Search

Polaritonic chemistry has ushered in new avenues for controlling molecular dynamics. However, two key questions remain: (i) Can classical light sources elicit the same effects as certain quantum light sources on molecular systems? (ii) Can semiclassical treatments of light-matter interaction capture nontrivial quantum effects observed in molecular dynamics? This work presents a quantum-classical approach addressing issues of realizing cavity chemistry effects without actual cavities. It also highlights the limitations of the standard semiclassical light-matter interaction. It is demonstrated that classical light sources can mimic quantum effects up to the second order of light-matter interaction, provided that the mean-field contribution, symmetrized two-time correlation function, and the linear response function are the same in both situations. Numerical simulations show that the quantum-classical method aligns more closely with exact quantum molecular-only dynamics for quantum light states such as Fock states, superpositions of Fock states, and vacuum squeezed states than the conventional semiclassical approach., Comment: 31 pages, 4 figures

$Q_\beta$ represents one of the most important factors characterizing unstable nuclei, as it can lead to a better understanding of nuclei behavior and the origin of heavy atoms. Recently, machine learning methods have been shown to be a powerful tool to increase accuracy in the prediction of diverse atomic properties such as energies, atomic charges, volumes, among others. Nonetheless, these methods are often used as a black box not allowing unraveling insights into the phenomena under analysis. Here, the state-of-the-art precision of the $\beta$-decay energy on experimental data is outperformed by means of an ensemble of machine-learning models. The explainability tools implemented to eliminate the black box concern allowed to identify uncertainty and atomic number as the most relevant characteristics to predict $Q_\beta$ energies. Furthermore, physics-informed feature addition improved models' robustness and raised vital characteristics of theoretical models of the nuclear structure.

Interaction between a quantum system and its environment can induce stationary coherences -- off-diagonal elements in the reduced system density matrix -- even at equilibrium. This work investigates the ``quantumness'' of such phenomena by examining the ability of classical and semiclassical models to describe equilibrium stationary coherence in the multi-level spin boson (MLSB) model, a common model for light-harvesting systems. A well justified classical harmonic oscillator model is found to fail to capture equilibrium coherence. This failure is attributed to the effective weakness of classical system-bath interactions due to the absence of a discrete system energy spectrum and, consequently, of quantized shifts in oscillator coordinates. Semiclassical coherences also vanish for a dimeric model with parameters typical of biological light-harvesting, i.e., where both system sites couple to the bath with the same reorganization energy. In contrast, equilibrium coherence persists in a fully quantum description of the same system, suggesting a uniquely quantum-mechanical origin for equilibrium stationary coherence in, e.g., photosynthetic systems. Finally, as a computational tool, a perturbative expansion is introduced that, at third order in $\hbar$, gives qualitatively correct behavior at ambient temperatures for all configurations examined., Comment: 14 pages, 2 figures

Experimental and theoretical evidence point out to the crucial role of specific resonant intramolecular vibrational modes in the interpretation of long-lived coherences observed in two-dimensional spectra of some natural and synthetic light harvesting complexes. For the natural situation of illumination by incoherent (sun)light, the relevance of these vibrations is analyzed here for light-harvesting vibronic prototype dimers. The detailed analysis of the density matrix dynamics reveals that the inclusion of the intramolecular vibrational modes reinforce up to one order of magnitude the exciton coherence and may increase the populations of lowest energy single exciton states, as well as populations and coherences in the site basis. In sharp contrast to the case of initial-state preparation by coherent (laser)light-sources, the initial thermal state of the local vibrational modes, as well as that of the anti-correlated mode, evolves devoid of non-classical correlations as confirmed by the absence of negative values of its phase-space quasi-probability distribution at all times. Therefore, not only the long-lived coherences observed in two-dimensional spectra are induced by the coherent character of pulsed laser sources, but it is unambiguously shown here that the non-classical character generally assigned to the anti-correlated vibrational mode also comes as the result of the preparation of the initial state by coherent pulsed laser sources., Comment: 10 pages, 6 figures

