Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order

We calculate the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order using the supersymmetry method in the formulation without a singlet particle. We include a nonzero imaginary chemical potential and show that the finite-volume corrections to the low-energy constants $\Sigma$ and $F$ for the partially quenched partition function, and hence for spectral correlation functions of the Dirac operator, are the same as for the unquenched partition function. We briefly comment on how to minimize these corrections in lattice simulations of QCD. As a side result, we show that the zero-momentum integral in the formulation without a singlet particle agrees with previous results from random matrix theory.Comment: 19 pages, 4 figures; minor changes, to appear in JHE

Random matrix analysis of the QCD sign problem for general topology

Motivated by the important role played by the phase of the fermion determinant in the investigation of the sign problem in lattice QCD at nonzero baryon density, we derive an analytical formula for the average phase factor of the fermion determinant for general topology in the microscopic limit of chiral random matrix theory at nonzero chemical potential, for both the quenched and the unquenched case. The formula is a nontrivial extension of the expression for zero topology derived earlier by Splittorff and Verbaarschot. Our analytical predictions are verified by detailed numerical random matrix simulations of the quenched theory.Comment: 33 pages, 9 figures; v2: minor corrections, references added, figures with increased statistics, as published in JHE

Deep Inspiration and the Emergence of Ventilation Defects during Bronchoconstriction: A Computational Study

Deep inspirations (DIs) have a dilatory effect on airway smooth muscle (ASM) that helps to prevent or reduce more severe bronchoconstriction in healthy individuals. However, this bronchodilation appears to fail in some asthmatic patients or under certain conditions, and the reason is unclear. Additionally, quantitative effects of the frequency and magnitude of DIs on bronchodilation are not well understood. In the present study, we used a computational model of bronchoconstriction to study the effects of DI volumes, time intervals between intermittent DIs, relative speed of ASM constriction, and ASM activation on bronchoconstriction and the emergence of ventilation defects (VDefs). Our results showed a synergistic effect between the volume of DIs and the time intervals between them on bronchoconstriction and VDefs. There was a domain of conditions with sufficiently large volumes of DIs and short time intervals between them to prevent VDefs. Among conditions without VDefs, larger volumes of DIs resulted in greater airway dilation. Similarly, the time interval between DIs, during which the activated ASM re-constricts, affected the amplitude of periodic changes in airway radii. Both the relative speed of ASM constriction and ASM activation affected what volume of DIs and what time interval between them could prevent the emergence of VDefs. In conclusion, quantitative characteristics of DIs, such as their volume and time interval between them, affect bronchoconstriction and may contribute to difficulties in asthma. Better understanding of the quantitative aspects of DIs may result in novel or improved therapeutic approaches

Eigenvalue density of Wilson loops in 2D SU(N) YM

In 1981 Durhuus and Olesen (DO) showed that at infinite N the eigenvalue density of a Wilson loop matrix W associated with a simple loop in two-dimensional Euclidean SU(N) Yang-Mills theory undergoes a phase transition at a critical size. The averages of det(z-W), 1/det(z-W), and det(1+uW)/(1-vW) at finite N lead to three different smoothed out expressions, all tending to the DO singular result at infinite N. These smooth extensions are obtained and compared to each other.Comment: 35 pages, 8 figure

İnhizam

Cemil Süleyman'ın Servet-i Fünun ve Tanin'de tefrika edilen İnhizam adlı romanıRoman 1910'da Servet-i Fünun'da, 1914'te Tanin'de tefrika edilmiş, her iki tefrika da yarım kalmıştır. Ancak romanın tamamlandığı bilinmektedir

The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential

We discuss chiral perturbation theory for two and three quark flavors in the epsilon expansion at next-to-next-to-leading order (NNLO) including a small imaginary chemical potential. We calculate finite-volume corrections to the low-energy constants $\Sigma$ and $F$ and determine the non-universal modifications of the theory, i.e., modifications that cannot be mapped to random matrix theory (RMT). In the special case of two quark flavors in an asymmetric box we discuss how to minimize the finite-volume corrections and non-universal modifications by an optimal choice of the lattice geometry. Furthermore we provide a detailed calculation of a special version of the massless sunset diagram at finite volume.Comment: 21 pages, 5 figure

