Quantal Fluctuations Research Articles

State densities of heavy nuclei in the static-path plus random-phase approximation

Nuclear state densities are important inputs to statistical models of compound-nucleus reactions. State densities are often calculated with self-consistent mean-field approximations that do not include important correlations and have to be augmented with empirical collective enhancement factors. Here, we benchmark the static-path plus random-phase approximation (SPA+RPA) to the state density in a chain of samarium isotopes $^{148-155}$Sm against exact results (up to statistical errors) obtained with the shell model Monte Carlo (SMMC) method. The SPA+RPA method incorporates all static fluctuations beyond the mean field together with small-amplitude quantal fluctuations around each static fluctuation. Using a pairing plus quadrupole interaction, we show that the SPA+RPA state densities agree well with the exact SMMC densities for both the even- and odd-mass isotopes. For the even-mass isotopes, we also compare our results with mean-field state densities calculated with the finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation. We find that the SPA+RPA repairs the deficiencies of the mean-field approximation associated with broken rotational symmetry in deformed nuclei and the violation of particle-number conservation in the pairing condensate. In particular, in deformed nuclei the SPA+RPA reproduces the rotational enhancement of the state density relative to the mean-field state density.

Dissipative dynamics within stochastic mean-field approach

The time-dependent Hartree-Fock (TDHF) and density functional theory (DFT) are among the most useful approaches within mean-field theories for studying static and dynamic properties of complex many-body systems in different branches of physics. Despite the fact that they provide a good approximation for the average properties of one-body degrees of freedoms, they are known to fail to include quantal fluctuations of collective observables and they do not provide sufficient dissipation of collective motion. In order to incorporate these missing effects the stochastic mean-field (SMF) approach was proposed (Ayik 2008). In the SMF approach a set of stochastic initial one-body densities are evolved. Each stochastic one-body density matrix consists of a set of stochastic Gaussian random numbers that satisfy the first and second moments of collective one-body observables. Recent works indicate that the SMF approach provides a good description of the dynamics of the nuclear systems (Yilmaz et al. 2018; Ayik et al. 2019). In this work, the one-dimensional Fermi-Hubbard model is simulated with the SMF approach by using different distributions such as Gaussian, uniform, bimodal and two-point distributions. The dissipative dynamics are discussed and the predictive power of the SMF approach with different probability distributions are compared with each other and the exact dynamics. As a result it is shown that by considering different distributions, the predictive power of the SMF approach can be improved.

Quantal Fluctuations in Central Mammalian Synapses: Functional Role of Vesicular Docking Sites.

Quantal fluctuations are an integral part of synaptic signaling. At the frog neuromuscular junction, Bernard Katz proposed that quantal fluctuations originate at "reactive sites" where specific structures of the presynaptic membrane interact with synaptic vesicles. However, the physical nature of reactive sites has remained unclear, both at the frog neuromuscular junction and at central synapses. Many central synapses, called simple synapses, are small structures containing a single presynaptic active zone and a single postsynaptic density of receptors. Several lines of evidence indicate that simple synapses may release several synaptic vesicles in response to a single action potential. However, in some synapses at least, each release event activates a significant fraction of the postsynaptic receptors, giving rise to a sublinear relation between vesicular release and postsynaptic current. Partial receptor saturation as well as synaptic jitter gives to simple synapse signaling the appearance of a binary process. Recent investigations of simple synapses indicate that the number of released vesicles follows binomial statistics, with a maximum reflecting the number of docking sites present in the active zone. These results suggest that at central synapses, vesicular docking sites represent the reactive sites proposed by Katz. The macromolecular architecture and molecular composition of docking sites are presently investigated with novel combinations of techniques. It is proposed that variations in docking site numbers are central in defining intersynaptic variability and that docking site occupancy is a key parameter regulating short-term synaptic plasticity.

Interaction of aberrations, diffraction, and quantal fluctuations determine the impact of pupil size on visual quality.