While the geodesic motion around a Kerr black hole is fully integrable and therefore regular, numerical explorations of the phase-space around other spacetime configurations, with a different multipolar structure, have displayed chaotic features. In most of these solutions, the role of the purely general relativistic effect of frame-dragging in chaos has eluded a definite answer. In this work, we show that, when considering neutral test particles around a family of stationary axially-symmetric analytical exact solution to the Einstein-Maxwell field equations, frame-dragging (as captured through spacetime vorticity) is capable of reconstructing KAM-tori from initially highly chaotic configurations. We study this reconstruction by isolating the contribution of the spacetime vorticity scalar to the dynamics, and exemplify our findings by computing rotation curves and the dimensionality of phase-space. Since signatures of chaotic dynamics in gravitational waves have been suggested as a way to test general relativity in the strong-field regime, we have computed gravitational waveforms using the semi-relativistic approximation and studied the frequency content of the gravitational wave spectrum. If this mechanism is generic, chaos suppression by frame-dragging may undermine present proposals to verify the hypothesis of the no-hair theorems and the validity of general relativity., Comment: 13 pages, 4 figures. (v3) Major revision; Matches version published in Class. Quant. Grav

Protracted conflict is one of the largest human challenges that have persistently undermined economic and social progress. In recent years, there has been increased emphasis on using statistical and physical science models to better understand both the universal patterns and the underlying mechanics of conflict. Whilst macroscopic power-law fractal patterns have been shown for death-toll in wars and self-excitation models have been shown for roadside ambush attacks, very few works deal with the challenge of complex dynamics between gangs at the intra-city scale. Here, based on contributions to the historical memory of the conflict in Colombia, Medellin's gang-confrontation-network is presented. It is shown that socio-economic and violence indexes are moderate to highly correlated to the structure of the network. Specifically, the death-toll of conflict is strongly influenced by the leading eigenvalues of the gangs' conflict adjacency matrix, which serves a proxy for unstable self-excitation from revenge attacks. The distribution of links based on the geographic distance between gangs in confrontation leads to the confirmation that territorial control is a main catalyst of violence and retaliation among gangs. Additionally, the Boltzmann-Lotka-Volterra (BLV) dynamic interaction network analysis is applied to quantify the spatial embeddedness of the dynamic relationship between conflicting gangs in Medellin, results suggest that more involved and comprehensive models are needed to described the dynamics of Medellin's armed conflict., Comment: 18 pages, 9 figures. Statistical analysis was largely improved. arXiv admin note: text overlap with arXiv:1107.0539 by other authors

A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables and is utilized here to (i) represent the binary character of answers to categories and (ii) introduce a new criterium for choosing between different measures of diversity, namely, robustness against uncertainty. The full potential of the formulation on a Hilbert space comes to play when addressing the reduction of categories problem, a common problem in data analysis. The present formalism solves the problem by incorporating strategies inspired by mathematical and physical statistics, specifically, it makes use of the concept of partial trace. In solving this problem, it is shown that properly normalizing the diversity measures is instrumental to provide a sensible interpretation of the results when the reduction of categories is performed. Finally, the approach presented here also allows for straightforwardly measuring diversity and performing category reduction in situations when simultaneous categories could be chosen.

The recent gravitational wave observations by the LIGO/Virgo collaboration have allowed the first tests of General Relativity in the extreme gravity regime, when comparable-mass black holes and neutron stars collide. Future space-based detectors, such as the Laser Interferometer Space Antenna, will allow tests of Einstein's theory with gravitational waves emitted when a small black hole falls into a supermassive one in an extreme mass-ratio inspiral. One particular test that is tailor-made for such inspirals is the search for chaos in extreme gravity. We here study whether chaos is present in the motion of test particles around spinning black holes of parity-violating modified gravity, focusing in particular on dynamical Chern-Simons gravity. We develop a resummation strategy that restores all spin terms in the General Relativity limit, while retaining up to fifth-order-in-spin terms in the dynamical Chern-Simons corrections to the Kerr metric. We then calculate Poincar\'e surfaces of section and rotation numbers of a wide family of geodesics of this resummed metric. We find no evidence for geodesic chaos, with at most deformations of the resonant torii that shrink as terms of higher-order in spin are included in the dynamical Chern-Simons corrections to the Kerr metric. Our numerical findings suggest that the geodesics of the as-of-yet unknown exact solution for spinning black holes in this theory may be integrable, and that there may thus exist a fourth integral of motion associated with this exact solution. The studies presented here begin to lay the foundations for chaotic tests of General Relativity with the observation of extreme mass ratio inspirals with the Laser Interferometer Space Antenna., Comment: 25 pages, 13 figures, V2: minor changes, typos corrected, version accepted by Class. and Quant. Gravity

