Non-unitary Model Research Articles

Estimating the intrahousehold costs and benefits of innovations to enhance smallholder farmers’ resilience

This paper introduces a new framework to quantify costs and benefits for resilience-related outcomes of agricultural innovations targeting smallholder farmers. The framework employs a non-unitary household model with expected utility to quantify welfare benefits associated with non-monetary outcomes that are important from a development perspective, such as improved consumption smoothing, empowerment, and changes in time use. We demonstrate the application of the framework using a case study of climate information services (CIS) in Ghana. We develop a set of individual bargaining weights based on the women’s empowerment in agriculture index, to demonstrate how benefits from CIS are distributed among men and women within households. We find that for the average risk-averse farmer, using CIS is associated with a 37-percent increase in expected utility, but male household heads benefit more than women living in male-headed households. Cost–benefit analyses that do not consider the intrahousehold distribution of benefits associated with agricultural innovations will overestimate benefits accruing to women with low bargaining power.

Positivity, low twist dominance and CSDR for CFTs

We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios u,vu,v interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around u=v=1/4u=v=1/4, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of \Phi_{1,2}Φ1,2 operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator (\Delta_\sigmaΔσ) is less than \frac{1}{2}12, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of \Delta_\sigmaΔσ, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in 4-\epsilon4−ϵ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.

Gender differences on the choices of a portfolio of climate change adaptation strategies in Ethiopia

Gender-based intra-household resource distributions constitute an important role in technology adoption-related decisions. Using a non-unitary household model and fitting an empirical adoption model for men and women individually and jointly, we examine how gender-based ownership, management and control of resources are correlated with adoptions of a portfolio of climate change adaptation strategies. Our analysis is based on recent household survey data with detailed household plot-level information about adaptation strategies, plot ownership, farm management decisions, and the right to control outputs from the plots among spouses within the household. The observed patterns of women’s ownership, management and economic rights of land suggest that all are important aspects of women’s bargaining power. We found compelling evidence regarding the overlapping effects of the different gender-linked-land-based rights on the adoption of a portfolio of adaptation strategies. The empirical findings emphasize the importance of incorporating gender-based intra-household interactions and joint resource ownership and decision making in climate change adaptation.

An index theorem for one-dimensional gapless non-unitary quantum walks

Recent developments in the index theory of discrete-time quantum walks allow us to assign a certain well-defined supersymmetric index to a pair of a unitary time-evolution $U$ and a $\mathbb{Z}_2$-grading operator $\varGamma$ satisfying the chiral symmetry condition $U^* = \varGamma U \varGamma.$ In this paper, this index theory will be extended to encompass non-unitary $U$. The existing literature for unitary $U$ makes use of the indispensable assumption that $U$ is essentially gapped; that is, we require that the essential spectrum of $U$ contains neither $-1$ nor $+1$ to define the associated index. It turns out that this assumption is no longer necessary, if the given time-evolution $U$ is non-unitary. As a concrete example, we shall consider a well-known non-unitary quantum walk model on the one-dimensional integer lattice, introduced by Mochizuki-Kim-Obuse.

The one-loop spectral problem of strongly twisted mathcal{N} = 4 Super Yang-Mills theory

We investigate the one-loop spectral problem of γ-twisted, planar mathcal{N} = 4 Super Yang-Mills theory in the double-scaling limit of infinite, imaginary twist angle and vanishing Yang-Mills coupling constant. This non-unitary model has recently been argued to be a simpler version of full-fledged planar mathcal{N} = 4 SYM, while preserving the latter model’s conformality and integrability. We are able to derive for a number of sectors one-loop Bethe equations that allow finding anomalous dimensions for various subsets of diagonalizable operators. However, the non-unitarity of these deformed models results in a large number of non-diagonalizable operators, whose mixing is described by a very complicated structure of non-diagonalizable Jordan blocks of arbitrarily large size and with a priori unknown generalized eigenvalues. The description of these blocks by methods of integrability remains unknown.

Pay-As-You-Go Pension, Bargaining Power, and Fertility

The effects of pension policies on fertility have been examined in the overlapping-generations (OLG) model of the unitary household in which no heterogeneity exists between wife and husband. This study departs from the OLG model to focus on marital bargaining arising from heterogeneity in a nonunitary model. Specifically, this paper examines how pension policies affect the fertility of a bargaining couple with different life spans. The analysis reveals a new channel from pension policies to fertility decisions, whereby an increase in pension size affects fertility not only via the changes in current and future income but also through a change in marital bargaining power. This result suggests that an increase in a pay-as-you-go pension may induce a negative effect on fertility through women's empowerment.

