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Quantum dynamics simulations are becoming a powerful tool for understanding photo-excited molecules. Their poor scaling, however, means that it is hard to study molecules with more than a few atoms accurately, and a major challenge at the moment is the inclusion of the molecular environment. Here, we present a proof of principle for a way to break the two bottlenecks preventing large but accurate simulations. First, the problem of providing the potential energy surfaces for a general system is addressed by parameterizing a standard force field to reproduce the potential surfaces of the molecule's excited-states, including the all-important vibronic coupling. While not shown here, this would trivially enable the use of an explicit solvent. Second, to help the scaling of the nuclear dynamics propagation, a hierarchy of approximations is introduced to the variational multi-configurational Gaussian method that retains the variational quantum wavepacket description of the key quantum degrees of freedom and uses classical trajectories for the remaining in a quantum mechanics/molecular mechanics like approach. The method is referred to as force field quantum dynamics (FF-QD), and a two-state ππ*/nπ* model of uracil, excited to its lowest bright ππ* state, is used as a test case. [ABSTRACT FROM AUTHOR]

The fewest switches surface hopping (FSSH) method proposed by Tully in 1990 [Tully, J. Chem. Phys. 93, 1061 (1990)]—along with its many later variations—forms the basis for most practical simulations of molecular dynamics with electronic transitions in realistic systems. Despite its popularity, a rigorous formal derivation of the algorithm has yet to be achieved. In this paper, we derive the energy-conserving momentum jumps employed by FSSH from the perspective of quantum trajectory surface hopping (QTSH) [Martens, J. Phys. Chem. A 123, 1110 (2019)]. In the limit of localized nonadiabatic transitions, simple mathematical and physical arguments allow the FSSH algorithm to be derived from first principles. For general processes, the quantum forces characterizing the QTSH method provide accurate results for nonadiabatic dynamics with rigorous energy conservation, at the ensemble level, within the consistency of the underlying stochastic surface hopping without resorting to the artificial momentum rescaling of FSSH. [ABSTRACT FROM AUTHOR]

We use quantum trajectory theory to study the dynamics of the first step in photosynthesis for a single photon interacting with photosystem II (PSII). By considering individual trajectories we are able to look beyond the ensemble average dynamics to compute the PSII system evolution conditioned upon individual photon counting measurements. Measurements of the transmitted photon beam strongly affects the system state, since detection of an outgoing photon confirms that the PSII must be in the electronic ground state, while a null measurement implies it is in an excited electronic state. We show that under ideal conditions, observing the null result transforms a state with a low excited state population to a state with nearly all population contained in the excited states. We study the PSII dynamics conditioned on such photon counting for both a pure excitonic model of PSII and a more realistic model with exciton-phonon coupling to a dissipative phononic environment. In the absence of such coupling, we show that the measured fluorescence rates show oscillations constituting a photon-counting witness of excitonic coherence. Excitonic coupling to the phonon environment has a strong effect on the observed rates of fluorescence, damping the oscillations. Addition of non-radiative decay and incoherent transitions to radical pair states in the reaction center to the phononic model allows extraction of a quantum efficiency of 92.5% from the long-time evolution, consistent with bulk experimental measurements. [ABSTRACT FROM AUTHOR]

Accurate solar power forecasting is pivotal for the global transition towards sustainable energy systems. This study conducts a meticulous comparison between Quantum Long Short-Term Memory (QLSTM) and classical Long Short-Term Memory (LSTM) models for solar power production forecasting. The primary objective is to evaluate the potential advantages of QLSTMs, leveraging their exponential representational capabilities, in capturing the intricate spatiotemporal patterns inherent in renewable energy data. Through controlled experiments on real-world photovoltaic datasets, our findings reveal promising improvements offered by QLSTMs, including accelerated training convergence and substantially reduced test loss within the initial epoch compared to classical LSTMs. These empirical results demonstrate QLSTM's potential to swiftly assimilate complex time series relationships, enabled by quantum phenomena like superposition. However, realizing QLSTM's full capabilities necessitates further research into model validation across diverse conditions, systematic hyperparameter optimization, hardware noise resilience, and applications to correlated renewable forecasting problems. With continued progress, quantum machine learning can offer a paradigm shift in renewable energy time series prediction, potentially ushering in an era of unprecedented accuracy and reliability in solar power forecasting worldwide. This pioneering work provides initial evidence substantiating quantum advantages over classical LSTM models while acknowledging present limitations. Through rigorous benchmarking grounded in real-world data, our study illustrates a promising trajectory for quantum learning in renewable forecasting. [ABSTRACT FROM AUTHOR]

