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We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree-Fock quantities and first-orderGWcalculations. This approach is applicable across a wide range of on-site Coulomb interaction strengthsU/t, ranging from weakly interacting systems (U/t≪1) to strong correlations (U/t>8). The predicted self-energy is transformed via Dyson's equation and analytic continuation to obtain the real-frequency Green's function, which allows access to the spectral function and density of states. This method can be used for nearest-neighbor interactionstand long-range hopping termst',t'', andt'''.
The lighting environment in intensive care units (ICUs) is markedly different from natural light, potentially disrupting patients' circadian rhythms and impacting staff wellbeing. New lighting technologies may mitigate these effects. A mixed methods service evaluation was conducted in a London ICU using Dyson Lightcycle™ luminaires (DLs) to evaluate staff wellbeing. Wellbeing assessments and user perceptions of the built environment were conducted using validated questionnaires before, during, and after DL deployment. Existing ambient light usage was measured using HOBO devices installed on the ceiling. Additionally, data on DL usage (including spectral data) were collected continuously using Raspberry Pi™ sensors. DL usage was high (>70% per 24 h), primarily as supplementary lighting. Users found DLs easy to control and beneficial for clinical and administrative tasks. Participants assigned a 12.5% higher satisfaction score rated from 0 to 8 of lighting overall during deployment compared to pre-deployment (6.06 ± 0.29 and 5.06 ± 0.60, respectively; p = 0.20). Control variables for the built environment (noise, temperature and air quality) remained unchanged. Staff reported improvements in mood (38%, p < 0.001), fatigue (17.7%, p < 0.001), and sleep quality (21.2%, p = 0.01) during DL use. In the first pilot feasibility service evaluation of its kind, the relationship between ICU lighting quality and staff wellbeing was investigated using DLs. We show that it is feasible to equip an ICU with a novel mode of lighting to evaluate both illuminance and user-centred outcomes. The study suggests a positive association between DL use and staff wellbeing, with notable improvements in mood, fatigue and sleep quality. The nature of the emitted light may enhance the space rather than simply illuminate, thus further adding to a feeling of wellbeing. These findings support data from studies which report effects of light brightness and colour on mood. Additionally, there appears to be a signal towards benefit to the user when additional lighting is provided, compared to the current overhead fluorescent luminaires prevalent in most ICUs. In this service evaluation these benefits were demonstrated in ICU staff operating the device. However, it is conceivable that effects such as improved mood and reduced sleep disturbance may have patient benefits too. Local lighting systems like DLs show promise in enhancing ICU staff wellbeing. Their impact on patient outcomes and the potential for broader implementation deserve further investigation in appropriately designed and powered larger-scale trials.
A typical quantum state with no symmetry can be realized by letting a random unitary act on a fixed state, and the subsystem entanglement spectrum follows the Laguerre unitary ensemble (LUE). For integer-spin time reversal symmetry, we have an analogous scenario where we prepare a time-reversal symmetric state and let random orthogonal matrices act on it, leading to the Laguerre orthogonal ensemble (LOE). However, for half-integer-spin time reversal symmetry, a straightforward analog leading to the Laguerre symplectic ensemble (LSE) is no longer valid because that time-reversal symmetric state is forbidden by the Kramers' theorem. We devise a system in which the global time reversal operator is fractionalized on the subsystems, and show that LSE arises in the system. Extending this idea, we incorporate general symmetry fractionalization into the system, and show that the statistics of the entanglement spectrum is decomposed into a direct sum of LOE, LUE, and/or LSE. Here, various degeneracies in the entanglement spectrum may appear, depending on the non-Abelian nature of the symmetry group and the cohomology class of the nontrivial projective representation on the subsystem. Our work establishes the entanglement counterpart of Dyson's threefold way for Hamiltonians with symmetries.