Based on the connection between the spectral form factor and the probability to return, the origin of the $1/f^\alpha$-noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of the classical dynamics and the dimensionality of those invariant manifolds. This connection and the order-to-chaos transition are analyzed in terms of the statistics of Floquet's quasienergies of a classically chaotic driving non-linear system. An immediate prediction of the connection established here is that in the presence of decoherence, the spectral exponent $\alpha$ takes the same value, $\alpha=2$, for both, fully chaotic and fully integrable systems., Comment: 5 pages, 2 figures

The nature of excited states of open quantum systems produced by incoherent natural thermal light is analyzed based on a description of the generator of the dynamics. Natural thermal light is shown to generate long-lasting coherent dynamics because of (i) the super-Ohmic character of the radiation, and (ii) the absence of pure dephasing dynamics. In the presence of an environment, the long-lasting coherences induced by suddenly turned-on incoherent light dissipate and stationary coherences are established. As a particular application, dynamics in a subunit of the PC-645 light-harvesting complex is considered where it is further shown that aspects of the energy pathways landscape depend on the nature of the exciting light and number of chromophores excited. Specifically, pulsed laser and natural broadband incoherent excitation induce significantly different energy transfer pathways. In addition, we discuss differences in perspective associated with the eigenstate vs site basis, and note an important difference in the phase of system coherences when coupled to blackbody radiation or when coupled to a phonon background. Finally, an Appendix contains an open systems example of the loss of coherence as the turn on time of the light assumes natural time scales., Comment: 25 pages, 11 figures

A sideband cooling strategy that incorporates (i) the dynamics induced by structured (non-Markovian) environments in the target and auxiliary systems and (ii) the optimally-time-modulated interaction between them is developed. For the context of cavity optomechanics, when non-Markovian dynamics are considered in the target system, ground state cooling is reached at much faster rates and at much lower phonon occupation number than previously reported. In constrast to similar current strategies, ground state cooling is reached here for coupling-strength rates that are experimentally accesible for the state-of-the-art implementations. After the ultrafast optimal-ground-state-cooling protocol is accomplished, an additional optimal control strategy is considered to maintain the phonon number as closer as possible to the one obtained in the cooling procedure. Contrary to the conventional expectation, when non-Markovian dynamics are considered in the auxiliary system, the efficiency of the cooling protocol is undermined.

It is generally recognized that a distinguishing feature of life is its peculiar capability to avoid equilibration. The origin of this capability and its evolution along the timeline of abiogenesis is not yet understood. We propose to study an analog of this phenomenon that could emerge in non-biological systems. To this end, we introduce the concept of sustainability of transient kinetic regimes. This concept is illustrated via investigation of cooperative effects in an extended system of compartmentalized chemical oscillators under batch and semi-batch conditions. The computational study of a model system shows robust enhancement of lifetimes of the decaying oscillations which translates into the evolution of the survival function of the transient non-equilibrium regime. This model does not rely on any form of replication. Rather, it explores the role of a structured effective environment as a contributor to the system-bath interactions that define non-equilibrium regimes. We implicate the noise produced by the effective environment of a compartmentalized oscillator as the cause of the lifetime extension., Comment: 11 pages, 5 figures

Frame dragging (Lense-Thirring effect) is generally associated with rotating astrophysical objects. However, it can also be generated by electromagnetic fields if electric and magnetic fields are simultaneously present. In most models of astrophysical objects, macroscopic charge neutrality is assumed and the entire electromagnetic field is characterized in terms of a magnetic dipole component. Hence, the purely electromagnetic contribution to the frame dragging vanishes. However, strange stars may posses independent electric dipole and neutron stars independent electric quadrupole moments that may lead to the presence of purely electromagnetic contributions to the frame dragging. Moreover, recent observations have shown that in stars with strong electromagnetic fields, the magnetic quadrupole may have a significant contribution to the dynamics of stellar processes. As an attempt to characterized and quantify the effect of electromagnetic frame-dragging in this kind of astrophysical objects, an analytic solution to the Einstein-Maxwell equations is constructed here on the basis that the electromagnetic field is generated by the combination of arbitrary magnetic and electric dipoles plus arbitrary magnetic and electric quadrupole moments. The effect of each multipole contribution on the vorticity scalar and the Poynting vector is described in detail. Corrections on important quantities such the innermost stable circular orbit (ISCO) and the epyciclic frequencies are also considered., Comment: 12 pages, 7 figures

