Exact and approximate dynamics of the quantum mechanical O(N) model

We study a quantum dynamical system of N, O(N) symmetric, nonlinear oscillators as a toy model to investigate the systematics of a 1/N expansion. The closed time path (CTP) formalism melded with an expansion in 1/N is used to derive time evolution equations valid to order 1/N (next-to-leading order). The effective potential is also obtained to this order and its properties areelucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schrodinger equation, we consider two initial conditions consistent with O(N) symmetry, one of them a quantum roll, the other a wave packet initially to one side of the potential minimum, whose center has all coordinates equal. For the case of the quantum roll we map out the domain of validity of the large-N expansion. We discuss unitarity violation in the 1/N expansion; a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are also compared to those given by the Hartree variational ansatz at given values of N. We conclude that late-time behavior, where nonlinear effects are significant, is not well-described by either approximation.Comment: 16 pages, 12 figrures, revte

Vacuum Structure of Two-Dimensional ϕ4\phi^4 Theory on the Orbifold S1/Z2S^{1}/Z_{2}

We consider the vacuum structure of two-dimensional $\phi^4$ theory on $S^{1}/Z_{2}$ both in the bosonic and the supersymmetric cases. When the size of the orbifold is varied, a phase transition occurs at $L_{c}=2\pi/m$, where $m$ is the mass of $\phi$. For $L<L_{c}$, there is a unique vacuum, while for $L>L_{c}$, there are two degenerate vacua. We also obtain the 1-loop quantum corrections around these vacuum solutions, exactly in the case of $L<L_{c}$ and perturbatively for $L$ greater than but close to $L_{c}$. Including the fermions we find that the "chiral" zero modes around the fixed points are different for $LL_{c}$. As for the quantum corrections, the fermionic contributions cancel the singular part of the bosonic contributions at L=0. Then the total quantum correction has a minimum at the critical length $L_{c}$.Comment: Revtex, 15 pages, 3 eps figure

Trade Promotion Authority (TPA): Frequently Asked Questions

Trade Promotion Authority (TPA), formerly called fast track, is the authority Congress has granted to the President for limited periods of time to negotiate reciprocal trade agreements. The authority lays out U.S. trade negotiating objectives, procedures for congressional-executive notification and consultation, and expedited legislative procedures under which bills implementing trade agreements negotiated by the executive branch are to be considered. The most recent authority was enacted in December 2002 and expired as of July 1, 2007. Legislation to reauthorize TPA has been introduced in the 113th Congress. The United States is engaged in several sets of trade agreement negotiations. The issue of TPA reauthorization has raised a number of questions regarding TPA itself and the pending legislation. This report addresses a number of those questions that are frequently asked, including: • What is trade promotion authority? • Is TPA necessary? • What are trade negotiating objectives and how are they reflected in TPA statutes? • What requirements does Congress impose on the President under TPA? • Does TPA affect congressional authority on trade policy

Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model

We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of $\lambda \phi^4$ field theory to order 1/N in the 2PI-1/N expansion. We show that the renormalization of the broken-symmetry theory depends only on the counter terms of the symmetric theory with $\phi = 0$. We find that the 2PI-1/N expansion violates the Goldstone theorem at order 1/N. In using the O(4) model as a low energy effective field theory of pions to study the time evolution of disoriented chiral condensates one has to {\em{explicitly}} break the O(4) symmetry to give the physical pions a nonzero mass. In this effective theory the {\em additional} small contribution to the pion mass due to the violation of the Goldstone theorem in the 2-PI-1/N equations should be numerically unimportant

Non-equilibrium dynamics in quantum field theory at high density: the tsunami

The dynamics of a dense relativistic quantum fluid out of thermodynamic equilibrium is studied in the framework of the Phi^4 scalar field theory in the large N limit. The time evolution of a particle distribution in momentum space (the tsunami) is computed. The effective mass felt by the particles in such a high density medium equals the tree level mass plus the expectation value of the squared field. The case of negative tree level squared mass is particularly interesting. In such case dynamical symmetry restoration as well as dynamical symmetry breaking can happen. Furthermore, the symmetry may stay broken with vanishing asymptotic squared mass showing the presence of out of equilibrium Goldstone bosons. We study these phenomena and identify the set of initial conditions that lead to each case. We compute the equation of state which turns to depend on the initial state. Although the system does not thermalize, the equation of state for asymptotically broken symmetry is of radiation type. We compute the correlation functions at equal times. The two point correlator for late times is the sum of different terms. One stems from the initial particle distribution. Another term accounts for the out of equilibrium Goldstone bosons created by spinodal unstabilities when the symmetry is asymptotically broken.Both terms are of the order of the inverse of the coupling for distances where causal signals can connect the two points. The contribution of the out of equilibrium Goldstones exhibits scaling behaviour in a generalized sense.Comment: LaTex, 49 pages, 15 .ps figure

