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The signal strength of primordial gravitational waves experiencing an epoch of early scalar domination is reduced with respect to radiation domination. In this paper, we demonstrate that the specific pattern of this reduction is sensitive to the coupling between the dominant field and gravity. When this coupling is zero, the impact of early matter domination on gravitational waves is solely attributed to the alteration of the Hubble parameter and the scale factor. In the presence of non-zero couplings, on the other hand, the evolution of primordial gravitational waves is directly affected as well, resulting in a distinct step-like feature in the power spectrum of the gravitational wave as a function of frequency. This feature serves as a smoking gun signature of this model. In this paper, we provide an analytical expression of the power spectrum that illustrates the dependence of power spectrum on model parameters and initial conditions. Furthermore, we provide analytical relations that specify the frequency interval in which the step occurs. We compare the analytical estimates with numerical analysis and show they match well., Comment: 19 pages, 7 figures, 1 table, and 2 appendices

The collective flow generated in relativistic heavy-ion collisions fluctuates from event to event. The fluctuations lead to a decorrelation of flow vectors measured in separate bins in phase space. These effects have been measured in experiments and observed in numerical simulations in hydrodynamic models. We present a simple random model of flow decorrelation in pseudorapidity. Analytical expressions for the flow factorization breaking coefficients for flow vectors, flow vector magnitudes, and flow angles are derived. The model explains the relations between different factorization breaking coefficients found in experimental data and model simulations. In particular, it is found that the flow angle decorrelation constitutes about one half of the total flow vector decorrelation.

We study the flow harmonic distribution in deformed nuclei. To do this, we use the standard Gram-Charlier method to find the higher-order correction to the well-known Bessel-Gaussian distribution. We find that, apart from the necessity of including a shift parameter $\bar v_n$, the modified flow distribution describes the flow distribution of quadrupole and octupole deformation accurately. Using the shifted radial distribution, arising from this method, we scrutinize the effect of deformation on flow distribution. Assuming a linear relation between observables of spherical and deformed collisions, $\mathcal{O}_D=\mathcal{O}_S+\left(\sum_{m=2}a_{k,m} \beta_m\right)^{2k}$, for events with a fixed centrality, we compare the flow distribution of deformed and spherical nuclei. We also propose a way to measure $\bar{v}_2$ in asymmetric nuclei collisions., Comment: 11 pages and 11 figures

In this paper, we study the simultaneous evolution of baryon asymmetry and hypermagnetic field amplitude assuming an early matter domination. We contrast our results to the conventional case where radiation domination during early universe is assumed. We show that the baryon asymmetry and the hypermagntic field amplitude can change by orders of magnitude if we assume a non-standard history of cosmology. That is because the Hubble rate determines which processes are efficient. We find that a change in Hubble rate can have a significant impact on when the weak sphalerons become active. As a result of a change in the evolution of baryonic asymmetry, alters the evolution of hypermagnetic field amplitude. It is known that if the hypermagnetic field amplitude is large enough, it can save the baryon asymmetry from diminishing. We show that whether a small seed of hypermagnetic field amplitude can be amplified to a large enough value will strongly depend on the history of cosmology., Comment: 15 pages, 10 figures

The information of the event-by-event fluctuations is extracted from flow harmonic distributions and cumulants, which can be done experimentally. In this work, we employ the standard method of Gram-Charlier series with the normal kernel to find such distribution, which is the generalization of recently introduced flow distributions for the studies of the event-by-event fluctuations. Also, we introduce a new set of cumulants $j_n\{2k\}$ which have more information about the fluctuations compared with other known cumulants. The experimental data imply that not only all of the information about the event-by-event fluctuations of collision zone properties and different stages of the heavy-ion process are not encoded in the radial flow distribution $p(v_n)$, but also the observables describing harmonic flows can generally be given by the joint distribution $\mathcal{P}(v_1,v_2,...)$. In such a way, we first introduce a set of joint cumulants $\mathcal{K}_{nm}$, and then we find the flow joint distribution using these joint cumulants. Finally, we show that the Symmetric Cumulants $SC(2,3)$ and $SC(2,4)$ obtained from ALICE data are explained by the combinations $\mathcal{K}_{22}+\frac{1}{2}\mathcal{K}_{04}-\mathcal{K}_{31}$ and $\mathcal{K}_{22}+4\mathcal{K}_{11}^2$., Comment: 12 pages, 6 figures

The correlation between the harmonic flow and the transverse flow in relativistic heavy ion collisions is calculated in the hydrodynamic model. The partial correlation coefficient, corrected for fluctuations of multiplicity, is compared to experimental data. Estimators of the final transverse and harmonic flow are used to predict the value of the correlation coefficient from the moments of the initial distribution. A good description of the hydrodynamic simulation results is obtained if the estimator for the final transverse flow, besides the most important transverse size and entropy, includes also the eccentricities.

Both collision geometry and event-by-event fluctuations are encoded in the experimentally observed flow harmonic distribution $p(v_n)$ and $2k$-particle cumulants $c_n\{2k\}$. In the present study, we systematically connect these observables to each other by employing Gram-Charlier A series. We quantify the deviation of $p(v_n)$ from Bessel-Gaussianity in terms of flow harmonic fine-splitting. Subsequently, we show that the corrected Bessel-Gaussian distribution can fit the simulated data better than the Bessel-Gaussian distribution in the more peripheral collisions. Inspired by Gram-Charlier A series, we introduce a new set of cumulants $q_n\{2k\}$ that are more natural to study distributions near Bessel-Gaussian. These new cumulants are obtained from $c_n\{2k\}$ where the collision geometry effect is extracted from it. By exploiting $q_2\{2k\}$, we introduce a new set of estimators for averaged ellipticity $\bar{v}_2$ which are more accurate compared to $v_2\{2k\}$ for $k>1$. As another application of $q_2\{2k\}$, we show we are able to restrict the phase space of $v_2\{4\}$, $v_2\{6\}$ and $v_2\{8\}$ by demanding the consistency of $\bar{v}_2$ and $v_2\{2k\}$ with $q_2\{2k\}$ equation. The allowed phase space is a region such that $v_2\{4\}-v_2\{6\}\gtrsim 0$ and $12 v_2\{6\}-11v_2\{8\}-v_2\{4\}\gtrsim 0$, which is compatible with the experimental observations., Comment: 24 pages; 9 figures; v2: published version; minor revision of the text

We investigate the exact evolution of the reduced dynamics of a one qubit system as central spin coupled to a femionic layered environment with unlimited number of layers. Also, we study the decoherence induced on central spin by analysis solution is obtained in the limit $N\rightarrow\infty$ of an infinite number of bath spins. Finally, the Nakajima-Zwanzig (NZ) and the time-convolutionless (TCL) projection operator techniques to second order are derived., Comment: 20 pages, 11 figures

Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of an exactly solvable dynamic of one-qubit open system in layered environment . On the other hand, we obtain exact Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the maps. Finally, we study a simple example to consider the relation between CP maps and initial quantum correlation and show that vanishing initial quantum correlation is not necessary for CP maps., Comment: 19 pages. arXiv admin note: text overlap with arXiv:quant-ph/0311091, arXiv:1005.1604, arXiv:quant-ph/0108136 by other authors