In this paper, we introduce a new stochastic process of N interacting particles on the line that evolve via Dyson Brownian motion (DBM) with Dyson's index β>0 and undergo simultaneous resetting to their initial positions at a constant rate r. We call this process the resetting Dyson Brownian motion (RDBM) with a parameter β>0, in short the β-RDBM process. For β=1,2,4, the positions of the particles in the RDBM can be interpreted as the eigenvalues of a new random matrix ensemble where the entries of an N×N Gaussian matrix evolve as simultaneously resetting Brownian motions (with rate r) in the presence or absence of a harmonic trap. For r=0 and in the presence of a harmonic trap, this system reaches an equilibrium Gibbs-Boltzmann state of the so called Dyson log-gas. However, the stochastic resetting drives the system at long time to a nonequilibrium stationary state (NESS). We compute exactly the joint distribution of the positions of the particles in this NESS for all β>0 and calculate several macroscopic and microscopic observables in the large N limit. These include the average density profile of the gas, the extreme value statistics, the spacing between two consecutive particles and the full counting statistics, i.e., the distribution of the number of particles in an interval [-L,L]. We show that a nonzero resetting rate r>0 drastically changes the nature of the fluctuations in the stationary state: while the log-gas (r=0) is rather rigid, the β-RDBM in its NESS becomes fluffy, i.e., the fluctuations of different observables are of the same order as their mean. In the absence of a harmonic trap, our results for the β=2 RDBM can be related to nonintersecting Brownian motions (vicious walkers) in the presence of resetting. Our model demonstrates interesting effects arising from the interplay between the eigenvalue repulsion and the all-to-all attraction (generated by stochastic resetting) in an interacting particle system. Numerical simulations are in excellent agreement with our analytical results.
Anthropogenic climate change is affecting people's health, including those with neurological and psychiatric diseases. Currently, making inferences about the effect of climate change on neurological and psychiatric diseases is challenging because of an overall sparsity of data, differing study methods, paucity of detail regarding disease subtypes, little consideration of the effect of individual and population genetics, and widely differing geographical locations with the potential for regional influences. However, evidence suggests that the incidence, prevalence, and severity of many nervous system conditions (eg, stroke, neurological infections, and some mental health disorders) can be affected by climate change. The data show broad and complex adverse effects, especially of temperature extremes to which people are unaccustomed and wide diurnal temperature fluctuations. Protective measures might be possible through local forecasting. Few studies project the future effects of climate change on brain health, hindering policy developments. Robust studies on the threats from changing climate for people who have, or are at risk of developing, disorders of the nervous system are urgently needed.
We present a machine learning (ML) framework for predicting Green's functions of molecular systems, from which photoemission spectra and quasiparticle energies at quantum many-body level can be obtained. Kernel ridge regression is adopted to predict self-energy matrix elements on compact imaginary frequency grids from static and dynamical mean-field electronic features, which gives direct access to real-frequency many-body Green's functions through analytic continuation and Dyson's equation. Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital basis to enforce rotational invariance. We demonstrate good transferability and high data efficiency of the proposed ML method across molecular sizes and chemical species by showing accurate predictions of density of states (DOS) and quasiparticle energies at the level of many-body perturbation theory (GW) or full configuration interaction. For the ML model trained on 48 out of 1995 molecules randomly sampled from the QM7 and QM9 data sets, we report the mean absolute errors of ML-predicted highest occupied and lowest unoccupied molecular orbital energies to be 0.13 and 0.10 eV, respectively, compared to GW@PBE0. We further showcase the capability of this method by applying the same ML model to predict DOS for significantly larger organic molecules with up to 44 heavy atoms.
We study a system of two non-interacting quantum wires with fermions of opposite chirality with a point contact junction at the origin across which tunneling can take place when an arbitrary time-dependent bias between the wires is applied. We obtain the exact dynamical non-equilibrium Green function by solving Dyson's equation analytically. Both the space-time dependent two and four-point functions are written down in a closed form in terms of simple functions of position and time. This allows us to obtain, among other things, theI-Vcharacteristics for an arbitrary time-dependent bias. Our method is a superior alternative to competing approaches to non-equilibrium as we are able to account for transient phenomena as well as the steady state. We study the approach to steady state by computing the time evolution of the equal-time one-particle Green function. Our method can be easily applied to the problem of a double barrier contact whose internal properties can be adjusted to induce resonant tunneling leading to a conductance maximum. We then consider the case of a finite bandwidth in the point contact and calculate the non-equilibrium transport properties which exhibit non-Markovian behaviour. When a subsequently constant bias is suddenly switched on, the current shows a transient build up before approaching its steady state value in contrast to the infinite bandwidth case. This transient property is consistent with numerical simulations of lattice systems using time-dependent density matrix renormalization group suggesting thereby that this transient build up is merely due to the presence of a short distance cutoff in the problem description and not on the other details.
