Quantum field theory on noncommutative spaces

It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

http://absimage.aps.org/image/DAMOP06/MWS_DAMOP06-2006-000603.pdf

A quantum Newton's cradle

Beyond the cosmological standard model

After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond \Lambda, or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests. We begin by reviewing attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must screen themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives become important, and those for which second derivatives are important. Examples of the first class, such as f(R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories. We describe experimental tests, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. We discuss future tests which will be sensitive to different signatures of new physics in the gravitational sector. Parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.

Beyond the Cosmological Standard Model

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classicalnematicsgenerally occur in liquids of rod-like molecules; given that electrons are point like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. Dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr3Ru2O7 in a strong magnetic field in 2007 established that such phases exist in nature. In this article, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr3Ru2O7 experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors.

/pdf/nematic-fermi-fluids-in-condensed-matter-physics-nuwy0ow3uq.pdf

Nematic Fermi Fluids in Condensed Matter Physics

Chern–Simons action in noncommutative space

We present wormhole solutions to Hořava nonrelativistic gravity theory in vacuum. We show that, if the parameter A is set to one, traversable wormholes connecting two asymptotically de Sitter or anti-de Sitter regions exist. In the case of arbitrary λ, the asymptotic regions have a more complicated metric with constant curvature. We also show that, when the detailed balance condition is violated softly, traversable and asymptotically Minkowski, de Sitter or anti-de Sitter wormholes exist.

Wormhole solutions to Hořava gravity

K fields, that is, fields with a non-standard kinetic term, allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and have finite thickness in higher dimensions. Here we demonstrate that, for an appropriately chosen kinetic term, the propagation of linear perturbations is completely suppressed outside the topological defect, confining the propagation of particles inside the domain wall. On the other hand, inside the topological defect the propagation of linear perturbations is of the standard type, in spite of the non-standard kinetic term. Consequently, this compacton domain wall may act like a brane of finite thickness which is embedded in a higher dimensional space, but to which matter fields are constrained. In addition, we find strong indications that, when gravity is taken into account, location of gravity in the sense of Randall–Sundrum works for these compacton domain walls. When seen from the bulk, these finite thickness branes, in fact, cannot be distinguished from infinitely thin branes.

https://iopscience.iop.org/article/10.1088/1751-8113/42/15/159801/pdf

K fields, compactons and thick branes

We formulate noncommutative three-dimensional (3D) gravity by making use of its connection with 3D Chern-Simons theory. In the Euclidean sector, we consider the topology ${T}^{2}\ifmmode\times\else\texttimes\fi{}R$ and show that the 3D black hole solves the noncommutative equations. We then consider the black hole on a constant U(1) background and show that the black hole charges (mass and angular momentum) are modified by the presence of this background.

/pdf/chern-simons-formulation-of-noncommutative-gravity-in-three-3rwnjkghgn.pdf

Chern-Simons formulation of noncommutative gravity in three dimensions

Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. First, K field theories allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite thickness in higher dimensions. Second, propagation of linear perturbations is confined inside the compacton domain wall. Further, these linear perturbations inside the topological defect are of the standard type, in spite of the non-standard kinetic term. Third, when gravity is taken into account, location of gravity in the sense of Randall–Sundrum works for these compacton domain walls provided that the backreaction of gravity does not destabilize the compacton domain wall. It is the purpose of the present paper to investigate in detail the existence and stability of compacton domain walls in the full K field and gravity system, using both analytical and numerical methods. We find that the existence of the domain wall in the full system requires a correlation between the gravitational constant and the bulk cosmological constant.

Nicolás Grandi

Papers

Chern–Simons action in noncommutative space

Wormhole solutions to Hořava gravity

K fields, compactons and thick branes

Chern-Simons formulation of noncommutative gravity in three dimensions

Compact self-gravitating solutions of quartic (K) fields in brane cosmology