Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential

In quantum chromodynamics (QCD) at nonzero chemical potential, the eigenvalues of the Dirac operator are scattered in the complex plane. Can the fluctuation properties of the Dirac spectrum be described by universal predictions of non-Hermitian random matrix theory? We introduce an unfolding procedure for complex eigenvalues and apply it to data from lattice QCD at finite chemical potential $\mu$ to construct the nearest-neighbor spacing distribution of adjacent eigenvalues in the complex plane. For intermediate values of $\mu$, we find agreement with predictions of the Ginibre ensemble of random matrix theory, both in the confinement and in the deconfinement phase.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

Imaginary chemical potential and finite fermion density on the lattice

Standard lattice fermion algorithms run into the well-known sign problem at real chemical potential. In this paper we investigate the possibility of using imaginary chemical potential, and argue that it has advantages over other methods, particularly for probing the physics at finite temperature as well as density. As a feasibility study, we present numerical results for the partition function of the two-dimensional Hubbard model with imaginary chemical potential. We also note that systems with a net imbalance of isospin may be simulated using a real chemical potential that couples to I_3 without suffering from the sign problem.Comment: 9 pages, LaTe

Quantum Chaos in Compact Lattice QED

Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator.Comment: 11 pages, 4 figure

On the predictability of supramolecular interactions in molecular cocrystals-the view from the bench

A series of cocrystals involving theophylline and fluorobenzoic acids highlights the difficulty of predicting supramolecular interactions in molecular crystals.MKC and DKB gratefully acknowledge financial support from the UCL Faculty of Mathematical and Physical Sciences. DKB and WJ thank the Royal Society for a Newton International Fellowship and the Isaac Newton Trust (Trinity College, University of Cambridge) for funding. MA thanks the EPSRC for a studentship, while SAS acknowledges funding through the EPSRC CASE scheme with Pfizer. We are grateful for computational support from the UK national high performance computing service, ARCHER, for which access was obtained via the UKCP consortium and funded by EPSRC grant (EP/K013564/1).This is the final version of the article. It first appeared from the Royal Society of Chemistry via https://doi.org//10.1039/C6CE00293

Chiral phase transition in a covariant nonlocal NJL model

The properties of the chiral phase transition at finite temperature and chemical potential are investigated within a nonlocal covariant extension of the Nambu-Jona-Lasinio model based on a separable quark-quark interaction. We consider both the situation in which the Minkowski quark propagator has poles at real energies and the case where only complex poles appear. In the literature, the latter has been proposed as a realization of confinement. In both cases, the behaviour of the physical quantities as functions of T and \mu is found to be quite similar. In particular, for low values of T the chiral transition is always of first order and, for finite quark masses, at certain "end point" the transition turns into a smooth crossover. In the chiral limit, this "end point" becomes a "tricritical" point. Our predictions for the position of these points are similar, although somewhat smaller, than previous estimates. Finally, the relation between the deconfining transition and chiral restoration is also discussed.Comment: 11 pages, 2 figures. Figures modified, minor changes in the text. To be published in Phys. Lett.

Chiral Phase Transition within Effective Models with Constituent Quarks

We investigate the chiral phase transition at nonzero temperature $T$ and baryon-chemical potential $\mu_B$ within the framework of the linear sigma model and the Nambu-Jona-Lasinio model. For small bare quark masses we find in both models a smooth crossover transition for nonzero $T$ and $\mu_B=0$ and a first order transition for T=0 and nonzero $\mu_B$. We calculate explicitly the first order phase transition line and spinodal lines in the $(T,\mu_B)$ plane. As expected they all end in a critical point. We find that, in the linear sigma model, the sigma mass goes to zero at the critical point. This is in contrast to the NJL model, where the sigma mass, as defined in the random phase approximation, does not vanish. We also compute the adiabatic lines in the $(T,\mu_B)$ plane. Within the models studied here, the critical point does not serve as a ``focusing'' point in the adiabatic expansion.Comment: 22 pages, 18 figure

Lattice determination of the critical point of QCD at finite T and \mu

Based on universal arguments it is believed that there is a critical point (E) in QCD on the temperature (T) versus chemical potential (\mu) plane, which is of extreme importance for heavy-ion experiments. Using finite size scaling and a recently proposed lattice method to study QCD at finite \mu we determine the location of E in QCD with n_f=2+1 dynamical staggered quarks with semi-realistic masses on $L_t=4$ lattices. Our result is T_E=160 \pm 3.5 MeV and \mu_E= 725 \pm 35 MeV. For the critical temperature at \mu=0 we obtained T_c=172 \pm 3 MeV.Comment: misprints corrected, version to appear in JHE

Critical point of QCD at finite T and \mu, lattice results for physical quark masses

A critical point (E) is expected in QCD on the temperature (T) versus baryonic chemical potential (\mu) plane. Using a recently proposed lattice method for \mu \neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of physical masses on L_t=4 lattices. Our result for the critical point is T_E=162 \pm 2 MeV and \mu_E= 360 \pm 40 MeV. For the critical temperature at \mu=0 we obtained T_c=164 \pm 2 MeV. This work extends our previous study [Z. Fodor and S.D.Katz, JHEP 0203 (2002) 014] by two means. It decreases the light quark masses (m_{u,d}) by a factor of three down to their physical values. Furthermore, in order to approach the thermodynamical limit we increase our largest volume by a factor of three. As expected, decreasing m_{u,d} decreased \mu_E. Note, that the continuum extrapolation is still missingComment: 10 pages, 2 figure

Bayesian mapping reveals that attention boosts neural responses to predicted and unpredicted stimuli

Predictive coding posits that the human brain continually monitors the environment for regularities and detects inconsistencies. It is unclear, however, what effect attention has on expectation processes, as there have been relatively few studies and the results of these have yielded contradictory findings. Here, we employed Bayesian model comparison to adjudicate between 2 alternative computational models. The “Opposition” model states that attention boosts neural responses equally to predicted and unpredicted stimuli, whereas the “Interaction” model assumes that attentional boosting of neural signals depends on the level of predictability. We designed a novel, audiospatial attention task that orthogonally manipulated attention and prediction by playing oddball sequences in either the attended or unattended ear. We observed sensory prediction error responses, with electroencephalography, across all attentional manipulations. Crucially, posterior probability maps revealed that, overall, the Opposition model better explained scalp and source data, suggesting that attention boosts responses to predicted and unpredicted stimuli equally. Furthermore, Dynamic Causal Modeling showed that these Opposition effects were expressed in plastic changes within the mismatch negativity network. Our findings provide empirical evidence for a computational model of the opposing interplay of attention and expectation in the brain