Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix ?1, ?2, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

Robust food supply supply chains:An integrated framework for vulnerability assessment and disturbance management

The operation of supply chains (SCs) has for many years been focused on efficiency, leanness and responsiveness. This has resulted in reduced slack in operations, compressed cycle times, increased productivity and minimised inventory levels along the SC. Combined with tight tolerance settings for the realisation of logistics and production processes, this has led to SC performances that are frequently not robust. SCs are becoming increasingly vulnerable to disturbances, which can decrease the competitive power of the entire chain in the market. Moreover, in the case of food SCs non-robust performances may ultimately result in empty shelves in grocery stores and supermarkets.
The overall objective of this research is to contribute to Supply Chain Management (SCM) theory by developing a structured approach to assess SC vulnerability, so that robust performances of food SCs can be assured. We also aim to help companies in the food industry to evaluate their current state of vulnerability, and to improve their performance robustness through a better understanding of vulnerability issues. The following research questions (RQs) stem from these objectives:
RQ1: What are the main research challenges related to (food) SC robustness?
RQ2: What are the main elements that have to be considered in the design of robust SCs and what are the relationships between these elements?
RQ3: What is the relationship between the contextual factors of food SCs and the use of disturbance management principles?
RQ4: How to systematically assess the impact of disturbances in (food) SC processes on the robustness of (food) SC performances?
To answer these RQs we used different methodologies, both qualitative and quantitative. For each question, we conducted a literature survey to identify gaps in existing research and define the state of the art of knowledge on the related topics. For the second and third RQ, we conducted both exploration and testing on selected case studies. Finally, to obtain more detailed answers to the fourth question, we used simulation modelling and scenario analysis for vulnerability assessment.
Main findings are summarised as follows.
Based on an extensive literature review, we answered RQ1. The main research challenges were related to the need to define SC robustness more precisely, to identify and classify disturbances and their causes in the context of the specific characteristics of SCs and to make a systematic overview of (re)design strategies that may improve SC robustness. Also, we found that it is useful to be able to discriminate between varying degrees of SC vulnerability and to find a measure that quantifies the extent to which a company or SC shows robust performances when exposed to disturbances.
To address RQ2, we define SC robustness as the degree to which a SC shows an acceptable performance in (each of) its Key Performance Indicators (KPIs) during and after an unexpected event that caused a disturbance in one or more logistics processes. Based on the SCM literature we identified the main elements needed to achieve robust performances and structured them together to form a conceptual framework for the design of robust SCs. We then explained the logic of the framework and elaborate on each of its main elements: the SC scenario, SC disturbances, SC performance, sources of food SC vulnerability, and redesign principles and strategies.
Based on three case studies, we answered RQ3. Our major findings show that the contextual factors have a consistent relationship to Disturbance Management Principles (DMPs). The product and SC environment characteristics are contextual factors that are hard to change and these characteristics initiate the use of specific DMPs as well as constrain the use of potential response actions. The process and the SC network characteristics are contextual factors that are easier to change, and they are affected by the use of the DMPs. We also found a notable relationship between the type of DMP likely to be used and the particular combination of contextual factors present in the observed SC.
To address RQ4, we presented a new method for vulnerability assessments, the VULA method. The VULA method helps to identify how much a company is underperforming on a specific Key Performance Indicator (KPI) in the case of a disturbance, how often this would happen and how long it would last. It ultimately informs the decision maker about whether process redesign is needed and what kind of redesign strategies should be used in order to increase the SC’s robustness. The VULA method is demonstrated in the context of a meat SC using discrete-event simulation. The case findings show that performance robustness can be assessed for any KPI using the VULA method.
To sum-up the project, all findings were incorporated within an integrated framework for designing robust SCs. The integrated framework consists of the following steps: 1) Description of the SC scenario and identification of its specific contextual factors; 2) Identification of disturbances that may affect KPIs; 3) Definition of the relevant KPIs and identification of the main disturbances through assessment of the SC performance robustness (i.e. application of the VULA method); 4) Identification of the sources of vulnerability that may (strongly) affect the robustness of performances and eventually increase the vulnerability of the SC; 5) Identification of appropriate preventive or disturbance impact reductive redesign strategies; 6) Alteration of SC scenario elements as required by the selected redesign strategies and repeat VULA method for KPIs, as defined in Step 3.
Contributions of this research are listed as follows. First, we have identified emerging research areas - SC robustness, and its counterpart, vulnerability. Second, we have developed a definition of SC robustness, operationalized it, and identified and structured the relevant elements for the design of robust SCs in the form of a research framework. With this research framework, we contribute to a better understanding of the concepts of vulnerability and robustness and related issues in food SCs. Third, we identified the relationship between contextual factors of food SCs and specific DMPs used to maintain robust SC performances: characteristics of the product and the SC environment influence the selection and use of DMPs; processes and SC networks are influenced by DMPs. Fourth, we developed specific metrics for vulnerability assessments, which serve as a basis of a VULA method. The VULA method investigates different measures of the variability of both the duration of impacts from disturbances and the fluctuations in their magnitude.
With this project, we also hope to have delivered practical insights into food SC vulnerability. First, the integrated framework for the design of robust SCs can be used to guide food companies in successful disturbance management. Second, empirical findings from case studies lead to the identification of changeable characteristics of SCs that can serve as a basis for assessing where to focus efforts to manage disturbances. Third, the VULA method can help top management to get more reliable information about the “health” of the company.
The two most important research opportunities are: First, there is a need to extend and validate our findings related to the research framework and contextual factors through further case studies related to other types of (food) products and other types of SCs. Second, there is a need to further develop and test the VULA method, e.g.: to use other indicators and statistical measures for disturbance detection and SC improvement; to define the most appropriate KPI to represent the robustness of a complete SC. We hope this thesis invites other researchers to pick up these challenges and help us further improve the robustness of (food) SCs.

Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600404]

Dynamics of the entanglement spectrum in spin chains

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.

Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, especially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

Vulnerability and robustness of SME supply chains: An empirical study of risk and disturbance management of fresh food processors in a developing market

The aim of this paper is to analyse vulnerability and robustness of small and medium size enterprises (SMEs) supply chains and to consider contextual factors that might influence the success of their disturbance management: Risky product and business environment. By using an exploratory case study it is shown how these contextual factors attribute vulnerability sources, contribute to the robustness of a company’s performance and supply chain vulnerability, as well as how a company seeks to manage internal and external vulnerability sources. The exploratory case is based on a fresh food supply chain of a manufacturing SME operating in a developing market.
Case findings suggest that fresh food supply chains of a manufacturing SME in developing markets are prone to disruptions of their logistics and production processes due to ‘riskiness’ of fresh food products, the ‘riskiness’ of developing markets, as well as ‘riskiness’ of SMEs themselves. However, this does not necessarily indicate the vulnerability of an SME and its entire supply chain. Findings indicate that SMEs can be very successful in disturbance management by selective use of redesign strategies that aim to prevent or reduce the impact of disturbances. More precise, it is likely that an SME can achieve robust performance by employing preventive redesign strategies in managing disturbances that result from internal, company related vulnerability sources, while impact reduction strategies are likely to contribute to robust performance of an SME if used to manage disturbances that result from internal, supply chain related vulnerability sources, as well as external vulnerability sources.