Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

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 figure

General pairing interactions and pair truncation approximations for fermions in a single-j shell

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 publishe

Effects of upregulated indoleamine 2, 3-dioxygenase 1 by interferon γ gene transfer on interferon γ-mediated antitumor activity.

Interferon γ (IFN-γ), an anticancer agent, is a strong inducer of indoleamine 2, 3-dioxygenase 1 (IDO1), which is a tryptophan-metabolizing enzyme involved in the induction of tumor immune tolerance. In this study, we investigated the IDO1 expression in organs after IFN-γ gene transfer to mice. IFN-γ gene transfer greatly increased the mRNA expression of IDO1 in many tissues with the highest in the liver. This upregulation was associated with reduced L-tryptophan levels and increased L-kynurenine levels in serum, indicating that IFN-γ gene transfer increased the IDO activity. Then, Lewis lung carcinoma (LLC) tumor-bearing wild-type and IDO1-knockout (IDO1 KO) mice were used to investigate the effects of IDO1 on the antitumor activity of IFN-γ. IFN-γ gene transfer significantly retarded the tumor growth in both strains without any significant difference in tumor size between the two groups. By contrast, the IDO1 activity was increased only in the wild-type mice by IFN-γ gene transfer, suggesting that cells other than LLC cells, such as tumor stromal cells, are the major contributors of IDO1 expression in LLC tumor. Taken together, these results imply that IFN-γ gene transfer mediated IDO1 upregulation in cells other than LLC cells has hardly any effect on the antitumor activity of IFN-γ

Lowest Eigenvalues of Random Hamiltonians

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

Patterns of the ground states in the presence of random interactions: nucleon systems

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 page