Reconstruction of the dynamics (quantum process tomography) of the single-exciton manifold in energy transfer systems is proposed here on the basis of two-dimensional fluorescence spectroscopy (2D-FS) with phase-modulation. The quantum-process-tomography protocol introduced here benefits from, e.g., the sensitivity enhancement ascribed to 2D-FS. Although the isotropically averaged spectroscopic signals depend on the quantum yield parameter $\Gamma$ of the doubly-excited-exciton manifold, it is shown that the reconstruction of the dynamics is insensitive to this parameter. Applications to foundational and applied problems, as well as further extensions, are discussed., Comment: 11 pages, 3 figures

A classical formulation of the quantum multichromophoric theory of resonance energy transfer is developed on the basis of classical electrodynamics. The theory allows for the identification of a variety of processes of different order-in-the-interactions that contribute to the energy transfer in molecular aggregates with intra-coupling in donors and acceptor chromophores. Enhanced rates in multichromophoric resonance energy transfer are shown to be well described by this theory. Specifically, in a coupling configuration between N_{\mathrm{A}}$ acceptors and $N_{\mathrm{D}}$ donors, the theory correctly predicts an enhancement of the energy transfer rate dependent on the total number of donor-acceptor pairs. As an example, the theory, applied to the transfer rate in LH~II, gives results in excellent agreement with experiment. Finally, it is explicitly shown that as long as linear response theory holds, the classical multichromophoric theory formally coincides with the quantum formulation., Comment: 9 pages, 2 figures. Supplementary Material added

The interplay between non-Markovian dynamics and driving fields in the survival of entanglement between two non-degenerate oscillators is considered here. Based on exact analytical results for the non-Markovian dynamics of two parametrically coupled non-degenerate oscillators in contact to non-identical independent thermal baths, the out-of-equilibrium quantum limit derived in [Phys. Rev. Lett. 105, 180501 (2010)] is generalized to the non-Markovian regime. Specifically, it is shown that non-Markovian dynamics, when compared to the Markovian case, allow for the survival of stationary entanglement at higher temperatures, with larger coupling strength to the baths and at smaller driving rates. The effect of the asymmetry of the (i) coupled oscillators, (ii) coupling strength to the baths at equal temperature and (iii) temperature at equal coupling strength is discussed., Comment: 28 pages, 7 figures

Determining the spectral density of a molecular system immersed in a proteomic scaffold and in contact to a solvent is a fundamental challenge in the coarse-grained description of, e.g., electron and energy transfer dynamics. Once the spectral density is characterized, all the time scales are captured and no artificial separation between fast and slow processes need be invoked. Based on the fluorescence Stokes shift function, we utilize a simple and robust strategy to extract the spectral density of a number of molecular complexes from available experimental data. Specifically, we show that experimental data for dye molecules in several solvents, amino acid proteins in water, and some photochemical systems (e.g., rhodopsin and green fluorescence proteins), are well described by a three-parameter family of sub-Ohmic spectral densities that are characterized by a fast initial Gaussian-like decay followed by a slow algebraic-like decay rate at long times., Comment: 20 pages, 5 figures

We show that an ensemble of organic dye molecules with permanent electric dipole moments embedded in a microcavity can lead to strong optical nonlinearities at the single photon level. The strong long-range electrostatic interaction between chromophores due to their permanent dipoles introduces the desired nonlinearity of the light-matter coupling in the microcavity. We obtain the absorption spectra of a weak probe field under the influence of strong exciton-photon coupling with the cavity field. Using realistic parameters, we demonstrate that a single cavity photon can significantly modify the absorptive and dispersive response of the medium to a probe photon at a different frequency. Finally, we show that the system is in the regime of cavity-induced transparency with a broad transparency window for dye dimers. We illustrate our findings using pseudoisocyanine chloride (PIC) J-aggregates in currently-available optical microcavities., Comment: 4 figures

Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that in quantum mechanics, these deviations originate from the uncertainty principle and are supported by the non-Markovian character of the dynamics. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum and therefore, quantum mechanics inhibits the system thermal-equilibrium-state from being described by the canonical Boltzmann's distribution. We show that for a wide class of systems, systems interacting via central forces with pairwise-self-interacting environments, this general observation is in sharp contrast to the classical case, for which the thermal equilibrium distribution, irrespective of the interaction strength, is \emph{exactly} characterized by the canonical Boltzmann distribution and therefore, no dependence on the bath power spectrum is present. We define an \emph{effective coupling} to the environment that depends on all energy scales in the system and reservoir interaction. Sample computations in regimes predicted by this effective coupling are demonstrated. For example, for the case of strong effective coupling, deviations from standard thermodynamics are present and, for the case of weak effective coupling, quantum features such as stationary entanglement are possible at high temperatures., Comment: 9 pages, 3 figures

A full-relativistic approach is used to compute the radius of the innermost stable circular orbit (ISCO), the Keplerian, frame-dragging, precession and oscillation frequencies of the radial and vertical motions of neutral test particles orbiting the equatorial plane of a magnetized neutron star. The space-time around the star is modelled by the six parametric solution derived by Pachon et al. It is shown that the inclusion of an intense magnetic field, such as the one of a neutron star, have non-negligible effects on the above physical quantities, and therefore, its inclusion is necessary in order to obtain a more accurate and realistic description of the physical processes occurring in the neighbourhood of this kind of objects such as the dynamics of accretion disk. The results discussed here also suggest that the consideration of strong magnetic fields may introduce non-negligible corrections in, e.g., the relativistic precession model and therefore on the predictions made on the mass of neutron stars., Comment: LaTeX file, 13 pages, 4 figures

Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rhythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide., Comment: Published version. Notice the change in the title

The ability of an environment to assist in one-photon phase control relies upon entanglement between the system and bath and on the breaking of the time reversal symmetry. Here, one photon phase control is examined analytically and numerically in a model system, allowing an analysis of the relative strength of these contributions. Further, the significant role of non-Markovian dynamics and of moderate system-bath coupling in enhancing one-photon phase control is demonstrated, and an explicit role for quantum mechanics is noted in the existence of initial non-zero stationary coherences. Finally, desirable conditions are shown to be required to observe such environmentally assisted control, since the system will naturally equilibrate with its environment at longer times, ultimately resulting in the loss of phase control., Comment: 26 pages, 8 figures. Minor changes. It matches the published version

Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement[1] and the Aharonov-Bohm effect[2,3]. Non-locality comes in two "flavours": a \emph{kinematic non-locality}-- arising from the structure of the Hilbert space--[4-6] and a \emph{dynamical non-locality}-- arising from the quantum equations of motion--[2,3,5,6]. Despite of its main role in quantum information processing, kinematic non-locality is unable to induce any change in the probability distributions, so that the "action-at-a-distance" cannot manifest[5,6]. Conversely, dynamical non-locality does create explicit changes in probability, though in a "causality-preserving" manner[6,7]. Recently, the origin of the kinematic non-locality was related to the uncertainty principle[8], here we trace the origin of dynamical non-locality to the superposition principle. This relation adds to the more fundamental understanding of the nature of quantum dynamics and allows us to establish and identify how the uncertainty and the superposition principles determine the non-local character of the outcome of a quantum measurement. Thus, dynamical non-locality emerges as the responsible of the breakdown of the dynamical classical realism[9] and therefore, as key feature in the classical-quantum transition. Most importantly, being based on group theoretical and path integral formulations, our formulation admits immediate generalizations and extensions to, e.g., quantum field theory., Comment: 12 pages

The underlying mechanisms for one photon phase control are revealed through a master equation approach. Specifically, two mechanisms are identified, one operating on the laser time scale and the other on the time scale of the system-bath interaction. The effect of the secular and non-secular Markovian approximations are carefully examined., Comment: 11 pages. It matches the published version

Under natural conditions, excitation of biological molecules, which display non-unitary open system dynamics, occurs via incoherent processes such as temperature changes or irradiation by sunlight/moonlight. The dynamics of such processes is explored analytically in a non-Markovian generic model. Specifically, a system S in equilibrium with a thermal bath TB is subjected to an external incoherent perturbation BB (such as sunlight) or another thermal bath TB', which induces time evolution in (S+TB). Particular focus is on (i) the extent to which the resultant dynamics is coherent, and (ii) the role of "stationary coherences", established in the (S+TB) equilibration, in the response to the second incoherent perturbation. Results for systems with parameters analogous to those in light harvesting molecules in photosynthesis show that the resultant dynamical behaviour is incoherent beyond a very short response to the turn-on of the perturbation., Comment: 10 pages, 8 figures. Minor changes. It matches the published version