Our purpose is to develop a computational approach that jointly assesses the impact of stimulus luminance and pupil size on visual quality. We compared traditional optical measures of image quality and those that incorporate the impact of retinal illuminance dependent neural contrast sensitivity. Visually weighted image quality was calculated for a presbyopic model eye with representative levels of chromatic and monochromatic aberrations as pupil diameter was varied from 7 to 1 mm, stimulus luminance varied from 2000 to 0.1 cd/m2, and defocus varied from 0 to -2 diopters. The model included the effects of quantal fluctuations on neural contrast sensitivity. We tested the model's predictions for five cycles per degree gratings by measuring contrast sensitivity at 5 cyc/deg. Unlike the traditional Strehl ratio and the visually weighted area under the modulation transfer function, the visual Strehl ratio derived from the optical transfer function was able to capture the combined impact of optics and quantal noise on visual quality. In a well-focused eye, provided retinal illuminance is held constant as pupil size varies, visual image quality scales approximately as the square root of illuminance because of quantum fluctuations, but optimum pupil size is essentially independent of retinal illuminance and quantum fluctuations. Conversely, when stimulus luminance is held constant (and therefore illuminance varies with pupil size), optimum pupil size increases as luminance decreases, thereby compensating partially for increased quantum fluctuations. However, in the presence of -1 and -2 diopters of defocus and at high photopic levels where Weber's law operates, optical aberrations and diffraction dominate image quality and pupil optimization. Similar behavior was observed in human observers viewing sinusoidal gratings. Optimum pupil size increases as stimulus luminance drops for the well-focused eye, and the benefits of small pupils for improving defocused image quality remain throughout the photopic and mesopic ranges. However, restricting pupils to <2 mm will cause significant reductions in the best focus vision at low photopic and mesopic luminances.

Elastic response of the atomic nucleus in gauge space: Giant Pairing Vibrations

Due to quantal fluctuations, the ground state of a closed shell system $ A_{0}$ can become virtually excited in a state made out of the ground state of the neighbour nucleus $ \vert gs(A_0+2) \rangle $ ( $ \vert gs(A_0-2) \rangle $ ) and of two uncorrelated holes (particles) below (above) the Fermi surface. These $ J^{\pi} = 0^{+}$ pairing vibrational states have been extensively studied with two-nucleon transfer reactions. Away from closed shells, these modes eventually condense, leading to nuclear superfluidity and thus to pairing rotational bands with excitation energies much smaller than $ \hbar\omega_{0}$ , the energy separation between major shells. Pairing vibrations are the plastic response of the nucleus in gauge space, in a similar way in which low-lying quadrupole vibrations, i.e. surface vibrations with energies much smaller than $ \hbar\omega_{0}$ whose eventual condensation leads to quadrupole deformed nuclei, provide an example of the plastic nuclear response in 3D space. While much is known, in particular concerning its damping, regarding the counterpart of quadrupole plastic modes, i.e. regarding the giant quadrupole resonances (GQR), $ J^{\pi} = 2^{+}$ elastic response of the nucleus with energies of the order of $ \hbar\omega_{0}$ , little is known regarding this subject concerning pairing modes (giant pairing vibrations, GPV). Consequently, the recently reported observation of L = 0 resonances, populated in the reactions 12C(18O,16O)14C and 13C(18O,16O)15C and lying at an excitation energy of the order of $ \hbar\omega_{0}$ , likely constitutes the starting point of a new field of research, that of the study of the elastic response of nuclei in gauge space. Not only that, but also the fact that the GPV have likely been serendipitously observed in these light nuclei when it has failed to show up in more propitious nuclei like Pb, provides unexpected and fundamental insight into the relation existing between basic mechanisms --Landau, doorway, compound damping-- through which giant resonances acquire a finite lifetime, let alone the radical difference regarding these phenomena displayed by correlated (ph) and (pp) modes.

