Classical Nonrelativistic Effective Field Theory and the Role of Gravitational Interactions

Coherent oscillation of axions or axion-like particles may give rise to long-lived clumps, called axion stars, because of the attractive gravitational force or its self-interaction. Such a kind of configuration has been extensively studied in the context of oscillons without the effect of gravity, and its stability can be understood by an approximate conservation of particle number in a non-relativistic effective field theory (EFT). We extend this analysis to the case with gravity to discuss the longevity of axion stars and clarify the EFT expansion scheme in terms of gradient energy and Newton's constant. Our EFT is useful to calculate the axion star configuration and its classical lifetime without any ad hoc assumption. In addition, we derive a simple stability condition against small perturbations. Finally, we discuss the consistency of other non-relativistic effective field theories proposed in the literature.Comment: 37 pages, 3 figure

Strong-coupling theory of superconductivity in a degenerate Hubbard model

In order to discuss superconductivity in orbital degenerate systems, a microscopic Hamiltonian is introduced. Based on the degenerate model, a strong-coupling theory of superconductivity is developed within the fluctuation exchange (FLEX) approximation where spin and orbital fluctuations, spectra of electron, and superconducting gap function are self-consistently determined. Applying the FLEX approximation to the orbital degenerate model, it is shown that the $d_{x^2-y^2}$-wave superconducting phase is induced by increasing the orbital splitting energy which leads to the development and suppression of the spin and orbital fluctuations, respectively. It is proposed that the orbital splitting energy is a controlling parameter changing from the paramagnetic to the antiferromagnetic phase with the $d_{x^2-y^2}$-wave superconducting phase in between.Comment: 4 figures, submitted to PR

Spin Fluctuation Induced Superconductivity Controlled by Orbital Fluctuation

A microscopic Hamiltonian reflecting the correct symmetry of $f$-orbitals is proposed to discuss superconductivity in heavy fermion systems. In the orbitally degenerate region in which not only spin fluctuations but also orbital fluctuations develop considerably, cancellation between spin and orbital fluctuations destabilizes $d_{x^{2}-y^{2}}$-wave superconductivity. Entering the non-degenerate region by increasing the crystalline electric field, $d_{x^{2}-y^{2}}$-wave superconductivity mediated by antiferromagnetic spin fluctuations emerges out of the suppression of orbital fluctuations. We argue that the present scenario can be applied to recently discovered superconductors CeTIn$_{5}$ (T=Ir, Rh, and Co).Comment: 4 pages, 3 figure

Laplace's rule of succession in information geometry

Laplace's "add-one" rule of succession modifies the observed frequencies in a sequence of heads and tails by adding one to the observed counts. This improves prediction by avoiding zero probabilities and corresponds to a uniform Bayesian prior on the parameter. The canonical Jeffreys prior corresponds to the "add-one-half" rule. We prove that, for exponential families of distributions, such Bayesian predictors can be approximated by taking the average of the maximum likelihood predictor and the \emph{sequential normalized maximum likelihood} predictor from information theory. Thus in this case it is possible to approximate Bayesian predictors without the cost of integrating or sampling in parameter space

Multipole correlations in low-dimensional f-electron systems

By using a density matrix renormalization group method, we investigate the ground-state properties of a one-dimensional three-orbital Hubbard model on the basis of a j-j coupling scheme. For $B_4^0 \ne 0$, where $B_4^0$ is a parameter to control cubic crystalline electric field effect, one orbital is itinerant, while other two are localized. Due to the competition between itinerant and localized natures, we obtain orbital ordering pattern which is sensitive to $B_4^0$, leading to a characteristic change of $\Gamma_{3g}$ quadrupole state into an incommensurate structure. At $B_4^0 = 0$, all the three orbitals are degenerate, but we observe a peak at $q = 0$ in $\Gamma_{3g}$ quadrupole correlation, indicating a ferro-orbital state, and the peak at $q = \pi$ in $\Gamma_{4u}$ dipole correlation, suggesting an antiferromagnetic state. We also discuss the effect of $\Gamma_{4u}$ octupole on magnetic anisotropy.Comment: 4 pages, 3 figures, Proceedings of ASR-WYP-2005 (September 27-29, 2005, Tokai