We show that quantum trajectories become exponentially fast supported by one of their minimal invariant subspaces. The exponential convergence is established in expectation by using Lyapunov techniques and carrying out an in-depth study of the identifiability of the different subspaces. Additionally, we introduce a feedback control strategy that enables targeted convergence to a desired subspace. This convergence is also achieved at exponential speed. [ABSTRACT FROM AUTHOR]

On 17 October 1947, Niels Bohr was made a knight of the Order of the Elephant by the King of Denmark in view of his outstanding achievements and contributions to science. Bohr designed his own coat of arms that featured a pattern of Yin and Yang (Tai Chi symbol) to symbolize the wave–particle complementarity. However, Bohr's Yin-Yang diagram (YYD) was neither drawn based on the principles of quantum mechanics, nor did it originate from the traditional Taoist YYD. Scientists still have doubts about the legitimacy of using YYD as the icon of the wave–particle complementarity, because the YYD belonging to quantum mechanics itself is unknown so far. This paper reports the YYDs existing in quantum mechanics and justifies the role of YYD in the wave–particle duality by showing that any system, whether classical or quantum, has an ideal YYD as long as it satisfies Bohr's principle of complementarity (BPC). The deviation of a deformed YYD from the ideal YYD indicates the extent to which a real system satisfies BPC. This paper constructs the quantum YYD by the complex quantum trajectory of a particle tunneling via a step barrier, which displays the continuous transition between the wave behavior and the particle behavior. It appears that the YYD designed by Bohr in his coat of arms resembles the YYD generated by tunneling motion, not only in appearance but also in the governing equation. [ABSTRACT FROM AUTHOR]

Stretching or compressing hydrogels creates anisotropic environments that lead to motionally averaged alignment of embedded guest quadrupolar nuclear spins such as 23Na+. These distorted hydrogels can elicit a residual quadrupolar coupling that gives an oscillation in the trajectories of single quantum coherences (SQCs) as a function of the evolution time during a spin-echo experiment. We present solutions to equations of motion derived with a Liouvillian superoperator approach, which encompass the coherent quadrupolar interaction in conjunction with relaxation, to give a full analytical description of the evolution trajectories of rank-1 ( T ^ 1 ± 1 ), rank-2 ( T ^ 2 ± 1 ), and rank-3 ( T ^ 3 ± 1 ) SQCs. We performed simultaneous numerical fitting of the experimental 23Na nuclear magnetic resonance (NMR) spectra and rank-2 ( T ^ 2 ± 1 ) and rank-3 ( T ^ 3 ± 1 ) SQC evolution trajectories measured in double and triple quantum filtered experiments, respectively. We estimated values of the quadrupolar coupling constant CQ, rotational correlation time τC, and 3 × 3 Saupe order matrix. We performed simultaneous fitting of the analytical expressions to the experimental data to estimate values of the quadrupolar coupling frequency ωQ/2π, residual quadrupolar coupling ω Q / 2 π , and corresponding spherical order parameter S 0 * , which showed a linear dependence on the extent of uniform hydrogel stretching and compression. The analytical expressions were completely concordant with the numerical approach. The insights gained here can be extended to more complicated (biological) systems such as 23Na+ bound to proteins or located inside and outside living cells in high-field NMR experiments and, by extension, to the anisotropic environments found in vivo with 23Na magnetic resonance imaging. [ABSTRACT FROM AUTHOR]

In a series of papers in the 1980s Alexander Holevo proved a classification theorem for continuous quantum measurement processes, or, as they would today be called, stationary quantum trajectories in continuous time. His main tools were functional analytic in character: starting from a Bochner-type inequality he employed dilation techniques for positive definite kernels. Here, we give an alternative, more probabilistic proof: we use weak convergence of measures and employ Lévy's Continuity Theorem. We clarify the boundedness conditions in Holevo's theorem, and supply a simple example from quantum optics. [ABSTRACT FROM AUTHOR]