Beyond a unitary household measure: Does Gender matter in Legume Seed Systems among Smallholder Farmers?

We employ a non-unitary household model to analyze the main Pigeonpea seed channels for in Kenya. The paper is based on a household survey conducted on a 500 randomly selected households within three counties of Eastern Kenya. The study sites are based on the distance from the main trading center (county headquarters) which informs agro business infrastructure. We assess the participation in seed channels with regards to joint plots, women plots and male plots for Pigeonpeas legumes. More than half of the Pigeonpea plots (>50 %) in the sample are managed jointly by men and women; while around 10% are managed entirely by women. There were very few plots (<1%) managed by men alone. The main legumes seed sources are own saved seeds and cereal stockists. There is very limited sourcing from the certified seed channel (<10%), the certified seeds from agrovets are only acquired for joint plots. Using a multinomial logistic regression, we analyze the factors influencing the choice of Pigeonpea seed channels, encompassing characteristics of the wife of the household head. Literate wives and wives with high exposure to extension services were more likely to access seed from the agrovets, these variables were however not significant for the male head. Other significant determinants were total livestock unit, distance to the source of seed, amount of seed required, location of the household, and occupation. We conclude that targeting women farmers with knowledge and capacity building on the advantages of using certified seeds for legumes has the potential to enhance adoption of legumes in Eastern Kenya, education levels notwithstanding.

Entanglement entropy of non-unitary conformal field theory

Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as , where is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic ( with N nilpotent), then there is an additional term proportional to . These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

Identifying Non-Cooperative Behavior Among Spouses: Child Outcomes in Migrant-Sending Households

In the presence of asymmetric information, allocations can only be coordinated to the extent that each can be monitored, and household decision-making may not be fully cooperative. Because this information problem is particularly acute when individuals are not co-resident, I examine households in which the father migrates without his spouse and children. Results from the China Health and Nutrition Survey indicate that, when the father is away, girls' household labor increases while mothers' total work hours decrease. This is inconsistent with a unitary model in which there is no non-cooperative behavior and household members simply reallocate time to compensate for the father's absence. Furthermore, outcomes that are easily observed by the father - child schooling and health - are not affected by migration, controlling for changes in income. This is also inconsistent with a non-unitary model in which mothers' bargaining power increases when fathers migrate, given existing evidence which suggests that mothers have stronger preferences than fathers for these goods. I propose a simple model of contracting under asymmetric information and argue that this is consistent with the data. Additional implications are then tested regarding how and which allocations are likely to be affected.

IS IT PHYSICALLY SOUND TO ADD A TOPOLOGICALLY MASSIVE TERM TO THREE-DIMENSIONAL MASSIVE ELECTROMAGNETIC OR GRAVITATIONAL MODELS?

The addition of a topologically massive term to an admittedly nonunitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its nonunitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? The electromagnetic models remain unitary after the topological augmentation but, surprisingly enough, the gravitational ones have their unitarity spoiled. Here we analyze these issues and present the explanation why unitary massive gravitational models, unlike unitary massive electromagnetic ones, cannot coexist from the viewpoint of unitarity with topologically massive terms. We also discuss the novel features of the three-term effective field models that are gauge-invariant.

Numerical simulation of non-unitary gravity-induced localization

The localization of a quantum state is numerically exhibited in a non-unitary Newtonian model for gravity. It is shown that an unlocalized state of a ball of mass just above the expected threshold of 10 11 proton masses evolves into a mixed state with vanishing coherences above some localization lengths.

Women's participation in rural credit programmes in Bangladesh and their demand for formal health care: is there a positive impact?

Within the overall aim of poverty alleviation, development efforts have included credit and self-employment programmes. In Bangladesh, the major beneficiaries of such group-based credit programmes are rural women who use the loans to initiate small informal income-generating activities. This paper explores the benefits of women's participation in credit programmes on their own health seeking. Using data from a sample of 1798 households from rural Bangladesh, conducted in 1991-1992 through repeated random sampling of 87 districts covered by Grameen Bank, Bangladesh Rural Advancement Committee (BRAC) and Bangladesh Rural Development Board (BRDB), this paper addresses the question: does women's participation in credit programmes significantly affect their use of formal health care? A non-unitary household preference model is suggested to test the hypothesis that women's empowerment through participation in these programmes results in greater control of resources for their own demand for formal health care. The analysis controls for endogeneity due to self-selection and other unobserved village level factors through the use of a weighted two stage instrumental variable approach with village level fixed effects. The findings indicate a positive impact of women's participation in credit programmes on their demand for formal health care. The policy simulations on the results of this study highlight the importance of credit programmes as a health intervention in addition to being a mechanism for women's economic empowerment.