Brightness in human rod vision depends on neural adaptation to the quantum statistics of light

In cone-mediated vision, light adaptation obeys Weber's law (constant visual response to constant contrast). Weber adaptation begins in the cones themselves and is well suited to support color constancy. In rod-mediated vision, the visual input consists of a retinal rain of discrete photons. Individual rods do not receive a sufficient number of light quanta within their integration time to light adapt. Instead, light adaptation occurs in post-receptoral circuitry. The nature of this adaptation is still poorly understood. Since the pioneering work of Barlow (1956, 1958), it has been known that psychophysical rod thresholds, when measured with small, brief test probes, increase in proportion to the square-root of adapting intensity, rather than in direct proportion to intensity (Weber's law). A bedrock idea of classical psychophysics ascribes the square-root law to the masking of dim threshold flashes by the naturally occurring variability in the photon rain from the adapting field (Shapley & Enroth-Cugell, 1975). Importantly, this classical explanation does not require actual physiological adaptation and, classically, none was assumed. Here, we present the results of three brightness matching experiments that together demonstrate that the square-root law arises from a neural adaptation (monocular gain control), driven by statistical photon inputs, that influences brightness as well as threshold. The experiments were performed in a haploscope with one eye's adaptive state manipulated and the other eye used as a reference. Our results show that: 1) brightness gain for supra-threshold flashes varies inversely with the standard deviation of the quantal fluctuations from the adapting field; 2) brightness gain is controlled by both the mean and variance of time-integrated photon inputs and changes only slowly (adaptation takes a few minutes). These properties suggest that brightness at low light levels evolved to encode the reliability (signal-to-noise ratio) of sparse statistical light inputs, rather than either luminance or contrast. Meeting abstract presented at VSS 2016

Thermal properties of the Tin odd isotopes 117,119,121Sn

We propose to study the thermal properties of the odd isotopes of Tin: [Formula: see text]Sn. To this end, one used two methods to evaluate the properties of these elements. The first theoretical consideration uses a simple prescription to perform the calculation of these properties based on those of even–even neighboring isotopes, assuming the quasi-particle entropy extensivity. The even–even elements are treated as part of the Modified Lipkin–Nogami (MLN) method that allows to take into account the quantal and statistical fluctuations. The second theoretical approach consists of the generalization of the MLN formalism in the case of odd systems, by using the blocking technique. Then, this approach is applied to evaluate the thermal properties of the considered elements. The obtained results by both theoretical approaches are compared to the experimental data. The latter are deduced from the experimental level density within the canonical ensemble. It appears that the assumption of quasi-particle entropy extensivity at low excitation energy allows a simple and an effective treatment of thermal properties of odd nuclei. Indeed, this approach allows to give a good reproduction of experimental data in the particular in the region where the pairing transition occurs.

Effects of thermal shape fluctuations and pairing fluctuations on the giant dipole resonance in warm nuclei

Apart from the higher limits of isospin and temperature, the properties of atomic nuclei are intriguing and less explored at the limits of lowest but finite temperatures. At very low temperatures there is a strong interplay between the shell (quantal fluctuations), statistical (thermal fluctuations), and residual pairing effects as evidenced from the studies on giant dipole resonance (GDR). In our recent work [Phys. Rev. C 90, 044308 (2014)], we have outlined some of our results from a theoretical approach for such warm nuclei where all these effects are incorporated along within the thermal shape fluctuation model (TSFM) extended to include the fluctuations in the pairing field. In this article, we present the complete formalism based on the microscopic-macroscopic approach for determining the deformation energies and a macroscopic approach which links the deformation to GDR observables. We discuss our results for the nuclei $^{97}\mathrm{Tc},^{120}\mathrm{Sn},^{179}\mathrm{Au}$, and $^{208}\mathrm{Pb}$, and corroborate with the experimental data available. The TSFM could explain the data successfully at low temperature only with a proper treatment of pairing and its fluctuations. More measurements with better precision could yield rich information about several phase transitions that can happen in warm nuclei.