In recent decades, the de Broglie-Bohm or 'pilot wave' interpretation of quantum mechanics–especially its concept of the 'quantum trajectory'–has inspired a plethora of computational methods in molecular and chemical physics. One particularly promising subclass of such methods are the 'interacting quantum trajectory' (IQT) methods, for which an ensemble of trajectories is propagated independently of–and without any recourse to–an underlying wavefunction. In this work, an IQT version of the Pauli equation is developed–enabling spin to be incorporated into IQT theories for the first time, to the authors' knowledge. The new trajectory-based dynamical equations are then used to solve two iconic quantum problems involving spin: the 'quantum spin flipper', and the Stern-Gerlach experiment. [ABSTRACT FROM AUTHOR]

Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. We extend this technique to develop a general approach to the dynamics of quantum/classical hybrid systems. By using two coupled stochastic differential equations, we can describe a classical component and a quantum one which have their own intrinsic dynamics and which interact with each other. A mathematically rigorous construction is given, under the restriction of having a Markovian joint dynamics and of involving only bounded operators on the Hilbert space of the quantum component. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative. We show also how this theory is connected to a suitable hybrid dynamical semigroup, which reduces to a quantum dynamical semigroup in the purely quantum case and includes Liouville and Kolmogorov–Fokker–Planck equations in the purely classical case. Moreover, this semigroup allows to compare the proposed stochastic dynamics with various other proposals based on hybrid master equations. Some simple examples are constructed in order to show the variety of physical behaviors which can be described; in particular, a model presenting hidden entanglement is introduced. [ABSTRACT FROM AUTHOR]

This study develops a technology analysis to detect technological trajectories in quantum computing that can lay the foundation of a quantum industry. Study design considers data of 10,089 scientific products in 'quantum computing' over 1989–2020 period and 19,266 scientific products in 'quantum computer' over 1967–2020 period to cover all scientific production in this research field; a complementary analysis considers 8,505 patents over 1977–2020 in 'quantum computing' and 9,792 patents in 'quantum computer' over 1985–2020 period. Models of technological evolution applied here show main technological trajectories in quantum computing and computer and their rates of growth that suggest path-breaking directions in quantum technology, such as quantum optics, quantum information, quantum algorithms, quantum entanglement, quantum communication and quantum cryptography. Findings here provide information to extend the knowledge in the evolution of quantum computing and computers to support the management of these new technologies and R&D investments towards innovations generating industrial, economic and social change. [ABSTRACT FROM AUTHOR]

We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by the propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is "less chaotic." In addition, we present numerical simulations of these effects. In proving this result, we provide a characterization of a type of semi-classical defect measure we call uniform defect measures. We also prove derivative estimates of a function composed with a flow on the torus. [ABSTRACT FROM AUTHOR]

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature and torsion coefficients play a key role. Specifically, we present a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced out by a parallel-transported pure quantum state evolving unitarily under a time-dependent Hamiltonian specifying the Schrödinger evolution equation. The time-varying curvature coefficient is specified by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and measures the bending of the quantum curve. The time-varying torsion coefficient, instead, is given by the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 , orthogonal to | T 〉 and | Ψ 〉 and, in addition, measures the twisting of the quantum curve. We find that the time-varying setting exhibits a richer structure from a statistical standpoint. For instance, unlike the time-independent configuration, we find that the notion of generalized variance enters nontrivially in the definition of the torsion of a curve traced out by a quantum state evolving under a nonstationary Hamiltonian. To physically illustrate the significance of our construct, we apply it to an exactly soluble time-dependent two-state Rabi problem specified by a sinusoidal oscillating time-dependent potential. In this context, we show that the analytical expressions for the curvature and torsion coefficients are completely described by only two real three-dimensional vectors, the Bloch vector that specifies the quantum system and the externally applied time-varying magnetic field. Although we show that the torsion is identically zero for an arbitrary time-dependent single-qubit Hamiltonian evolution, we study the temporal behavior of the curvature coefficient in different dynamical scenarios, including off-resonance and on-resonance regimes and, in addition, strong and weak driving configurations. While our formalism applies to pure quantum states in arbitrary dimensions, the analytic derivation of associated curvatures and orbit simulations can become quite involved as the dimension increases. Thus, finally we briefly comment on the possibility of applying our geometric formalism to higher-dimensional qudit systems that evolve unitarily under a general nonstationary Hamiltonian. [ABSTRACT FROM AUTHOR]