Machine learning with the hierarchy‐of‐hypotheses (HoH) approach discovers novel pattern in studies on biological invasions

Research synthesis on simple yet general hypotheses and ideas is challenging in scientific disciplines studying highly context‐dependent systems such as medical, social, and biological sciences. This study shows that machine learning, equation‐free statistical modeling of artificial intelligence, is a promising synthesis tool for discovering novel patterns and the source of controversy in a general hypothesis. We apply a decision tree algorithm, assuming that evidence from various contexts can be adequately integrated in a hierarchically nested structure. As a case study, we analyzed 163 articles that studied a prominent hypothesis in invasion biology, the enemy release hypothesis. We explored if any of the nine attributes that classify each study can differentiate conclusions as classification problem. Results corroborated that machine learning can be useful for research synthesis, as the algorithm could detect patterns that had been already focused in previous narrative reviews. Compared with the previous synthesis study that assessed the same evidence collection based on experts' judgement, the algorithm has newly proposed that the studies focusing on Asian regions mostly supported the hypothesis, suggesting that more detailed investigations in these regions can enhance our understanding of the hypothesis. We suggest that machine learning algorithms can be a promising synthesis tool especially where studies (a) reformulate a general hypothesis from different perspectives, (b) use different methods or variables, or (c) report insufficient information for conducting meta‐analyses

The Trans-Pacific Partnership: Negotiations and Issues for Congress

[Excerpt] The Trans-Pacific Partnership (TPP) is a potential free trade agreement (FTA) among 11, and perhaps more, countries. The United States and 10 other countries of the Asia-Pacific region— Australia, Brunei, Canada, Chile, Malaysia, Mexico, New Zealand, Peru, Singapore, and Vietnam—are negotiating the text of the FTA. Canada and Mexico participated for the first time in the Auckland round of negotiations in December 2012, and Japan recently announced it would seek to participate in the negotiations. With 29 chapters under negotiation, the TPP partners envision the agreement to be “comprehensive and high-standard,” in that they seek to eliminate tariffs and non-tariff barriers to trade in goods, services, and agriculture, and to establish rules on a wide range of issues including foreign direct investment and other economic activities. They also strive to create a “21st-century agreement” that addresses new and cross-cutting issues presented by an increasingly globalized economy. The TPP draws congressional interest on a number of fronts. Congress would have to approve implementing legislation for U.S. commitments under the agreement to enter into force. In addition, under long-established executive-legislative practice, the Administration notifies and consults with congressional leaders, before, during, and after trade agreements have been negotiated. Furthermore, the TPP will likely affect a range of sectors and regions of the U.S. economy of direct interest to Members of Congress and could influence the shape and path of U.S. trade policy for the foreseeable future. This report examines the issues related to the proposed TPP, the state and substance of the negotiations (to the degree that the information is publically available), the specific areas under negotiation, the policy and economic contexts in which the TPP would fit, and the issues for Congress that the TPP presents. The report will be revised and updated as events warrant

qq-graded Heisenberg algebras and deformed supersymmetries

The notion of $q$-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for $q$ complex number in the unit disc. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary $\mathbb{Z}_2$ grading or Grassmann parity for associative superalgebra, and a modified version of the usual supersymmetry. As a specific problem, we focus on the interesting limit $q\to -1$ for which the Arik and Coon deformation of the Heisenberg algebra allows to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.Comment: 2 figure

The von Neumann-Wigner type potentials and the wave functions' asymptotics for the discrete levels in continuum

One to one correspondence between the decay law of the von Neumann-Wigner type potentials and the asymptotic behaviour of the wave functions representing bound states in the continuum is established.Comment: latex, 7 page

Perceptually smooth timbral guides by state-space analysis of phase-vocoder parameters

Sculptor is a phase-vocoder-based package of programs that allows users to explore timbral manipulation of sound in real time. It is the product of a research program seeking ultimately to perform gestural capture by analysis of the sound a performer makes using a conventional instrument. Since the phase-vocoder output is of high dimensionality — typically more than 1,000 channels per analysis frame—mapping phase-vocoder output to appropriate input parameters for a synthesizer is only feasible in theory