Origin and effect of phototransduction noise in primate cone photoreceptors

Noise in the responses of cone photoreceptors sets a fundamental limit to visual sensitivity, yet the origin of noise in mammalian cones and its relation to behavioral sensitivity are poorly understood. Our work here on primate cones improves understanding of these issues in three ways. First, we find that cone noise is not dominated by spontaneous photopigment activation or by quantal fluctuations in photon absorption but instead by other sources, namely channel noise and fluctuations in cGMP. Second, we find that adaptation in cones, unlike that in rods, affects signals and noise differently. This difference helps explain why thresholds for rod- and cone-mediated signals have different dependencies on background light level. Third, past estimates of noise in mammalian cones are too high to explain behavioral sensitivity. Our measurements indicate a lower level of cone noise, and thus help reconcile physiological and behavioral estimates of cone noise and sensitivity.

STATISTICAL AND QUANTAL EFFECTS ON PAIRING PHASE TRANSITION IN THE CASE OF HOT EVEN–EVEN NEUTRON-RICH TIN ISOTOPES

The thermal properties of Tin isotopes such as 68≤N≤78, are studied. The calculations are performed by means of the modified Lipkin–Nogami (MLN) approach that takes into account the thermal and quantal fluctuations. The obtained results are compared to the conventional finite-temperature Bardeen–Cooper–Schrieffer (FTBCS) approach and to the modified Bardeen–Cooper–Schrieffer (MBCS) method. The numerical results illustrate the effect of the statistical and quantal fluctuations on the description of the phenomenon of pairing phase transition.

Thermodynamics of ultrasmall metallic grains in the presence of pairing and exchange correlations: Mesoscopic fluctuations

We study the mesoscopic fluctuations of thermodynamic observables in a nanosized metallic grain in which the single-particle dynamics are chaotic and the dimensionless Thouless conductance is large. Such a grain is modeled by the universal Hamiltonian describing the competition between exchange and pairing correlations. The exchange term is taken into account exactly by a spin-projection method, and the pairing term is treated in the static-path approximation together with small-amplitude quantal fluctuations around each static fluctuation of the pairing field. Odd-even particle-number effects induced by pairing correlations are included using a number-parity projection. We find that the exchange interaction shifts the number-parity effects in the heat capacity and spin susceptibility to lower temperatures. In the regime where the pairing gap is similar to or smaller than the single-particle mean level spacing, these number-parity effects are suppressed by exchange correlations, and the fluctuations of the spin susceptibility may be particularly large. However, for larger values of the pairing gap, the number-parity effects may be enhanced by exchange correlations.

Advanced model for the prediction of the neutron-rich fission product yields

The consistent models for the description of the independent fission product formation cross sections in the spontaneous fission and in the neutron and proton induced fission at the energies up to 100MeV is developed. This model is a combination of new version of the two-component exciton model and a time-dependent statistical model for fusion-fission process with inclusion of dynamical effects for accurate calculations of nucleon composition and excitation energy of the fissioning nucleus at the scission point. For each member of the compound nucleus ensemble at the scission point, the primary fission fragment characteristics: kinetic and excitation energies and their yields are calculated using the scission-point fission model with inclusion of the nuclear shell and pairing effects, and multimodal approach. The charge distribution of the primary fragment isobaric chains was considered as a result of the frozen quantal fluctuations of the isovector nuclear matter density at the scission point with the finite neck radius. Model parameters were obtained from the comparison of the predicted independent product fission yields with the experimental results and with the neutron-rich fission product data measured with a Penning trap at the Accelerator Laboratory of the University of Jyvaskyla (JYFLTRAP).