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 , orthogonal to both | T 〉 and | Ψ 〉. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit | GHZ 〉 and | W 〉 states under evolution by a quantum Heisenberg Hamiltonian. [ABSTRACT FROM AUTHOR]

Einstein–Podolsky–Rosen (EPR) steering is the key resources in quantum information processing. EPR steering light sources typically obtained through spontaneous parametric down conversion below a threshold are relatively weak. Strong bright EPR steering light source can be obtained by operating the resonant cavity above the threshold. Here, the quantum steering correlations of the system above the threshold are analyzed using numerical simulations based on the quantum random trajectory method in Wigner representation. By employing the genuine multipartite EPR steering criterion, it is demonstrated that genuine bright tripartite EPR steering can be generated above the threshold, and investigate the influences of the nonlinear parameters on the genuine tripartite EPR steering. The scheme of bright EPR steering light source generated by cascaded nonlinear process can be used as a quantum repeater in quantum communication. [ABSTRACT FROM AUTHOR]

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase's resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results. [ABSTRACT FROM AUTHOR]

We consider a free-fermion chain undergoing dephasing, described by two different random-measurement protocols (unravelings): a quantum-state-diffusion and a quantum-jump one. Both protocols keep the state in a Slater-determinant form, allowing to address quite large system sizes. We find a bifurcation in the distribution of the measurement operators along the quantum trajectories, that's to say, there is a point where the shape of this distribution changes from unimodal to bimodal. The value of the measurement strength where this phenomenon occurs is similar for the two unravelings, but the distributions and the transition have different properties reflecting the symmetries of the two measurement protocols. We also consider the scaling with the system size of the inverse participation ratio of the Slater-determinant components and find a power-law scaling that marks a multifractal behaviour, in both unravelings and for any nonvanishing measurement strength. Position of the maxima of Pn vs γ for the QSD protocol. The two maxima stem continuously and symmetrically at the bifurcation point γ QSD ∼ 0.2 , with a discontinuity of the derivative. [ABSTRACT FROM AUTHOR]

In this paper, we employ the quantum trajectory Monte Carlo model to simulate the momentum distribution of Argon atoms during tunneling ionization. Our analysis illustrates the use of semi-classical models to study the changes in electron trajectories under different laser field intensities. And by studying the different subcycles, the changes of the interference pattern are observed. Our approach successfully observes the interference patterns resembling fishbone and spider stripes. We delve into the subperiodic interference structures present in the photoelectron momentum distributions. Specifically, we investigate the correlation effects of ionization trajectories on the interference fringes within the same period and in adjacent periods. Our analysis demonstrates that the holographic interference fringe results from the superposition of direct ionization trajectories and scattering trajectories. We elucidate the mechanisms underlying the formation of above-threshold ionization (ATI) ring structures and temporal double-slit interference patterns. Additionally, we investigate how wave packets perceive the Coulomb potential and its impact on interference phenomena under varying field intensities. Notably, without the Coulomb potential, the original spider-like holographic interference pattern disappears, replaced by temporal double-slit interference fringes similar to those observed within a comparable time frame. [ABSTRACT FROM AUTHOR]

Modeling the non-equilibrium dissipative dynamics of strongly interacting quantized degrees of freedom is a fundamental problem in several branches of physics and chemistry. We implement a quantum state trajectory scheme for solving Lindblad quantum master equations that describe coherent and dissipative processes for a set of strongly coupled quantized oscillators. The scheme involves a sequence of stochastic quantum jumps with transition probabilities determined by the system state and the system-reservoir dynamics. Between consecutive jumps, the wave function is propagated in a coordinate space using the multi-configuration time-dependent Hartree method. We compare this hybrid propagation methodology with exact Liouville space solutions for physical systems of interest in cavity quantum electrodynamics, demonstrating accurate results for experimentally relevant observables using a tractable number of quantum trajectories. We show the potential for solving the dissipative dynamics of finite size arrays of strongly interacting quantized oscillators with high excitation densities, a scenario that is challenging for conventional density matrix propagators due to the large dimensionality of the underlying Hilbert space. [ABSTRACT FROM AUTHOR]

