On the entanglement of a quantum field with a dispersive medium

In this Letter we study the entanglement of a quantum radiation field interacting with a dielectric medium. In particular, we describe the quantum mixed state of a field interacting with a dielectric through plasma and Drude models and show that these generate very different entanglement behavior, as manifested in the entanglement entropy of the field. We also present a formula for a "Casimir" entanglement entropy, i.e., the distance dependence of the field entropy. Finally, we study a toy model of the interaction between two plates. In this model, the field entanglement entropy is divergent; however, as in the Casimir effect, its distance-dependent part is finite, and the field matter entanglement is reduced when the objects are far.Comment: Final published PRL versio

String-net condensation: A physical mechanism for topological phases

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and condense. We derive exactly soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states. Those ground states correspond to 2D parity invariant topological phases. These models reveal the mathematical framework underlying topological phases: tensor category theory. One of the Hamiltonians - a spin-1/2 system on the honeycomb lattice - is a simple theoretical realization of a fault tolerant quantum computer. The higher dimensional case also yields an interesting result: we find that 3D string-net condensation naturally gives rise to both emergent gauge bosons and emergent fermions. Thus, string-net condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions.Comment: 21 pages, RevTeX4, 19 figures. Homepage http://dao.mit.edu/~we

Coating thermal noise of a finite-size cylindrical mirror

Thermal noise of a mirror is one of the limiting noise sources in the high precision measurement such as gravitational-wave detection, and the modeling of thermal noise has been developed and refined over a decade. In this paper, we present a derivation of coating thermal noise of a finite-size cylindrical mirror based on the fluctuation-dissipation theorem. The result agrees to a previous result with an infinite-size mirror in the limit of large thickness, and also agrees to an independent result based on the mode expansion with a thin-mirror approximation. Our study will play an important role not only to accurately estimate the thermal-noise level of gravitational-wave detectors but also to help analyzing thermal noise in quantum-measurement experiments with lighter mirrors.Comment: 13 pages, 4 figure

Field-Induced Magnetization Steps in Intermetallic Compounds and Manganese Oxides: The Martensitic Scenario

Field-induced magnetization jumps with similar characteristics are observed at low temperature for the intermetallic germanide Gd5Ge4and the mixed-valent manganite Pr0.6Ca0.4Mn0.96Ga0.04O3. We report that the field location -and even the existence- of these jumps depends critically on the magnetic field sweep rate used to record the data. It is proposed that, for both compounds, the martensitic character of their antiferromagnetic-to-ferromagnetic transitions is at the origin of the magnetization steps.Comment: 4 pages,4 figure

Warping the young stellar disc in the Galactic Centre

We examine influence of the circum-nuclear disc (CND) upon the orbital evolution of young stars in the Galactic Centre. We show that gravity of the CND causes precession of the orbits which is highly sensitive upon the semi-major axis and inclination. We consider such a differential precession within the context of an ongoing discussion about the origin of the young stars and suggest a possibility that all of them have originated in a thin disc which was partially destroyed due to the influence of the CND during the period of ~6Myr.Comment: proc. conf. "The Universe Under the Microscope - Astrophysics at High Angular Resolution", 21-25 April 2008, Bad Honnef, German

Arithmetic complexity via effective names for random sequences

We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions. More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persistent elements. While some classes (such as Martin-L\"{o}f randoms and Kurtz non-randoms) have left-r.e. numberings, there is no canonical, or acceptable, left-r.e. numbering for any class of left-r.e. randoms. Finally, we note some fundamental differences between left-r.e. numberings for sets and reals

Comment on "Gravity Waves, Chaos, and Spinning Compact Binaries"

In this comment, I argue that chaotic effects in binary black hole inspiral will not strongly impact the detection of gravitational waves from such systems.Comment: 1 page, comment on gr-qc/991004

Gravity Waves, Chaos, and Spinning Compact Binaries

Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.Comment: Final version published in PR

Next-to-leading-order corrections to exclusive processes in kTk_T factorization

We calculate next-to-leading-order (NLO) corrections to exclusive processes in $k_T$ factorization theorem, taking $\pi\gamma^*\to\gamma$ as an example. Partons off-shell by $k_T^2$ are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the $k_T$-dependent hard kernel as their difference. The gauge invariance of the hard kernel is then proven to all orders by induction. The light-cone singularities in the $k_T$-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. This regularization introduces a factorization-scheme dependence into the hard kernel, which can be minimized in the standard way. Both the large double logarithms $\ln^2k_T$ and $\ln^2 x$, $x$ being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function and organized by the $k_T$ resummation, and the latter absorbed into a jet function and organized by the threshold resummation. The NLO corrections are found to be only few-percent for $\pi\gamma^*\to\gamma$, if setting the factorization scale to the momentum transfer from the virtual photon.Comment: 13 pages; version to appear in Physical Review

Ion-ion correlations: an improved one-component plasma correction

Based on a Debye-Hueckel approach to the one-component plasma we propose a new free energy for incorporating ionic correlations into Poisson-Boltzmann like theories. Its derivation employs the exclusion of the charged background in the vicinity of the central ion, thereby yielding a thermodynamically stable free energy density, applicable within a local density approximation. This is an improvement over the existing Debye-Hueckel plus hole theory, which in this situation suffers from a "structuring catastrophe". For the simple example of a strongly charged stiff rod surrounded by its counterions we demonstrate that the Poisson-Boltzmann free energy functional augmented by our new correction accounts for the correlations present in this system when compared to molecular dynamics simulations.Comment: 5 pages, 2 figures, revtex styl