The Generalized Model for the Description of Prompt Neutrons in the Low-energy Fission

Abstract The generalized model for the description of neutron emission from the spontaneous and neutron-induced fission in the energy interval up to 20 MeV is developed. For accurate calculations of nucleon composition and excitation energy of the fissioning nucleus at the scission point, the time-dependent statistical model including the pre-equilibrium neutron emission and nuclear friction effects is used. For each member of the compound nucleus ensemble at the scission point, the primary fission-fragment characteristics such as kinetic and excitation energies and yields are calculated using the scission-point fission model with nuclear shell and pairing effects, and based on the multimodal approach. The charge distribution for the primary fragment isobaric chains is considered as a result of the frozen quantal fluctuations of the isovector nuclear matter density at the finite scission neck radius. The post-scission neutron spectra are calculated as the result of the equilibrium emission from the fully accelerated fission fragments with calculated kinetic energies. The pre- scission neutron multiplicity and spectra for multi-chance fission are also calculated. The neutron and γ-ray emission during the saddle-to-scission time is also included in the consideration. This mechanism may partially explain the long standing problem of the so-called isotropic component of prompt fission neutrons.

Consistent theoretical model for the description of the neutron-rich fission product yields

The consistent model for the description of the independent fission product formation cross-section at light projectile energies up to about 100MeV is described. Pre-compound nucleon emission is described in the framework of the two-component exciton model using the Monte Carlo method, which allows one to incorporate a time duration criterion for the pre-equilibrium stage of the reaction. The decay of the excited compound nuclei, formed after the pre-equilibrium neutron and proton emission, is treated within the time-dependent statistical model with the inclusion of the main dynamical effects of nuclear friction on the fission width and saddle-to-scission descent time. For each member of the compound nucleus ensemble at scission point, the primary fragment isobaric chain yields are calculated using the multimodal approach with the inclusion two superasymmetric fission modes. The charge distribution of the primary fragment isobaric chains was considered as a results of frozen quantal fluctuations of the isovector nuclear matter density at the finite scission neck radius. The calculated fission product formation cross-sections in the neutron, proton, and γ-rays induced fission of the heavy actinides are presented.

Theoretical and experimental studies of the neutron rich fission product yields at intermediate energies

A new method to measure the fission product independent yields employing the ion guide technique and a Penning trap as a precision mass filter, which allows an unambiguous identification of the nuclides is presented. The method was used to determine the independent yields in the proton-induced fission of 232Th and 238U at 25 MeV. The data were analyzed with the consistent model for description of the fission product formation cross section at the projectile energies up to 100 MeV. Pre-compound nucleon emission is described with the two-component exciton model using Monte Carlo method. Decay of excited compound nuclei is treated within time-dependent statistical model with inclusion of the nuclear friction effect. The charge distribution of the primary fragment isobaric chain was considered as a result of frozen quantal fluctuations of the isovector nuclear density. The theoretical predictions of the independent fission product cross sections are used for normalization of the measured fission product isotopic distributions.

Chemical potential beyond the quasiparticle mean field

The effects of quantal and thermal fluctuations beyond the BCS quasiparticle mean field on the chemical potential are studied within a model, which consists of $N$ particles distributed amongst $\ensuremath{\Omega}$ doubly folded equidistant levels interacting via a pairing force with parameter $G$. The results obtained at zero and finite temperatures $T$ within several approaches, which include the fluctuations beyond the BCS theory, are compared with the exact results. The chemical potential, defined as the Lagrangian multiplier to preserve the average number of particles, is compared with the corresponding quantity, which includes the effect from fluctuations of particle and quasiparticle numbers beyond the BCS quasiparticle mean field. The analysis of the results shows that the latter differs significantly from the former as functions of $G$ and $T$. The chemical potential loses its physical meaning in the system with a fixed number of particles or after eliminating quantal fluctuations of particle (quasiparticle) numbers by means of particle number projection. The validity of the criterion for the signature of the transition to Bose-Einstein condensation, which occurs in infinite systems when the chemical potential hits the bottom of the energy spectrum, is reexamined for the finite multilevel model.

Quantum fluctuations in insulating ferroelectrics

It has been proposed that in a ferroelectric insulator, an applied magnetic field may couple the transverse phonon modes and produce left and right circularly polarized phonon modes which are no longer degenerate. We quantize the theory and examine the effects of quantal fluctuations. In particular, we show that the zero-point fluctuations result in a large diamagnetic contribution to the magnetic susceptibility.