We consider the general open system problem of a charged quantum oscillator confined in a harmonic trap, whose frequency can be arbitrarily modulated in time, that interacts with both an incoherent quantized (blackbody) radiation field and with an arbitrary coherent laser field. We assume that the oscillator is initially in thermodynamic equilibrium with its environment, a non-factorized initial density matrix of the system and the environment, and that at $t=0$ the modulation of the frequency, the coupling to the incoherent and the coherent radiation are switched on. The subsequent dynamics, induced by the presence of the blackbody radiation and the laser field, is studied in the framework of the influence functional approach. This approach allows incorporating, in \emph{analytic closed formulae}, the non-Markovian character of the oscillator-environment interaction at any temperature as well the non-Markovian character of the blackbody radiation and its zero-point fluctuations. Expressions for the time evolution of the covariance matrix elements of the quantum fluctuations and the reduced density-operator are obtained., Comment: 11 pages. It matches the published version

We examine computational techniques and methodologies currently in use to explore electronic excitation energy transfer in the context of light-harvesting complexes in photosynthetic antenna systems, and comment on some new insights into the underlying physics. Advantages and pitfalls of these methodologies are discussed, as are some physical insights into the photosynthetic dynamics. By combining results from molecular modelling of the complexes (structural description) with an effective non-equilibrium statistical description (time evolution), we identify some general features, regardless of the particular distribution in the protein scaffold, that are central to light-harvesting dynamics and, that could ultimately be related to the high efficiency of the overall process. Based on these general common features, some possible new directions in the field are discussed., Comment: Invited Perspective Article for Phys. Chem. Chem. Phys

Whether analytic exact vacuum(electrovacuum) solutions of the Einstein(Einstein-Maxwell) field equations can accurately describe or not the exterior spacetime of compact stars remains still an interesting open question in Relativistic Astrophysics. As an attempt to establish their level of accuracy, the radii of the Innermost Stable Circular Orbits (ISCOs) of test particles given by analytic exterior spacetime geometries have been compared with the ones given by numerical solutions for neutron stars (NSs) obeying a realistic equation of state (EoS). It has been so shown that the six-parametric solution of Pach\'on, Rueda, and Sanabria (2006) (hereafter PRS) is more accurate to describe the NS ISCO radii than other analytic models. We propose here an additional test of accuracy for analytic exterior geometries based on the comparison of orbital frequencies of neutral test particles. We compute the Keplerian, frame-dragging, as well as the precession and oscillation frequencies of the radial and vertical motions of neutral test particles for the Kerr and PRS geometries; then we compare them with the numerical values obtained by Morsink and Stella (1999) for realistic NSs. We identify the role of high-order multipole moments such as the mass quadrupole and current octupole in the determination of the orbital frequencies especially in the rapid rotation regime. The results of this work are relevant to cast a separatrix between black hole (BH) and NS signatures as well as probe the nuclear matter EoS and NS parameters from the Quasi-Periodic Oscillations (QPOs) observed in Low Mass X-Ray Binaries., Comment: 14 pages, 10 figures

The physical basis for observed long-lived electronic coherence in photosynthetic light-harvesting systems is identified using an analytically soluble model. Three physical features are found to be responsible for their long coherence lifetimes: i) the small energy gap between excitonic states, ii) the small ratio of the energy gap to the coupling between excitonic states, and iii) the fact that the molecular characteristics place the system in an effective low temperature regime, even at ambient conditions. Using this approach, we obtain decoherence times for a dimer model with FMO parameters of $\approx$ 160 fs at 77 K and $\approx$ 80 fs at 277 K. As such, significant oscillations are found to persist for 600 fs and 300 fs, respectively, in accord with the experiment and with previous computations. Similar good agreement is found for PC645 at room temperature, with oscillations persisting for 400 fs. The analytic expressions obtained provide direct insight into the parameter dependence of the decoherence time scales., Comment: 5 figures; J. Phys. Chem. Lett. (2011)

We study the electromagnetic and gravitational fields of the proton and electron in terms of the Einstenian gravity via the introduction of an arbitrary Lande $g$-factor in the Kerr-Newman solution. We show that at length scales of the order of the reduced Compton wavelength, corrections from different values of the $g$-factor are not negligible and discuss the presence of general relativistic effects in highly ionized heavy atoms. On the other hand, since at the Compton-wavelength scale the gravitational field becomes spin dominated rather than mass dominated, we also point out the necessity of including angular momentum as a source of corrections to Newtonian gravity in the quantum description of gravity at this scale., Comment: 11 pages, 2 figures