Several studies have confirmed the existence of zero-determinant (ZD) strategies in repeated social dilemmas since Press and Dyson's ingenious discovery of ZD strategies in iterated prisoner's dilemmas. However, less research studies evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective. Here, we use a state-clustering method to theoretically analyze evolutionary dynamics of two representative ZD strategies: generous ZD strategies and extortionate ZD strategies. We consider two new settings for multiplayer ZD strategies: competitions with all ZD strategies and competitions with all memory-one strategies, apart from the competitions between these strategies and some classical ones. Moreover, we investigate the influence of the level of generosity and extortion on evolutionary dynamics of generous and extortionate ZD strategies, which was commonly ignored in previous studies. Theoretical results show that players with limited generosity are at an advantageous place and extortioners extorting more severely hold their ground more readily. Our results may provide new insights into better understanding evolutionary dynamics of ZD strategies in repeated multiplayer games.
We consider the N particle classical Riesz gas confined in a one-dimensional external harmonic potential with power-law interaction of the form 1/r^{k}, where r is the separation between particles. As special limits it contains several systems such as Dyson's log-gas (k→0^{+}), the Calogero-Moser model (k=2), the 1D one-component plasma (k=-1), and the hard-rod gas (k→∞). Despite its growing importance, only large-N field theory and average density profile are known for general k. In this Letter, we study the fluctuations in the system by looking at the statistics of the gap between successive particles. This quantity is analogous to the well-known level-spacing statistics which is ubiquitous in several branches of physics. We show that the variance goes as N^{-b_{k}} and we find the k dependence of b_{k} via direct Monte Carlo simulations. We provide supporting arguments based on microscopic Hessian calculation and a quadratic field theory approach. We compute the gap distribution and study its system size scaling. Except in the range -1<k<0, we find scaling for all k>-2 with both Gaussian and non-Gaussian scaling forms.
A theory of Brownian motion is presented for an assembly of vortices. The attempt is motivated by a realization of Dyson's Coulomb gas in the context of quantum condensates. By starting with the time-dependent Landau-Ginzburg (LG) theory, the dynamics of the vortex gas is constructed, which is governed by the canonical equation of motion. The dynamics of point vortices is converted to the Langevin equation, which results in the generalized Fokker-Planck (GFP) (or Smolkovski) equation using the functional integral on the ansatz of the Gaussian white noise. The GFP, which possesses a non-Hermitian property, is characterized by two regimes called the overdamping and the underdamping regimes. In the overdamping regime, where the dissipation is much larger that the vortex strength, the GFP becomes the standard Fokker-Planck equation, which is transformed into the two-dimensional many-particle system. Several specific applications are given of the Fokker-Planck equation. An asymptotic limit of small diffusion is also discussed for the two-vortices system. The underdamping limit, for which the vortex charge is much larger than the dissipation, is briefly discussed.
We study the extreme statistics of N nonintersecting Brownian motions (vicious walkers) over a unit time interval in one dimension. Using path-integral techniques we compute exactly the joint distribution of the maximum M and of the time τ(M) at which this maximum is reached. We focus in particular on nonintersecting Brownian bridges ("watermelons without wall") and nonintersecting Brownian excursions ("watermelons with a wall"). We discuss in detail the relationships between such vicious walkers models in watermelon configurations and stochastic growth models in curved geometry on the one hand and the directed polymer in a disordered medium (DPRM) with one free end point on the other hand. We also check our results using numerical simulations of Dyson's Brownian motion and confront them with numerical simulations of the polynuclear growth model (PNG) and of a model of DPRM on a discrete lattice. Some of the results presented here were announced in a recent letter [J. Rambeau and G. Schehr, Europhys. Lett. 91, 60006 (2010)].
