Development of a relativistic coupled-cluster method for one electron detachment theory: Application to Mn IX, Fe X, Co XI and Ni XII ions

We have developed one electron detachment theory from a closed-shell atomic configuration in the relativistic Fock-space coupled-cluster ansatz. Using this method, we determine sensitivity coefficients to the variation of the fine structure constant in the first three important low-lying transitions of the astrophysically interesting highly charged Mn IX, Fe X, Co XI and Ni XII ions. The potential of this method has been assessed by evaluating the detachment energies of the removed electrons and determining lifetimes of the atomic states in the above ions. To account the sensitivity of the higher order relativistic effects, we have used the four component wave functions of the Dirac-Coulomb-Breit Hamiltonian with the leading order quantum electrodynamics (QED) corrections. A systematic study has been carried out to highlight the importance of the Breit and QED interactions in the considered properties of the above ions

Hyperskewness of (1+1)(1+1)-dimensional KPZ Height Fluctuations

We evaluate the fifth order normalized cumulant, known as hyperskewness, of height fluctuations dictated by the $(1+1)$-dimensional KPZ equation for the stochastic growth of a surface on a flat geometry in the stationary state. We follow a diagrammatic approach and invoke a renormalization scheme to calculate the fifth cumulant given by a connected loop diagram. This, together with the result for the second cumulant, leads to the hyperskewness value $\widetilde{S} = 0.0835$.Comment: 11 pages, 2 figures, version accepted for publication in J. Stat. Mech.: Theory and Ex

Effect of minimal length uncertainty on the mass-radius relation of white dwarfs

Generalized uncertainty relation that carries the imprint of quantum gravity introduces a minimal length scale into the description of space-time. It effectively changes the invariant measure of the phase space through a factor $(1+\beta \mathbf{p}^2)^{-3}$ so that the equation of state for an electron gas undergoes a significant modification from the ideal case. It has been shown in the literature (Rashidi 2016) that the ideal Chandrasekhar limit ceases to exist when the modified equation of state due to the generalized uncertainty is taken into account. To assess the situation in a more complete fashion, we analyze in detail the mass-radius relation of Newtonian white dwarfs whose hydrostatic equilibria are governed by the equation of state of the degenerate relativistic electron gas subjected to the generalized uncertainty principle. As the constraint of minimal length imposes a severe restriction on the availability of high momentum states, it is speculated that the central Fermi momentum cannot have values arbitrarily higher than $p_{\rm max}\sim\beta^{-1/2}$. When this restriction is imposed, it is found that the system approaches limiting mass values higher than the Chandrasekhar mass upon decreasing the parameter $\beta$ to a value given by a legitimate upper bound. Instead, when the more realistic restriction due to inverse $\beta$-decay is considered, it is found that the mass and radius approach the values close to $1.45$ M$_{\odot}$ and $600$ km near the legitimate upper bound for the parameter $\beta$. On the other hand, when $\beta$ is decreased sufficiently from the legitimate upper bound, the mass and radius are found to be approximately $1.46$ M$_{\odot}$ and $650$ km near the neutronization threshold

Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth

We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we calculate the second and third order moments of height distribution using the diagrammatic method in the large scale and long time limits. The moments so calculated lead to the value $S=0.3237$ for the skewness. This value is comparable with numerical and experimental estimates.Comment: 3 figures, version published in Phys. Rev.

Kurtosis of height fluctuations in (1+1)(1+1) dimensional KPZ Dynamics

We study the fourth order normalized cumulant of height fluctuations governed by $1+1$ dimensional Kardar-Parisi-Zhang (KPZ) equation for a growing surface. Following a diagrammatic renormalization scheme, we evaluate the kurtosis $Q$ from the connected diagrams leading to the value $Q=0.1523$ in the large-scale long-time limit.Comment: 12 pages, 2 figures, version accepted in J. Stat. Mec

Prospect of Chandrasekhar's limit against modified dispersion relation

Newtonian gravity predicts the existence of white dwarfs with masses far exceeding the Chandrasekhar limit when the equation of state of the degenerate electron gas incorporates the effect of quantum spacetime fluctuations (via a modified dispersion relation) even when the strength of the fluctuations is taken to be very small. In this paper, we show that this Newtonian "super-stability" does not hold true when the gravity is treated in the general relativistic framework. Employing dynamical instability analysis, we find that the Chandrasekhar limit can be reassured even for a range of high strengths of quantum spacetime fluctuations with the onset density for gravitational collapse practically remaining unaffected

General Relativistic Calculations for White Dwarf Stars

The mass-radius relations for white dwarf stars are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of $1.4562M_\odot$ is modified to $1.4166M_\odot$ in the general relativistic case for $^4_2$He (and $^{12}_{\ 6}$C) white dwarf stars. Using the same general relativistic treatment, the critical mass for$^{56}_{26}$Fe white dwarf is obtained as$1.2230M_\odot$. In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter's EoS along with the TOV equations yielding slightly lower values for the critical masses, namely$1.4081M_{\odot}$for$^4_2$He,$1.3916M_{\odot}$for$^{12}_{\ 6}$C and$1.1565M_{\odot}$for$^{56}_{26}$Fe white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that$^4_2$He and$^{12}_{\ 6}$C white dwarf stars are stable against neutronization with the critical values of$1.4081M_\odot$and$1.3916M_{\odot}$, respectively. However the critical masses for$^{16}_{\ 8}$O,$^{20}_{10}$Ne,$^{24}_{12}$Mg,$^{28}_{14}$Si,$^{32}_{16}$S and$^{56}_{26}$Fe white dwarf stars are lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS

Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state

We study a class of periodically driven $d-$dimensional integrable models and show that after $n$ drive cycles with frequency $\omega$, pure states with non-area-law entanglement entropy $S_n(l) \sim l^{\alpha(n,\omega)}$ are generated, where $l$ is the linear dimension of the subsystem, and $d-1 \le \alpha(n,\omega) \le d$. We identify and analyze the crossover phenomenon from an area ($S \sim l^{ d-1}$ for $d\geq1$) to a volume ($S \sim l^{d}$) law and provide a criterion for their occurrence which constitutes a generalization of Hastings' theorem to driven integrable systems in one dimension. We also find that $S_n$ generically decays to $S_{\infty}$ as $(\omega/n)^{(d+2)/2}$ for fast and $(\omega/n)^{d/2}$ for slow periodic drives; these two dynamical phases are separated by a topological transition in the eigensprectrum of the Floquet Hamiltonian. This dynamical transition manifests itself in the temporal behavior of all local correlation functions and does not require a critical point crossing during the drive. We find that these dynamical phases show a rich re-entrant behavior as a function of $\omega$ for $d=1$ models, and also discuss the dynamical transition for $d>1$ models. Finally, we study entanglement properties of the steady state and show that singular features (cusps and kinks in $d=1$) appear in $S_{\infty}$ as a function of $\omega$ whenever there is a crossing of the Floquet bands. We discuss experiments which can test our theory.Comment: v3; 17 pages + 15 figures, expanded version with new results on dynamical phase transitions and steady state entanglement; changed title and added a co-autho

Periodically driven integrable systems with long-range pair potentials

We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent $\alpha$. Starting from an initial unentangled state, we show that all local quantities relax to well-defined steady state values in the thermodynamic limit and after $n \gg 1$ drive cycles for any $\alpha$ and driving frequency $\omega$. We introduce a distance measure, $\mathcal{D}_l(n)$, that characterizes the approach of the reduced density matrix of a subsystem of $l$ sites to its final steady state. We chart out the $n$ dependence of ${\mathcal D}_l(n)$ and identify a critical value $\alpha=\alpha_c$ below which they generically decay to zero as $(\omega/n)^{1/2}$. For $\alpha > \alpha_c$, in contrast, ${\mathcal D}_l(n) \sim (\omega/n)^{3/2}[(\omega/n)^{1/2}]$ for $\omega \to \infty [0]$ with at least one intermediate dynamical transition. We also study the mutual information propagation to understand the nature of the entanglement spreading in space with increasing $n$ for such systems. We point out existence of qualitatively new features in the space-time dependence of mutual information for $\omega < \omega^{(1)}_c$, where $\omega^{(1)}_c$ is the largest critical frequency for the dynamical transition for a given $\alpha$. One such feature is the presence of {\it multiple} light cone-like structures which persists even when $\alpha$ is large. We also show that the nature of space-time dependence of the mutual information of long-ranged Hamiltonians with $\alpha \le 2$ differs qualitatively from their short-ranged counterparts with $\alpha > 2$ for any drive frequency and relate this difference to the behavior of the Floquet group velocity of such driven system.Comment: v2; two-column format, 19 pages, 16 figures (Shortened abstract due to character limit for arXiv submission; see main text); slightly modified version submitted for revie

Revisiting Nuclear Quadrupole Moments in 39−41^{39-41}K Isotopes

Nuclear quadrupole moments ($Q$s) in three isotopes of potassium (K) with atomic mass numbers 39, 40 and 41 are evaluated more precisely in this work. The $Q$ value of $^{39}$K is determined to be 0.0614(6) $b$ by combining the available experimental result of the electric quadrupole hyperfine structure constant ($B$) with our calculated $B/Q$ result of its $4P_{3/2}$ state. Furthermore combining this $Q$ value with the measured ratios $Q$($^{40}$K)$/Q$($^{39}$K) and $Q$($^{41}$K)$/Q$($^{39}$K), we obtain $Q$($^{40}$K)$=-0.0764(10) \ b$ and $Q$($^{41}$K)$=0.0747(10) \ b$, respectively. These results disagree with the recently quoted standard values in the nuclear data table within the given uncertainties. The calculations are carried out by employing the relativistic coupled-cluster theory at the singles, doubles and involving important valence triples approximation. The accuracies of the calculated $B/Q$ results can be viewed on the basis of comparison between our calculated magnetic dipole hyperfine structure constants ($A$s) with their corresponding measurements for many low-lying states. Both $A$ and $B$ results in few more excited states are presented for the first time.Comment: 9 pages, 1 figur