Interaction Quench in the Hubbard model

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: i) An initial buildup of correlations where the quasiparticles are formed. ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. iii) The long time limit described by a quantum Boltzmann equation leading to thermalization with a temperature T proportional to U.Comment: Final version as publishe

Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential

Donald Saari conjectured that the $N$-body motion with constant configurational measure is a motion with fixed shape. Here, the configurational measure $\mu$ is a scale invariant product of the moment of inertia $I=\sum_k m_k |q_k|^2$ and the potential function $U=\sum_{i<j} m_i m_j/|q_i-q_j|^\alpha$, $\alpha >0$. Namely, $\mu = I^{\alpha/2}U$. We will show that this conjecture is true for planar equal-mass three-body problem under the strong force potential $\sum_{i<j} 1/|q_i-q_j|^2$

Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity

Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure \mu=\sqrt{I}U, which is the product of square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the motion is homographic. Where m_k represents mass of body k and r_{ij} represents distance between bodies i and j. We prove this conjecture for planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use \zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k. Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu and \rho make our proof simple

Symmetry, bifurcation and stacking of the central configurations of the planar 1+4 body problem

In this work we are interested in the central configurations of the planar 1+4 body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think this problem as a stacked central configuration too. We show that the configuration are necessarily symmetric and the other sattelites has the same mass. Moreover we proved that the number of central configuration in this case is in general one, two or three and in the special case where the satellites diametrically opposite have the same mass we proved that the number of central configuration is one or two saying the exact value of the ratio of the masses that provides this bifurcation.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with arXiv:1103.627

Large normally hyperbolic cylinders in a priori stable Hamiltonian systems

We prove the existence of normally hyperbolic invariant cylinders in nearly integrable hamiltonian systems

Chaos around a H\'enon-Heiles-inspired exact perturbation of a black hole

A solution of the Einstein's equations that represents the superposition of a Schwarszchild black hole with both quadrupolar and octopolar terms describing a halo is exhibited. We show that this solution, in the Newtonian limit, is an analog to the well known H\'enon-Heiles potential. The integrability of orbits of test particles moving around a black hole representing the galactic center is studied and bounded zones of chaotic behavior are found.Comment: 7 pages Revte

Multiple-Planet Scattering and the Origin of Hot Jupiters

Exoplanets show a pile-up of Jupiter-size planets in orbits with a 3-day period. A fraction of these hot Jupiters have retrograde orbits with respect to the parent star's rotation. To explain these observations we performed a series of numerical integrations of planet scattering followed by the tidal circularization. We considered planetary systems having 3 and 4 planets initially. We found that the standard Kozai migration is an inefficient mechanism for the formation of hot Jupiters. Our results show the formation of two distinct populations of hot Jupiters. The inner population of hot Jupiters with semimajor axis a < 0.03 AU formed in the systems where no planetary ejections occurred. This group contained a significant fraction of highly inclined and retrograde orbits, with distributions largely independent of the initial setup. However, our follow-up integrations showed that this populations was transient with most planets falling inside the Roche radius of the star in <1 Gyr. The outer population of hot Jupiters formed in systems where at least one planet was ejected. This population survived the effects of tides over >1 Gyr. The semimajor axis distribution of Population II fits nicely the observed 3-day pile-up. The inclination distribution of the outer hot planets depends on the number of planets in the initial systems and the 4-planet case showed a larger proportion (up to 10%), and a wider spread in inclination values. As the later results roughly agrees with observations, this may suggest that the planetary systems with observed hot Jupiters were originally rich in the number of planets, some of which were ejected. In a broad perspective, our work therefore hints on an unexpected link between the hot Jupiters and recently discovered free floating planets.Comment: submitted to Ap

Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics

The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: For the particular example of a linear ramp we examine the transient regime of prethermalization [M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008)] under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime the momentum distribution resembles a zero temperature Fermi liquid as the energy inserted by the ramp remains located in high energy modes. Thus ultracold fermions prove robust to heating which simplifies the observation of nonequilibrium BCS dynamics in optical lattices.Comment: 27 pages, 8 figures Second version with small modifications in section

A Multi-Epoch Study of the Radio Continuum Emission of Orion Source I: Constraints on the Disk Evolution of a Massive YSO and the Dynamical History of Orion BN/KL

We present new 7mm continuum observations of Orion BN/KL with the VLA. We resolve the emission from the protostar radio Source I and BN at several epochs. Source I is highly elongated NW-SE, and remarkably stable in flux density, position angle, and overall morphology over nearly a decade. This favors the extended emission component arising from an ionized disk rather than a jet. We have measured the proper motions of Source I and BN for the first time at 43 GHz. We confirm that both sources are moving at high speed (12 and 26 km/s, respectively) approximately in opposite directions, as previously inferred from measurements at lower frequencies. We discuss dynamical scenarios that can explain the large motions of both BN and Source I and the presence of disks around both. Our new measurements support the hypothesis that a close (~50 AU) dynamical interaction occurred around 500 years ago between Source I and BN as proposed by Gomez et al. From the dynamics of encounter we argue that Source I today is likely to be a binary with a total mass on the order of 20 Msun, and that it probably existed as a softer binary before the close encounter. This enables preservation of the original accretion disk, though truncated to its present radius of ~50 AU. N-body numerical simulations show that the dynamical interaction between a binary of 20 Msun total mass (I) and a single star of 10 Msun mass (BN) may lead to the ejection of both and binary hardening. The gravitational energy released in the process would be large enough to power the wide-angle flow traced by H2 and CO emission in the BN/KL nebula. Assuming the proposed dynamical history is correct, the smaller mass for Source I recently estimated from SiO maser dynamics (>7 Msun) by Matthews et al., suggests that non-gravitational forces (e.g. magnetic) must play an important role in the circumstellar gas dynamics.Comment: 17 pages, 7 figures, 4 tables, accepted by Ap

Straight Line Orbits in Hamiltonian Flows

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar H\'enon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized H\'enon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.Comment: laTeX with 6 figure