The mathematical formalism of the steady-state Poisson equation is applied to a variant of Freeman Dyson's "Toy Model" for a first origin. Our kinetic approach allows for an examination of the requisite conditions under which metabolism is quantized into discrete eigenstates (e.g. Dyson's disordered, saddle point, and metabolically active toy cell states). The surface reaction machinery additionally allows for more realistic modeling, whence the crucial role of sticking coefficients (catalyst precursors) as prebiotic selectors emerges. In our interior source model, a steady influx of vent nutrients fuels the intracellular synthesis of (impermeable) monomers within a rock-encradled cavity. Random adsorptions and desorptions occur at inactive "cell" wall sites (where the inert monomers remain impermeable until their eventual return to the intracellular metabolite pool). Occasionally, metabolizing reactions also occur due to endogeneous source monomers adsorbing at their "active" sites. Dyson's mean field approach is used to simplify the species-specific sticking coefficients at empty active (substrate) sites to functions of the fraction x of sites occupied by (catalytically) active monomers. In short, our work suggests that disorder-order transition models based on random drift between discrete metabolic eigenstates (Dyson's Toy Model) do not, in general, extend to more realistic metabolisms. From a perspective based on quasi-random feedback kinetics, the contraindication for discretization (spontaneous generation) in non-autocatalytic metabolisms is consistent with the emergence of ordered metabolism under hydrothermal driving forces, a provisio the occurrence of each period of vent dormancy coincides with a discrete zero-source (dormant) metabolic state. Cell drift to higher order is induced by the random reactions which happen to enhance the substrate specificity (chemical selectivity) of the sticking coefficients for active monomers. The result is stronger sink effects for metabolizing species, whence active adsorptions are promoted in favor of inactive adsorptions at substrate sites. Positive feedback plays a crucial role in preserving ("propagating") order in the cell wall reaction kinetics and is held in check by negative feedback inhibition of excessive cell growth. Finally, the eventual desorption of randomly growing dysfunctional proteins is postulated as a deterrent to deterioration catastrophes.
We present a method for calculating the transmission spectra, dispersion, and time delay characteristics of optical-waveguide gratings based on Green's functions and Dyson's equation. Starting from the wave equation for transverse electric modes we show that the method can solve exactly both the problems of coupling of counterpropagating waves (Bragg gratings) and co-propagating waves (long-period gratings). In both cases the method applies for gratings with arbitrary dielectric modulation, including all kinds of chirp and apodization and possibly also imperfections in the dielectric modulation profile of the grating. Numerically, the method scales as O(N) where N is the number of points used to discretize the grating along the propagation axis. We consider optical fiber gratings although the method applies to all one-dimensional (1D) optical waveguide gratings including high-index contrast gratings and 1D photonic crystals.
The molecular orbital (MO) concept is a useful tool, which relates the molecular ground-state energy with the energies (and occupations) of the individual orbitals. However, analysis of the excited states from linear response computations is performed in terms of the initial state MOs or some other forms of orbitals, e.g., natural or natural transition orbitals. Because these orbitals lack the respective energies, they do not allow developing a consistent orbital picture of the excited states. Herein, we argue that Dyson's orbitals enable description of the response states compatible with the concepts of molecular orbital theory. The Dyson orbitals and their energies obtained by mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) for the response ground state are remarkably similar to the canonical MOs obtained by the usual DFT calculation. For excited states, the Dyson orbitals provide a chemically sensible picture of the electronic transitions, thus bridging the chasm between orbital theory and response computations.
Penrose and Hameroff assert that brain computations, including quantum computations, involving hydrophobic areas of microtubules whose electron clouds go into orchestrated superpositions and reductions that lead to proto-conscious elements, or "bings" that become orchestrated into conscious experiences. Their assertion, however, like the findings of the neural correlates of consciousness, does not explain subjectivity, but rather describes necessary conditions for it. Many scientists, including Panksepp, Demasio, and Tononi, have each made great contributions to the field, but none explains how material biological processes acquire subjectivity. Yet, the fact is that subjectivity exists and is and of great importance to evolution. Penrose argues that understanding, which involves subjectivity, must be brought into physics, perhaps an undiscovered aspect. Subjectivity is always of or about certain living brain information even though most brain functions do not have subjectivity. Many quantum fields are known to exist and follow Dyson's definition: "a kind of tension or stress which can exist in empty space in the absence of matter. It reveals itself by producing forces, which act on any material objects that happen to lie in the space the field occupies." My hypothesis is that there may be undiscovered quantum fields, which unlike known fields, induce subjectivity when they interact with certain brain information. They emit quantum particles that exert force and cause changes to material objects (brain patterns conveying information) with which they interact. Information that transports meaning to living material exerts force through the understanding it conveys. There is a continuous interplay between experience and brain information. Experiences profoundly inform the brain and alter brain structure, function, and behavior, and local and integrated brain functions process information and initiate multiple associated experiences. Most experience is non-conscious, as discussed by Wright and others, like the soundtrack of a movie to which our brains respond continuously and emotionally even though, we are only intermittently consciously aware of it. I will explore how non-conscious experience may relate to the self, and how it might become conscious. I will offer present support and directions for testing this plausible hypothesis, as well as potential clinical applications in psychology.