Square-Root Law Light Adaptation in Rod-Mediated Vision is Due to Retinal Gain Control

Fully dark-adapted human observers are remarkably sensitive to light, coming close to the detection limits imposed by the discrete nature of photon absorptions and quantum uncertainty. In rod-mediated vision, classical experiments by Barlow and others revealed the existence of three laws relating detection threshold to adapting luminance. At very low light levels, threshold is independent of adapting luminance and is thought to be limited by neural noise. At high adapting luminances, threshold is set by the physiological gain mechanism responsible for Weber's law. Between these regimes, threshold rises in proportion to the square-root of the adapting luminance (Rose-deVries law). It is not known whether the square-root law is due to physiological gain control or simply to a tendency for the appearance of weak probe flashes to be masked by the larger quantal fluctuation noise associated with more intense adapting fields. We addressed this question using a combination of psychophysical and physiological methods. The psychophysical experiments were based on the technique of dichoptic brightness matching. A 10 msec, 0.55 deg., 492 nm flash of fixed intensity was presented to a rod-dominated region of one of the observer's two retinas, superimposed on a 7.4 deg adapting field producing an average of either 0.01, 0.1, or 1.0 photoisomerizations per rod-sec. Simultaneously in the observer's other eye, an otherwise identical flash of adjustable intensity was presented on an adapting field of fixed intensity. The intensity of the adjustable flash causing the two flashes to appear equally bright was determined using a staircase procedure. We found that the square-root law holds for brightness matching of superthreshold flashes having intensities as high as 1000 times threshold. This effect cannot be due to noise masking but must be due to monocular gain control. On half the trials, random flicker was added to the adjustable background to discover whether the added noise would affect the neural gain in that eye. The added noise slightly increased the brightness of superthreshold flashes at high background luminances. Since the direction of this effect is opposite to that expected if the neural gain was set by noise fluctuations, we tentatively conclude that the gain control responsible for the square-root law is deterministic. The existence of square-root gain control was further confirmed by preliminary intra- and extra-cellular recordings from ON-parasol ganglion cells in intact macaque retina, indicating that the gain control results from a rod-mediated network adaptation in primate retina.

The impact of synaptic conductance on action potential waveform: Evoking realistic action potentials with a simulated synaptic conductance

Most current clamp studies trigger action potentials (APs) by step current injection through the recording electrode and assume that the resulting APs are essentially identical to those triggered by orthodromic synaptic inputs. However this assumption is not always valid, particularly when the synaptic conductance is of large magnitude and of close proximity to the axon initial segment. We addressed this question of similarity using the Calyx of Held/MNTB synapse; we compared APs evoked by long duration step current injections, short step current injections and orthodromic synaptic stimuli. Neither injected current protocol evoked APs that matched the evoked orthodromic AP waveform, showing differences in AP height, half-width and after-hyperpolarization. We postulated that this ‘error’ could arise from changes in the instantaneous conductance during the combined synaptic and AP waveforms, since the driving forces for the respective ionic currents are integrating and continually evolving over this time-course. We demonstrate that a simple Ohm's law manipulation of the EPSC waveform, which accounts for the evolving driving force on the synaptic conductance during the AP, produces waveforms that closely mimic those generated by physiological synaptic stimulation. This stimulation paradigm allows supra-threshold physiological stimulation (single stimuli or trains) without the variability caused by quantal fluctuation in transmitter release, and can be implemented without a specialised dynamic clamp system. Combined with pharmacological tools this method provides a reliable means to assess the physiological roles of postsynaptic ion channels without confounding affects from the presynaptic input.

A stochastic mean-field approach for nuclear dynamics

We propose a microscopic stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. It is shown that, for small amplitude fluctuations, the proposed model gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, by projecting the proposed stochastic mean-field evolution on a collective path, a generalized Langevin equation is derived for collective variable, which incorporates one-body dissipation and one-body fluctuation mechanism in accordance with quantal fluctuation–dissipation relation.