We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes. [ABSTRACT FROM AUTHOR]

This paper presents a quantum formulation for classical abstract dynamical systems (ADS), defined by coupled sets of first-order differential equations. They are referred to as "abstract" because their dynamical variables can be of different interrelated natures, not necessarily corresponding to physics, such as populations, socioeconomic variables, behavioral variables, etc. A classical linear Hamiltonian can be derived for ADS by using Dirac's dynamics for singular Hamiltonian systems. Also, a corresponding first-order Schrödinger equation (which involves the existence of a system Planck constant particular of each system) can be derived from this Hamiltonian. However, Madelung's reinterpretation of quantum mechanics, followed by the Bohm and Hiley work, produces no further information about the mathematical formulation of ADS. However, a classical quadratic Hamiltonian can also be derived for ADS, as well as a corresponding second-order Schrödinger equation. In this case, the Madelung reinterpretation of quantum mechanics provides a quantum Hamiltonian that does provide the quantum formulation for ADS, which provides new quantum variables interrelated dynamically with the classical variables. An application case is presented: the one-dimensional autonomous system given by the logistic dynamics. The differences between the classical and the quantum trajectories are highlighted in the context of this application case. [ABSTRACT FROM AUTHOR]

The theoretical connections between quantum trajectories and quantum dwell times, previously explored in the context of 1D time-independent stationary scattering applications, are here generalized for multidimensional time-dependent wavepacket applications for particles with spin 1/2. In addition to dwell times, trajectory-based dwell time distributions are also developed, and compared with previous distributions based on the dwell time operator and the flux–flux correlation function. Dwell time distributions are of interest, in part because they may be of experimental relevance. In addition to standard unipolar quantum trajectories, bipolar quantum trajectories are also considered, and found to relate more directly to the dwell time (and other quantum time) quantities of greatest relevance for scattering applications. Detailed calculations are performed for a benchmark 3D spin-1/2 particle application, considered previously in the context of computing quantum arrival times. [ABSTRACT FROM AUTHOR]

Recent experimental tests of Bell inequalities confirm that entangled quantum systems cannot be described by local classical theories but still do not answer the question whether or not quantum systems could, in principle, be modeled by linear hidden variable theories. In this paper, we study the quantum trajectories of a single qubit that experiences a sequence of repeated generalized measurements. It is shown that this system, which constitutes a hidden quantum Markov model, is more likely to produce complex time correlations than any classical hidden Markov model with two output symbols. From this, we conclude that quantum physics cannot be replaced by linear hidden variable theories. Indeed, it has already been recognized that not only entanglement but also non-classical time correlations of quantum systems with quantum feedback are a valuable resource for quantum technology applications. [ABSTRACT FROM AUTHOR]

The Welsh Government's Welsh language strategy, Cymraeg: A million Welsh speakers [Welsh Government. 2017a. Cymraeg 2050: A Million Welsh Speakers. Cardiff: Welsh Government], aims to increase the numbers of Welsh speakers to one million by 2050. The creation of new Welsh speakers and immersion education form an integral part of the Welsh Government's language revitalisation strategy and this study revisits new Welsh speakers from the Rhymney Valley, South Wales in 2016/2017 a decade on from the 2006 research study [Hodges, R. 2009. "Welsh Language Use Among Young People in the Rhymney Valley." Contemporary Wales 22: 16–35. http://www.ingentaconnect.com/content/uwp/cowa/2009/00000022/00000001/art00004]. This longitudinal research provides further insights into their continuing language journeys, and indicates there has been a sustained reduction in this group's use of Welsh by 2016/2017 due to factors relating to fluency, confidence and a lack of opportunities to use Welsh. However, the results indicate that new speakers play an important role in influencing family language transmission and in increasing language awareness within the workplace. This paper calls for further longitudinal research on new Welsh speakers' language journeys so that this group may be appropriately supported as they make a crucial contribution to language revitalisation in Wales. [ABSTRACT FROM AUTHOR]