Adaptive Regret Minimization in Bounded-Memory Games

Online learning algorithms that minimize regret provide strong guarantees in situations that involve repeatedly making decisions in an uncertain environment, e.g. a driver deciding what route to drive to work every day. While regret minimization has been extensively studied in repeated games, we study regret minimization for a richer class of games called bounded memory games. In each round of a two-player bounded memory-m game, both players simultaneously play an action, observe an outcome and receive a reward. The reward may depend on the last m outcomes as well as the actions of the players in the current round. The standard notion of regret for repeated games is no longer suitable because actions and rewards can depend on the history of play. To account for this generality, we introduce the notion of k-adaptive regret, which compares the reward obtained by playing actions prescribed by the algorithm against a hypothetical k-adaptive adversary with the reward obtained by the best expert in hindsight against the same adversary. Roughly, a hypothetical k-adaptive adversary adapts her strategy to the defender's actions exactly as the real adversary would within each window of k rounds. Our definition is parametrized by a set of experts, which can include both fixed and adaptive defender strategies. We investigate the inherent complexity of and design algorithms for adaptive regret minimization in bounded memory games of perfect and imperfect information. We prove a hardness result showing that, with imperfect information, any k-adaptive regret minimizing algorithm (with fixed strategies as experts) must be inefficient unless NP=RP even when playing against an oblivious adversary. In contrast, for bounded memory games of perfect and imperfect information we present approximate 0-adaptive regret minimization algorithms against an oblivious adversary running in time n^{O(1)}.Comment: Full Version. GameSec 2013 (Invited Paper

Double-Exchange Ferromagnetism and Orbital-Fluctuation-Induced Superconductivity in Cubic Uranium Compounds

A double-exchange mechanism for the emergence of ferromagnetism in cubic uranium compounds is proposed on the basis of a $j$-$j$ coupling scheme. The idea is {\it orbital-dependent duality} of $5f$ electrons concerning itinerant $\Gamma_8^-$ and localized $\Gamma_7^-$ states in the cubic structure. Since orbital degree of freedom is still active in the ferromagnetic phase, orbital-related quantum critical phenomenon is expected to appear. In fact, odd-parity p-wave pairing compatible with ferromagnetism is found in the vicinity of an orbital ordered phase. Furthermore, even-parity d-wave pairing with significant odd-frequency components is obtained. A possibility to observe such exotic superconductivity in manganites is also discussed briefly.Comment: 4 pages, 4 figures. To appear in J. Phys. Soc. Jp

Quasiparticle Interactions for f2^2-Impurity Anderson Model with Crystalline-Electric-Field: Numerical Renormalization Group Study

The aspect of the quasiparticle interaction of a local Fermi liquid, the impurity version of f$^2$-based heavy fermions, is studied by the Wilson numerical renormalization group method. In particular, the case of the f$^2$-singlet crystalline-electric-field ground state is investigated assuming the case of UPt$_3$ with the hexagonal symmetry. It is found that the interorbital interaction becomes larger than the intraorbital one in contrast to the case of the bare Coulomb interaction for the parameters relevant to UPt$_3$. This result offers us a basis to construct a microscopic theory of the superconductivity of UPt$_3$ where the interorbital interactions are expected to play important roles.Comment: 9 pages, 5 figure

Effective Crystalline Electric Field Potential in a j-j Coupling Scheme

We propose an effective model on the basis of a $j$-$j$ coupling scheme to describe local $f$-electron states for realistic values of Coulomb interaction $U$ and spin-orbit coupling $\lambda$, for future development of microscopic theory of magnetism and superconductivity in $f^n$-electron systems, where $n$ is the number of local $f$ electrons. The effective model is systematically constructed by including the effect of a crystalline electric field (CEF) potential in the perturbation expansion in terms of $1/\lambda$. In this paper, we collect all the terms up to the first order of $1/\lambda$. Solving the effective model, we show the results of the CEF states for each case of $n$=2$\sim$5 with $O_{\rm h}$ symmetry in comparison with those of the Stevens Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF energy levels in an intermediate coupling region with $\lambda/U$ in the order of 0.1 corresponding to actual $f$-electron materials between the $LS$ and $j$-$j$ coupling schemes. Note that the relevant energy scale of $U$ is the Hund's rule interaction. It is found that the CEF energy levels in the intermediate coupling region can be quantitatively reproduced by our modified $j$-$j$ coupling scheme, when we correctly take into account the corrections in the order of $1/\lambda$ in addition to the CEF terms and Coulomb interactions which remain in the limit of $\lambda$=$\infty$. As an application of the modified $j$-$j$ coupling scheme, we discuss the CEF energy levels of filled skutterudites with $T_{\rm h}$ symmetry.Comment: 12 pages, 7 figures. Typeset with jpsj2.cl