Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines

Using the framework of infinite Matrix Product States, the existence of an \textit{anomalous} dynamical phase for the transverse-field Ising chain with sufficiently long-range interactions was first reported in [J.~C.~Halimeh and V.~Zauner-Stauber, arXiv:1610:02019], where it was shown that \textit{anomalous} cusps arise in the Loschmidt-echo return rate for sufficiently small quenches within the ferromagnetic phase. In this work we further probe the nature of the anomalous phase through calculating the corresponding Fisher-zero lines in the complex time plane. We find that these Fisher-zero lines exhibit a qualitative difference in their behavior, where, unlike in the case of the regular phase, some of them terminate before intersecting the imaginary axis, indicating the existence of smooth peaks in the return rate preceding the cusps. Additionally, we discuss in detail the infinite Matrix Product State time-evolution method used to calculate Fisher zeros and the Loschmidt-echo return rate using the Matrix Product State transfer matrix. Our work sheds further light on the nature of the anomalous phase in the long-range transverse-field Ising chain, while the numerical treatment presented can be applied to more general quantum spin chains.Comment: Journal article. 9 pages and 6 figures. Includes in part what used to be supplemental material in arXiv:1610:0201

Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex

The asymptotics of some spin foam amplitudes for a quantum 4-simplex is known to display rapid oscillations whose frequency is the Regge action. In this note, we reformulate this result through a difference equation, asymptotically satisfied by these models, and whose semi-classical solutions are precisely the sine and the cosine of the Regge action. This equation is then interpreted as coming from the canonical quantization of a simple constraint in Regge calculus. This suggests to lift and generalize this constraint to the phase space of loop quantum gravity parametrized by twisted geometries. The result is a reformulation of the flat model for topological BF theory from the Hamiltonian perspective. The Wheeler-de-Witt equation in the spin network basis gives difference equations which are exactly recursion relations on the 15j-symbol. Moreover, the semi-classical limit is investigated using coherent states, and produces the expected results. It mimics the classical constraint with quantized areas, and for Regge geometries it reduces to the semi-classical equation which has been introduced in the beginning.Comment: 16 pages, the new title is that of the published version (initial title: A taste of Hamiltonian constraint in spin foam models

Analysing long-term interactions between demand response and different electricity markets using a stochastic market equilibrium model. ESRI WP585, February 2018

Power systems based on renewable energy sources (RES) are characterised by increasingly distributed, volatile and uncertain supply leading to growing requirements for flexibility. In this paper, we explore the role of demand response (DR) as a source of flexibility that is considered to become increasingly important in future. The majority of research in this context has focussed on the operation of power systems in energy only markets, mostly using deterministic optimisation models. In contrast, we explore the impact of DR on generator investments and profits from different markets, on costs for different consumers from different markets, and on CO2 emissions under consideration of the uncertainties associated with the RES generation. We also analyse the effect of the presence of a feed-in premium (FIP) for RES generation on these impacts. We therefore develop a novel stochastic mixed complementarity model in this paper that considers both operational and investment decisions, that considers interactions between an energy market, a capacity market and a feed-in premium and that takes into account the stochasticity of electricity generation by RES. We use a Benders decomposition algorithm to reduce the computational expenses of the model and apply the model to a case study based on the future Irish power system. We find that DR particularly increases renewable generator profits. While DR may reduce consumer costs from the energy market, these savings may be (over)compensated by increasing costs from the capacity market and the feed-in premium. This result highlights the importance of considering such interactions between different markets

Comment on the paper by Y.Komura and Y.Okabe [arXiv:1011.3321]

We point out that the claim of strong universality in the paper J.Phys. A 44, 015002, arXiv:1011.3321 is incorrect, as it contradicts known rigorous results.Comment: submitted to J.Phys.

Relaxation of a Colloidal Particle into a Nonequilibrium Steady State

We study the relaxation of a single colloidal sphere which is periodically driven between two nonequilibrium steady states. Experimentally, this is achieved by driving the particle along a toroidal trap imposed by scanned optical tweezers. We find that the relaxation time after which the probability distributions have been relaxed is identical to that obtained by a steady state measurement. In quantitative agreement with theoretical calculations the relaxation time strongly increases when driving the system further away from thermal equilibrium

Gauge symmetries in spinfoam gravity: the case for "cellular quantization"

The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent with the gauge symmetries of discrete BF theory. We discuss a suitable generalization, called "cellular quantization", which (1) is finite, (2) produces a topological invariant, (3) matches with the properties of the continuum BF theory, (4) corresponds to its loop quantization. These results significantly clarify the foundations - and limitations - of the spinfoam formalism, and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.Comment: 6 page