The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath., Comment: 8 pages, 3 figures, accepted for publication in Chemical Physics

We show the existence of an entangled nonequilibrium state at very high temperatures when two linearly coupled harmonic oscillators are parametrically driven and dissipate into two independent heat baths. This result has a twofold meaning: first, it fundamentally shifts the classical-quantum border to temperatures as high as our experimental ability allows us, and second, it can help increase by at least one order of magnitude the temperature at which current experimental setups are operated., Comment: accepted in Phys. Rev. Lett

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed: The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schr\"odinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo--Metropolis algorithms suitable for high-dimensional systems., Comment: 19 figures. Published version

We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to identify and resolve manifolds in phase space that contribute to the form factor. They can be associated to classical invariant manifolds such as periodic orbits, but also to non-classical structures like sets of midpoints between periodic points. By contrast to scars in wavefunctions, these features are not subject to the uncertainty relation and therefore need not show any smearing. They constitute important exceptions from a continuous convergence in the classical limit of the Wigner towards the Liouville propagator. We support our theory with numerical results for the quantum cat map and the harmonically driven quartic oscillator., Comment: 10 pages, 4 figures

The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Gu\'eron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the existence of chaotic behavior for the geodesics of the test particles orbiting compact objects like black holes induced by specific values of the quadrupolar deformation of the source using as models the Erez--Rosen solution and the Kerr black hole deformed by an internal multipole term. In this work, we are interesting in the study of the dynamic behavior of geodesics around astrophysical objects with intrinsic quadrupolar deformation or nonisotropic stresses, which induces nonvanishing quadrupolar deformation for the nonrotating limit. For our purpose, we use the Tomimatsu-Sato spacetime [Phys. Rev. Lett. \textbf{29} 1344 (1972)] and its arbitrary deformed generalization obtained as the particular vacuum case of the five parametric solution of Manko et al [Phys. Rev. D 62, 044048 (2000)], characterizing the geodesic dynamics throughout the Poincar\'e sections method. In contrast to the results by Gu\'eron and Letelier we find chaotic motion for oblate deformations instead of prolate deformations. It opens the possibility that the particles forming the accretion disk around a large variety of different astrophysical bodies (nonprolate, e.g., neutron stars) could exhibit chaotic dynamics. We also conjecture that the existence of an arbitrary deformation parameter is necessary for the existence of chaotic dynamics., Comment: 7 pages, 5 figures

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine., Comment: 20 pages, PDF file

A new six-parametric, axisymmetric and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass--quadrupole moment, current octupole moment, electric charge and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti & Stergioulas (Mon. Not. Roy. Astron. Soc. 350, 1416 (2004)), imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained from Berti & Stergioulas numerical solutions, Kerr solution (Phys. Rev. Lett. 11, 237 (1963)), Hartle & Thorne solution (Ap. J. 153, 807, (1968)), an analytic series expansion derived by Shibata & Sasaki (Phys. Rev. D. 58 104011 (1998)) and, our exact solution. We found that radii of ISCOs from our solution fits better than others with realistic numerical interior solutions., Comment: 13 pages, 13 figures, LaTeX document

We dispose of some objections raised by Manko et al. (gr-qc/0604091) on a recently published paper on the role of Poynting vector in the ocurrence of vorticity in electrovaccum spacetimes (2006, Class. Quantum Grav. 23, 2395), Comment: Latex, 2 pages

Recently Kordas (1995, Class. Quantum Grav. 12 2037) and Meinel and Neugebauer (1995, Class. Quantum Grav. 12 2045) studied the conditions for reflection symmetry in stationary axisymmetric space--times in vacuum. They found that a solution to the Einstein field equations is reflectionally symmetric if their Ernst's potential ${\cal E}(\rho=0,z)= e(z)$ on a portion of the positive z-axis extending to infinity satisfies the condition $e_{+}(z){e}_{+}^{*}(-z)=1$. In this note, we formulate an analogous conditions for two complex Ernst potentials in electrovacuum. We also present the special case of rational axis potentials., Comment: 6 pages, LaTex. Some minor changes in the text