlations, all in sharp contrast to realistic nuclei. Considering a mixture of a random and a realistic interaction, we observe a second order phase transition for the $\alpha$-cluster correlation probability., Comment: 7 pages

The ground states of all even-even nuclei have angular momentum, $I$, equal to zero, I=0, and positive parity, $\pi=+$. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, in the presence of two-body random interactions, the predominance of $I^{\pi}=0^+$ ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as $d$ bosons, $sp$ bosons, $sd$ bosons, and a few fermions in single-$j$ shells for small $j$, there are a few approaches to predict and/or explain spin $I$ ground state ($I$ g.s.) probabilities. An empirical approach to predict $I$ g.s. probabilities is available for general cases, such as fermions in a single-$j$ ($j>7/2$) or many-$j$ shells and various boson systems, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Further interesting results are also reviewed concerning other robust phenomena of many-body systems in the presence of random two-body interactions, such as the odd-even staggering of binding energies, generic collectivity, the behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced two-body random ensemble., Comment: finalized version, review article (103 pages, 23 figures). accepted by Physics Reports

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems., Comment: a latex text file and 2 figures, to be published

In this paper we report our systematic calculations of angular momentum $I$ ground state probabilities ($P(I)$) of boson systems with spin $l$ in the presence of random two-body interactions. It is found that the P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the $P(I_{max})$'s of bosons with spin $l$ do not follow the 1/N ($N=l+1$, referring to the number of independent two-body matrix elements) relation. The properties of the $P(I)$'s obtained in boson systems with spin $l$ are discussed., Comment: 8 pages and 3 figures

In this paper, we discuss the regularities of energy of each angular momentum $I$ averaged over all the states for a fixed angular momentum (denoted as $\bar{E}_I$'s) in many-body systems interacting via a two-body random ensemble. It is found that $\bar{E}_I$'s with $I \sim I_{min}$ (minimum of $I$) or $I_{max}$ have large probabilities (denoted as ${\cal P}(I)$) to be the lowest, and that ${\cal P}(I)$ is close to zero elsewhere. A simple argument based on the randomness of the two-particle cfp's is given. A compact trajectory of the energy $\bar{E}_I$ vs. $I(I+1)$ is found to be robust. Regular fluctuations of the $P(I)$ (the probability of finding $I$ to be the ground state) and ${\cal P}(I)$ of even fermions in a single-$j$ shell and boson systems are found to be reverse, and argued by the dimension fluctuation of the model space. Other regularities, such as why there are 2 or 3 sizable ${\cal P}(I)$'s with $I\sim I_{min}$ and ${\cal P}(I) \ll {\cal P}(I_{max})$'s with $I\sim I_{max}$, why the coefficients $C$ defined by $<\bar{E}_I >$=$CI(I+1)$ is sensitive to the orbits and not sensitive to particle number, are found and studied for the first time., Comment: 19 pages and 6 figures

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities., Comment: 39 pages and 8 figures

We propose a simple approach to predict the angular momentum I ground state (I g.s.) probabilities of many-body systems that does not require the diagonalization of hamiltonians with random interactions. This method is found to be applicable to {\bf all} cases that have been discussed: even and odd fermion systems (both in single-j and many-j shells), and boson (both sd and sdg) systems. A simple relation for the highest angular momentum g.s. probability is found. Furthermore, it is suggested for the first time that the 0g.s. dominance in boson systems and in even-fermion systems is given by two-body interactions with specific features., Comment: 8 pages, 3 figures, to be published

The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free paramenter $q$, is used to generate a deformed Dyson boson expansion of the quadrupole operator. Then we obtain a quadrupole-quadrupole hamiltonian, for a single j-shell, in terms of this deformed bosonic operator. The hamiltonian is diagonalized and its eigenvalues are compared with the ones obtained from the fermionic quadrupole-quadrupole hamiltonian. The deformation parameter helps in achieving the correct energy levels, what cannot be encountered in practice with the usual non-deformed Dyson expansion., Comment: 11 pages, latex file, 1 figure (available upon request)

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail., Comment: 11 pages, REVTeX file, 3 PostScript Figures