Perturbed gauged WZNW models

We discuss a new type of unitary perturbations around conformal theories inspired by the σ-model perturbation of the nonunitary WZNW model. We show that the nonunitary level k WZNW model perturbed by its sigma model term goes to the unitary level − k WZNW model. When plugged into the gauged WZNW model the given perturbation results in the perturbed gauged WZNW model which no longer describes a coset construction. We consider the BRST invariant generalization of the sigma model perturbation around the gauged WZNW model. In this way we obtain perturbed coset constructions. In the case of the SU m−2 (2) × SU 1(2)/ SU m−1 (2) coset, the BRST invariant sigma model perturbation is identical to Zamolodchikov's ifΦ (3,1) perturbation of the minimal conformal series. The existence of general geometry flows is clarified.

Two-point correlation function in integrable QFT with anti-crossing symmetry

The two point correlation function of the stress-energy tensor for the φ 1,3 massive deformation of the non-unitary model ▪ 3,5 is computed. We compare the ultraviolet CFT perturbative expansion of this correlation function with its spectral representation given by a summation over matrix elements of the intermediate asymptotic massive particles. The fast rate of convergence of both approaches provides an explicit example of an accurate interpolation between the infrared and ultraviolet behaviours of a Quantum Field Theory.

MASSLESS FLOWS II: THE EXACT S-MATRIX APPROACH

We study the spectrum, the massless S matrices and the ground-state energy of the flows between successive minimal models of conformal field theory, and within the sine-Gordon model with imaginary coefficient of the cosine term (related to the minimal models by “truncation”). For the minimal models, we find exact S matrices which describe the scattering of massless kinks, and show using the thermodynamic Bethe ansatz that the resulting non-perturbative c function (defined by the Casimir energy on a cylinder) flows appropriately between the two theories, as conjectured earlier. For the nonunitary sine-Gordon model, we find unusual behavior. For the range of couplings we can study analytically, the natural S matrix deduced from the minimal one by “undoing” the quantum-group truncation does not reproduce the proper c function with the TBA. It does, however, describe the correct properties of the model in a magnetic field.

The relationship between buccofacial and limb apraxia

There are at least two possible models depicting the relationship between buccofacial and limb apraxia. First, apraxia can be viewed as a unitary motor disorder which transcends the output modalities of both buccofacial and limb output. A high degree of similarity between the two types of apraxia would support this model. Alternatively, the relationship between buccofacial and limb apraxia may not include a unitary mechanism. The presence of quantitative and qualitative differences between buccofacial and limb performance would support this nonunitary model. The results of the present study support the nonunitary model.

Complete S-matrices of supersymmetric sine-gordon theory and perturbed superconformal minimal model

We derive the first complete S-matrices of the supersymmetric sine-Gordon theory for a general value of coupling constant. The spectrum includes not only solitons and antisolitons but also their bound states. The S-matrices are computed based on the soliton S-matrix which was obtained from the S-matrix of perturbed superconformal unitary model. After constructing a superconformal non-unitary model from the coset CFT with admissible representations, we derive the S-matrices of the perturbed superconformal non-unitary model by restricting the SSG S-matrices. We generalize these results to the theories with the fractional supersymmetries.

Non-unitary minimal models and RSOS models

We study a class of RSOS models whose universal classes are the non-unitary minimal models of the W n algebra. The ground-state structure is investigated, and the parametrization the dominant integral weights of A n−1 (1) is given. Using it, the local-state probabilities are constructed in terms of the W n characters. This shows the scaling relations between the critical exponents of a non-unitary RSOS model and the anomalous dimensions of the primary fields of the corresponding minimal model.

The one-dimensional dimerised spin-1/2 XY chain with arbitrary boundary conditions and related unitary and non-unitary models

The central charge of the Virasoro algebra of the one-dimensional dimerised XY model with arbitrary boundary conditions is obtained at criticality. The authors obtain c=1-12 tau 2 where tau (0 1/26. This corresponds to the non-unitary Potts model (0<or=q<2) and the O(N) one (-2<or=N<1).

A formula for the charge form factor of closed-shell nuclei and its application to16O

An expression for the charge form factor of light closed-shell nuclei previously derived in the framework of the non-unitary model operator approach is simplified by considering normalised correlated wavefunctions of the relative motion that are suitably parameterised. The expression is applied to the 16O nucleus and the correlation parameters (which are taken to be state dependent) together with the harmonic oscillator parameter are determined by fitting to experimental values of the charge form factor of 16O. The diffraction minima are well reproduced.