Numerical and experimental studies of the FeₓNi₁₋ₓCl₂ mixed magnetic system

Previous Mössbauer studies of the FeₓNi₁₋ₓCl₂ system led to conflicting hypothesises about the exact magnetic behaviour of the Fe₲⁺ ions in the mixed magnetic phase. This phase occurs between the Fe₲⁺ concentration values of x=0.03 and 0.12, and at temperatures less than 45 K. Tamaki and Ito (1991,1993) used a model which had co-existing magnetic order, with some Fe₲⁺ and Ni₲⁺ spins aligned near the crystalline c axis, while the others aligned near the perpendicular xy plane (model1). The relative population of the two sites is dependent on the concentration x and the temperature. Pollard et al (1982,1991) used a similar model, but with the spins aligned parallel to the x axis or in the xy plane (model 2). Again, the populations of the two sites depended on x and temperature. New Mössbauer studies were done, and the results are displayed and discussed in this thesis. The new studies concerned mixtures within the mixed phase (x=0.031 and 0.052) and the pure anti-ferromagnetic phase (x=0.15). Models 1 and 2 both generated similar simulated spectra, which gave similar fits to the experimental spectra. Model 1 generated spectra which fit only marginally better than model 2 spectra. Therefore it was not possible to conclude which model gave a better description of the FeₓNi₁₋ₓCl₂ system, using the new Mössbauer studies. Monte Carlo studies were also done, to provide a possible explanation for the complex magnetic behaviour which occurs in the mixed phase of FeₓNi₁₋ₓCl₂. The results showed that a random distribution of metal ions does not create co-existing spin order. However, clusters of Fe₲⁺ ions embedded in regions of FeₓNi₁₋ₓCl₂ with low values of x did create co-existing magnetic order. The spins aligned near the crystalline c axis or the xy plane, in agreement with model 1. Hence it was concluded that an un-even distribution of metal ions in FeₓNi₁₋ₓCl₂ exists, and directs the complex mixed phase behaviour which has been observed experimentally by workers using Mössbauer spectroscopy and Neutron diffraction techniques. The Monte Carlo programs mentioned in this thesis were written by the Author

The QCD sign problem and dynamical simulations of random matrices

At nonzero quark chemical potential dynamical lattice simulations of QCD are hindered by the sign problem caused by the complex fermion determinant. The severity of the sign problem can be assessed by the average phase of the fermion determinant. In an earlier paper we derived a formula for the microscopic limit of the average phase for general topology using chiral random matrix theory. In the current paper we present an alternative derivation of the same quantity, leading to a simpler expression which is also calculable for finite-sized matrices, away from the microscopic limit. We explicitly prove the equivalence of the old and new results in the microscopic limit. The results for finite-sized matrices illustrate the convergence towards the microscopic limit. We compare the analytical results with dynamical random matrix simulations, where various reweighting methods are used to circumvent the sign problem. We discuss the pros and cons of these reweighting methods.Comment: 34 pages, 3 figures, references added, as published in JHE

Synaptic signalling in a network of dopamine neurons:What prevents proper inter-cellular crosstalk?

Open access via the Jisc Wiley Agreement Acknowledgements: This work was supported by the Chancellor’s Fellow Grant and the Moray Endowment Grant to SS. YC and TK were supported by Medical Research Council (Award Number: MR/K017276/1) and UK Centre for Mammalian Synthetic Biology. The authors gratefully acknowledge the financial support of NHS Research Scotland (NRS), through Edinburgh Clinical Research Facility. Authors thank Prof. Andrey Abramov (UCL) for his valuable suggestions on design of this study and Scott Denham from the Mass Spectrometry Core for his technical expertise and assistance in this work.Peer reviewedPublisher PD