Monte Carlo simulations of dissipative quantum Ising models

The dynamical critical exponent $z$ is a fundamental quantity in characterizing quantum criticality, and it is well known that the presence of dissipation in a quantum model has significant impact on the value of $z$. Studying quantum Ising spin models using Monte Carlo methods, we estimate the dynamical critical exponent $z$ and the correlation length exponent $\nu$ for different forms of dissipation. For a two-dimensional quantum Ising model with Ohmic site dissipation, we find $z \approx 2$ as for the corresponding one-dimensional case, whereas for a one-dimensional quantum Ising model with Ohmic bond dissipation we obtain the estimate $z \approx 1$.Comment: 9 pages, 8 figures. Submitted to Physical Review

Criticality of compact and noncompact quantum dissipative Z4Z_4 models in (1+1)(1+1) dimensions

Using large-scale Monte Carlo computations, we study two versions of a $(1+1)D$ $Z_4$-symmetric model with Ohmic bond dissipation. In one of these versions, the variables are restricted to the interval $[0,2\pi>$, while the domain is unrestricted in the other version. The compact model features a completely ordered phase with a broken $Z_4$ symmetry and a disordered phase, separated by a critical line. The noncompact model features three phases. In addition to the two phases exhibited by the compact model, there is also an intermediate phase with isotropic quasi-long-range order. We calculate the dynamical critical exponent $z$ along the critical lines of both models to see if the compactness of the variable is relevant to the critical scaling between space and imaginary time. There appears to be no difference between the two models in that respect, and we find $z\approx1$ for the single phase transition in the compact model as well as for both transitions in the noncompact model

The Montana Kaimin, February 24, 1948

Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/3359/thumbnail.jp

Modelling of corrective actions in power system reliability analysis

Consequence analysis, including the modelling of corrective actions, is an important component when performing power system reliability analyses. Using an integrated methodology for power system reliability analysis, we investigate the impact of different modelling choices for the consequence analysis on estimates for the energy not supplied. These investigations corroborate the large impact modelling assumptions for corrective actions have on the resulting reliability indices. We have also identified other features of the consequence analysis, such as islanding and distributed slack, that can be important to take into account. The findings and the underlying structured approach contribute to improving the accuracy of power system reliability analyses.Modelling of corrective actions in power system reliability analysisacceptedVersio

Quantum criticality in spin chains with non-ohmic dissipation

We investigate the critical behavior of a spin chain coupled to bosonic baths characterized by a spectral density proportional to $\omega^s$, with $s>1$. Varying $s$ changes the effective dimension $d_\text{eff} = d + z$ of the system, where $z$ is the dynamical critical exponent and the number of spatial dimensions $d$ is set to one. We consider two extreme cases of clock models, namely Ising-like and U(1)-symmetric ones, and find the critical exponents using Monte Carlo methods. The dynamical critical exponent and the anomalous scaling dimension $\eta$ are independent of the order parameter symmetry for all values of $s$. The dynamical critical exponent varies continuously from $z \approx 2$ for $s=1$ to $z=1$ for $s=2$, and the anomalous scaling dimension evolves correspondingly from $\eta \gtrsim 0$ to $\eta = 1/4$. The latter exponent values are readily understood from the effective dimensionality of the system being $d_\text{eff} \approx 3$ for $s=1$, while for $s=2$ the anomalous dimension takes the well-known exact value for the 2D Ising and XY models, since then $d_{\rm{eff}}=2$. A noteworthy feature is, however, that $z$ approaches unity and $\eta$ approaches 1/4 for values of $s < 2$, while naive scaling would predict the dissipation to become irrelevant for $s=2$. Instead, we find that $z=1,\eta=1/4$ for $s \approx 1.75$ for both Ising-like and U(1) order parameter symmetry. These results lead us to conjecture that for all site-dissipative $Z_q$ chains, these two exponents are related by the scaling relation $z = \text{max} {(2-\eta)/s, 1}$. We also connect our results to quantum criticality in nondissipative spin chains with long-range spatial interactions.Comment: 8 pages, 6 figure

Understanding barriers to utilising flexibility in operation and planning of the electricity distribution system – classification frameworks with applications to Norway

publishedVersio

Demand flexibility modelling for long term optimal distribution grid planning

Optimisation tools for long-term grid planning considering flexibility resources require aggregated flexibility models that are not too computationally demanding or complex. Still, they should capture the operational benefits of flexibility sufficiently accurately for planning purposes. This article investigates the sufficiency of an aggregated flexibility model for planning tools by comparing it against a detailed flexibility model. Two different constraint formulations, namely based on recovery period and temporal proximity, were tested to account for post activation dynamics of flexibility resources. The results show that the recovery period based formulation results in excessive demand reduction. The proximity constraint formulation on the other hand results in realistic activation of flexibility resources, which represents an improvement over the base formulation without constraints for post activation dynamics. The results show how a too simple model of the operational behaviour of demand flexibility may overestimate its benefits as an alternative or supplement to grid investments.Demand flexibility modelling for long term optimal distribution grid planningpublishedVersio

Identifying high-impact operating states in power system reliability analysis

The reliability of a power system depends, among other things, on the operating states of the system. For reliability analysis for long-term planning purposes, it may be necessary to consider a large set of representative operating states, and clustering techniques can be applied to reduce this set to make the analysis computationally tractable. However, the values of reliability indices for the system may be dominated by the contributions from a relatively small number of high-impact operating states that are not easily captured in the analysis. The objective of this paper is to identify high-impact operating states in the context of power system reliability analysis based on clustering techniques. A secondary objective is to characterize features of these operating states to better understand how they could be recognized, prepared for, and if possible avoided. An approach and an algorithm are proposed, and they are illustrated using a reliability analysis case study for a region of the Norwegian transmission grid with realistic operating states for the Nordic power systemIdentifying high-impact operating states in power system reliability analysisacceptedVersio