The Rivers of Reading methodology has been used previously to explore children's reading development, but very little research focusing on multilingual children exists. Similarly, reading for pleasure in multiple languages has received little attention. This paper addresses both these gaps. Seven children aged 8-13, across six multilingual families in England, constructed Rivers of Reading – a critical incident technique linked to reading resources and experiences. These were supported by three interviews per family, over a period of 10–12 months, with children sharing detailed narratives linked to their reading and languages. This data set was coded to explore what influenced children's choices for inclusion of resources in their narratives, as well as surrounding strategies and experiences. The study found that children had complex reasons for the inclusion of books and other reading material, many of which linked to what books represented for them in their language and literacy development. Asynchronous literacy development frustrated several children, but many had innovative ways to overcome these in their journey towards biliteracy. The Rivers of Reading methodology is particularly useful in exploring multilingual children's reading pathways, facilitating family discussion around frustrations, support needs, and positive memories. [ABSTRACT FROM AUTHOR]

The method of “quantum trajectories”, i.e. transitions from a pure to a pure quantum state, is a useful tool in the open quantum systems theory and applications. This method relies on the nonlinear stochastic differential equations as a dynamical model. In contrast to this, we pose the question of existence of quantum trajectories for the pure states, each of which would be a solution to a linear, deterministic master equation. It turns out that this task is rather delicate. In its full generality, the task is practically intractable. On the other hand, we do not obtain a general answer even for certain well-established and widely used Markovian processes. Only for a few models for the case of the environment on the absolute zero temperature, we obtain existence of the desired quantum trajectories. In all other cases, there is not even a single such quantum trajectory. In conjunction with the standard method of quantum trajectories, our findings pose some nontrivial challenges for the foundations of the open systems theory and some interpretational and cosmological contexts. [ABSTRACT FROM AUTHOR]

In looking at possible alternative trajectories of quantum computation it is important to revisit the famous double-slit experiment that launched inquiry into the quantum realm and arguably bootstrapped the birth of the quantum age. In the doubleslit experiment the behavior of light epitomized by dual wave-particle dynamics can be seen from both a bottom-up and top-down perspective. If viewed from the bottom-up it gives rise to the classical interpretation of superposition and entanglement, primary pillars of modern day quantum computation. If viewed from the top-down, however, photons in the double-slit experiment may also be viewed as correlated with "functional" properties of light giving rise to a different interpretation of superposition and entanglement and proposing different trajectories of quantum computing development. By taking several observer views in the double-slit experiment there are several distinct quantum computational trajectories that can arise. This brief overview paper will relate today's rendition of quantum computation with one such observer perspective and highlight several other observer perspectives leading to possible different ways to grapple with the quantum realm and different potential quantum computational architectures to realize this. [ABSTRACT FROM AUTHOR]

The exact factorization of the electron–nuclear wavefunction is applied to the study of photo-isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects. Analysis of the potentials is, thus, essential—when possible—to predict the time-dependent behavior of the system of interest. In this work, we employ the exact time-dependent potentials, available for the numerically exactly solvable model used here, to propagate quantum nuclear trajectories representing the isomerization reaction of the retinal chromophore. The quantum trajectories are the best possible trajectory-based description of the reaction when using the exact-factorization formalism and, thus, allow us to assess the performance of the coupled-trajectory, fully approximate schemes derived from the exact-factorization equations. [ABSTRACT FROM AUTHOR]

Due to its capacity to handle data in fundamentally novel ways and produce computational powers that were previously unreachable, the multidisciplinary subject of quantum computing has recently grown quickly and attracted significant interest from both academia and business. The full impact of quantum computing on healthcare has not yet been fully explored, despite its promise. The technology makes several important security recommendations. Healthcare has issues and obligations related to data privacy, and security is a crucial component. Quantum computing and its applications have positive effects on healthcare. This tool is useful for making healthcare predictions about a person. The models of technological evolution that were used in this study show the main technological trajectories in quantum computing (QC) as well as computers as well as their rates of development, which point to ground-breaking directions in quantum technology like quantum optics, quantum data, quantum method, quantum entanglement, quantum communication, and quantum cryptography with sports technology. [ABSTRACT FROM AUTHOR]