We consider a one-dimensional classical Coulomb gas of N-like charges in a harmonic potential-also known as the one-dimensional one-component plasma. We compute, analytically, the probability distribution of the position x_{max} of the rightmost charge in the limit of large N. We show that the typical fluctuations of x_{max} around its mean are described by a nontrivial scaling function, with asymmetric tails. This distribution is different from the Tracy-Widom distribution of x_{max} for Dyson's log gas. We also compute the large deviation functions of x_{max} explicitly and show that the system exhibits a third-order phase transition, as in the log gas. Our theoretical predictions are verified numerically.
We present a method to self-consistently evaluate quasiparticle energies of periodic systems within the diagonal approximation for solving Dyson's equation. Our method is based on the Laplace transform of the second-order Møller-Plesset perturbation (MP2) theory kernel in the atomic basis formulation. The overhead computational cost of evaluating the fully self-consistent diagonal correction over the MP2 band energy calculation is negligible. We present numerical benchmark results for the band structure of trans-polyacetylene and compare it with MP2 and other approaches.
Sudden polarization (SP) is one of the manifestations of electron transfer in the electronically excited states of molecules. Proposed initially to explain the unusual reactivity of photoexcited olefins, SP often occurs in the excited states of molecules possessing strongly correlated diradical ground state. Theoretical description of SP involves mixing between the singly excited and the doubly excited zwitterionic states, which makes it inaccessible with the use of the popular linear-response time-dependent density functional theory methods. In this work, an extended variant of the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS, or SSR) method is applied to study SP in a number of organic diradical systems. To this end, the analytical derivative formalism is derived and implemented for the SSR(3,2) method (see the main text for explanation of the acronym), which enables the automatic geometry optimization and obtains the relaxed density matrices as well as the electron binding energies and respective Dyson's orbitals. Application of the new method to SP in the lowest singlet excited state of ethylene agrees with the results obtained previously with the use of multireference methods of wavefunction theory. A number of interesting manifestations of SP are observed, such as the charge transfer in photoexcited tetramethyleneethene (TME) diradical mediated by the vibrational motion and conductivity switching in the excited state of a donor-acceptor dyad placed in an external electric field.
Colloidal particles endowed with specific time-dependent interactions are a promising route for realizing artificial materials that have the properties of living ones. Previous work has demonstrated how this system can give rise to self-replication. Here, we introduce the process of colloidal catalysis, in which clusters of particles catalyze the creation of other clusters through templating reactions. Surprisingly, we find that simple templating rules generically lead to the production of huge numbers of clusters. The templating reactions among this sea of clusters give rise to an exponentially growing catalytic cycle, a specific realization of Dyson's notion of an exponentially growing metabolism. We demonstrate this behavior with a fixed set of interactions between particles chosen to allow a catalysis of a specific six-particle cluster from a specific seven-particle cluster, yet giving rise to the catalytic production of a sea of clusters of sizes between 2 and 11 particles. The fact that an exponentially growing cycle emerges naturally from such a simple scheme demonstrates that the emergence of exponentially growing metabolisms could be simpler than previously imagined.
We describe full multiple-scattering calculations of localized surface photonic states set up by lithographically designed nanostructures made of a finite number of dielectric pads deposited on a planar surface. The method is based on a numerical solution of the dyadic Dyson's equation. When the pads are arranged to form a closed circle, we find field patterns that look like the electronic charge density recently observed above quantum corrals. We propose two experimental techniques that could be used to observe these electromagnetic modes in direct space.