Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson-Schwinger equations. The quark-propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, $\mu_{EP}/T_{EP} \approx 3$. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.Comment: 4 pages, 4 figures. v2: minor changes, comments adde

Hybridization and spin decoherence in heavy-hole quantum dots

We theoretically investigate the spin dynamics of a heavy hole confined to an unstrained III-V semiconductor quantum dot and interacting with a narrowed nuclear-spin bath. We show that band hybridization leads to an exponential decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips, and that the accordant single-hole-spin decoherence time T2 can be tuned over many orders of magnitude by changing external parameters. In particular, we show that, under experimentally accessible conditions, it is possible to suppress hyperfine-mediated nuclear-pair-flip processes so strongly that hole-spin quantum dots may be operated beyond the `ultimate limitation' set by the hyperfine interaction which is present in other spin-qubit candidate systems.Comment: 7 pages, 3 figure

Exponential decay in a spin bath

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.Comment: 4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices with extensive technical details, version to appear in Phys. Rev. B

Free-induction decay and envelope modulations in a narrowed nuclear spin bath

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi contact hyperfine interaction. Our perturbative treatment is valid for special (narrowed) bath initial conditions and when the Zeeman energy of the electron $b$ exceeds the total hyperfine coupling constant $A$: $b>A$. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find a new and unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give sub-leading corrections to the decoherence rate, and show that, in general, the decoherence rate has a non-monotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly-interacting system with non-Markovian (history-dependent) dynamics.Comment: 13 pages, 9 figure

Correlated projection operator approach to non-Markovian dynamics in spin baths

The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach is not justified. We apply a recently proposed correlated projection superoperator technique to the model of a central spin coupled to a spin bath via full Heisenberg interaction. Analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution. The correlated projection operator technique significantly improves the standard methods and can be applied to many physical problems such as the hyperfine interaction in a quantum dot

On the relation between income inequality and happiness: Do fairness perceptions matter?

In this paper, we revisit the association between happiness and inequality. We argue that the perceived fairness of the income generation process affects this association. Building on a two-period model of individual life-time utility maximization, we predict that persons with higher perceived fairness will experience higher levels of life-time utility and are less in favor of income redistribution. In societies with a high level of actual social mobility, income inequality is perceived more positively with increased expected fairness. The opposite is expected for countries with low actual social mobility, due to an increasing relevance of a disappointment effect resulting from unsuccessful individual investments. Using the World Values Survey data and a broad set of fairness measures, we find strong support for the negative (positive) association between fairness perceptions and the demand for more equal incomes (subjective well-being). We also find strong empirical support for the disappointment effect in low social mobility countries. In contrast, the results for high-mobility countries turn out to be ambiguous

On the infrared freezing of perturbative QCD in the Minkowskian region

The infrared freezing of observables is known to hold at fixed orders of perturbative QCD if the Minkowskian quantities are defined through the analytic continuation from the Euclidean region. In a recent paper [1] it is claimed that infrared freezing can be proved also for Borel resummed all-orders quantities in perturbative QCD. In the present paper we obtain the Minkowskian quantities by the analytic continuation of the all-orders Euclidean amplitudes expressed in terms of the inverse Mellin transform of the corresponding Borel functions [2]. Our result shows that if the principle of analytic continuation is preserved in Borel-type resummations, the Minkowskian quantities exhibit a divergent increase in the infrared regime, which contradicts the claim made in [1]. We discuss the arguments given in [1] and show that the special redefinition of Borel summation at low energies adopted there does not reproduce the lowest order result obtained by analytic continuation.Comment: 19 pages, 1 figur

Reentrant behavior of superconducting alloys

A dirty BCS superconductor with magnetic impurities is studied. Asymptotic solution of the thermodynamics of such superconductor with spin $1/2$ and $7/2$ magnetic impurities, is found. To this end, the system's free energy $f(H, \beta)$ is bounded from above and below by mean-field type bounds, which are shown to coalesce almost exactly in the thermodynamic limit, provided the impurity concentration is sufficiently small. The resulting mean-field equations for the gap $\Delta$ and a parameter $\nu$, characterizing the impurity subsystem, are solved and the solution minimizing $f$ is found for various values of magnetic coupling constant $g$ and impurity concentration $x$. The phase diagrams of the system are depicted with five distinct phases: the normal phase, unperturbed superconducting phase, perturbed superconducting phase with nonzero gap in the excitation spectrum, perturbed gapless superconducting phase and impurity phase with completely suppressed superconductivity. Furthermore, evidence of reentrant superconductivity and Jaccarino-Peter compensation is found. The credibility of the theory is verified by testing the dependence of the superconducting transition temperature $T_{\text{c}}$ on $x$. Very good quantitative agreement with experimental data is obtained for several alloys: (La$_{1-x}$Ce$_{x}$)Al$_{2}$, (La$_{1-x}$Gd$_{x}$)Al$_{2}$ and (La$_{0.8-x}$Y$_{0.20}$)Ce$_{x}$. The theory presented improves earlier developments in this field.Comment: 15 pages, 8 figures, full length articl