This study explores the quantum leapfrog mechanism within the context of quantum finance and presents a new interpretation of established financial models through a quantum perspective. In quantum physics, the well-documented phenomenon of particles tunneling through energy barriers has a parallel in finance. We propose a quantum financial leapfrog model in which asset prices make quantum leaps, penetrating market "energy barriers" in non-sequential advances. By leveraging the Hamiltonian operator and the Schrödinger equation, our approach simulates the dynamics of asset prices in a manner akin to the trajectories of particles in quantum mechanics. We draw an analogy between financial markets and gravitational fields, and from this we derive energy equations for pricing orbits. Using path integration techniques, we map out potential price transitions between these orbits, which are guided by the calculation of minimal energy barriers. Furthermore, we introduce a market "propagator" that aligns with the uncertainty principle, identifying the optimal price pathways. Our findings provide new insights and methodologies for navigating the complexities of financial markets, underscoring the significant potential of quantum approaches in the field of finance. These findings have theoretical implications for a variety of market stakeholders, offering strategic guidance and a reference point. We expect that the advancement of the quantum financial leapfrog theory will refine analytical methods and enhance investment strategies in practical financial applications. [ABSTRACT FROM AUTHOR]

We quantize the Oppenheimer–Snyder model of black holes using the integral quantization method. We treat spatial and temporal coordinates on the same footing at both the classical and quantum levels. Our quantization resolves or smears the singularities of the classical curvature invariants. Quantum trajectories with bounces can replace singular classical trajectories. The considered quantum black hole may have finite bouncing time. As a by-product, we obtain the resolution of the gravitational singularity of the Schwarzschild black hole at the quantum level. [ABSTRACT FROM AUTHOR]

In this study, we investigate the autodetachment dynamics of the 1-nitropropane anion after vibrational excitation of the energetically lowest C–H stretching mode using our recently developed extended quantum classical surface hopping approach including the detachment continuum. Therein the detachment from an electronic bound anion state is treated as a nonadiabatic transition into discretized detachment continuum states for an ensemble of classical nuclear trajectories propagated on quantum mechanical potential energy surfaces. The initial ensemble is obtained by sampling a phase space distribution accounting for the vibrational excitation of the C–H stretching mode of the molecule to match the experimental conditions. The simulated kinetic energy distribution of the ejected electrons reproduces characteristic features of the available experimental data. Analysis of the nuclear dynamics points out that the approach to neutral-like geometries with decreased pyramidalization angle of the NO 2 group and reduced the N–O bond lengths are the crucial factors enhancing the ultrafast autodetachment process in vibrationally excited 1-nitropropane. This is facilitated when the dipole-bound first excited state of the anion is populated, which is structurally similar to the neutral system. Although only a small transient population of this state is observed, it acts as an efficient doorway to the detachment continuum and is responsible for a significant amount of the ejected electrons. [ABSTRACT FROM AUTHOR]

We study order, chaos and ergodicity in the Bohmian trajectories of a 2D quantum harmonic oscillator. We first present all the possible types (chaotic, ordered) of Bohmian trajectories in wavefunctions made of superpositions of two and three energy eigenstates of the oscillator. There is no chaos in the case of two terms and in some cases of three terms. Then, we show the different geometries of nodal points in bipartite Bohmian systems of entangled qubits. Finally, we study multinodal wavefunctions and find that a large number of nodal points does not always imply the dominance of chaos. We show that, in some cases, the Born distribution is dominated by ordered trajectories, something that has a significant impact on the accessibility of Born's rule P = | Ψ | 2 by initial distributions of Bohmian particles with P 0 ≠ | Ψ 0 | 2 . [ABSTRACT FROM AUTHOR]

Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs—in principle exact in FMS—are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born–Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation. [ABSTRACT FROM AUTHOR]

Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Under purification and irreducibility assumptions, these Markov processes admit a unique invariant measure — see Benoist et al. (2019). In this article we prove finer limit theorems such as Law of Large Numbers (LLN), Functional Central Limit Theorem, Law of Iterated Logarithm and Moderate Deviation Principle. The proof of the LLN is based on Birkhoff's ergodic theorem and an analysis of harmonic functions. The other theorems are proved using martingale approximation of empirical sums. [ABSTRACT FROM AUTHOR]

We report an efficient approach to accurately and efficiently compute transmission probabilities in resonant deep tunneling regime. Dynamical systems subjects to this phenomenon prove hard to simulate numerically even with exact methods, which motivates new methodological developments owing to the impact resonant phenomena have in several processes such as chemical reactions and electronic transport. Our approach is based on the original reformulation of stationary quantum scattering as the propagation of a quantum trajectory in extended phase space. The present paper discusses in detail the node problem occurring to the time-independent quantum trajectory method in this very challenging situation, and introduces an efficient semi-analytical node-skipping scheme to circumvent expensive numerical integration in their vicinity. We illustrate how this numerical extension allows to treat all regimes of quantum tunneling with great versatility by comparison to existing approaches of the litterature. The quantum trajectory, thus, represents a very promising tool for the study of complex chemical reactions characterized by resonant tunneling effect. [ABSTRACT FROM AUTHOR]

We compare algorithms to sample initial positions and momenta of a molecular system for classical trajectory simulations. We aim at reproducing the phase space quantum distribution for a vibrational eigenstate, as in Wigner theory. Moreover, we address the issue of controlling the total energy and the energy partition among the vibrational modes. In fact, Wigner's energy distributions are very broad, quite at variance with quantum eigenenergies. Many molecular processes depend sharply on the available energy, so a better energy definition is important. Two approaches are introduced and tested: the first consists in constraining the total energy of each trajectory to equal the quantum eigenenergy. The second approach modifies the phase space distribution so as to reduce the deviation of the single mode energies from the correct quantum values. A combination of the two approaches is also presented. [ABSTRACT FROM AUTHOR]

The theoretical connections between quantum trajectories and quantum dwell times, previously explored in the context of 1D time-independent stationary scattering applications, are here generalized for multidimensional time-dependent wavepacket applications for particles with spin 1/2. In addition to dwell times, trajectory-based dwell time distributions are also developed, and compared with previous distributions based on the dwell time operator and the flux–flux correlation function. Dwell time distributions are of interest, in part because they may be of experimental relevance. In addition to standard unipolar quantum trajectories, bipolar quantum trajectories are also considered, and found to relate more directly to the dwell time (and other quantum time) quantities of greatest relevance for scattering applications. Detailed calculations are performed for a benchmark 3D spin-1/2 particle application, considered previously in the context of computing quantum arrival times.

An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'. [ABSTRACT FROM AUTHOR]

The author shows by embodying the Einstein equivalence principle—local Poincaré invariance—and general covariance in quantum theory that wave‐function spreading rules out the universality of free fall, that is, the free‐fall trajectory of a quantum (test) particle depends on its internal properties. The author provides a quantitative estimate of the free‐fall non‐universality in terms of the Eötvös parameter, which turns out to be measurable in atom interferometry. [ABSTRACT FROM AUTHOR]

In the present work we study the critical points of the Bohmian quantum flow, namely the nodal point and its associated X-point, which are responsible for the generation of chaos in Bohmian trajectories. In the first part of the paper we find an analytical equation for the position of the X-point in a planar 2-d Bohmian system with a single nodal point and test its accuracy numerically. We then calculate its asymptotic curves and comment on the way they affect the evolution of the nearby Bohmian trajectories. In the second part we present our first results on the position of the X-point and its asymptotic curves in a 3-d partially integrable system, where the Bohmian trajectories evolve on spherical surfaces. [ABSTRACT FROM AUTHOR]

A study of open quantum systems and dynamical regimes that emerge in such systems is an actively developing field of the theoretical and experimental physics. Although the bifurcation analysis and the theory of dynamical chaos are very important branches of nonlinear dynamics, their use for describing the processes occurring in open dissipative quantum systems has been restricted until recently. In this work, we present a review of recent results on the generalization of the methods of the oscillation theory for such systems. We present quantum analogs of the classical bifurcations, which are observed in the structural changes of the asymptotic density matrix, namely, the pitchfork bifurcation, saddle-node bifurcation, transition to quantum chaos via a period-doubling cascade, and the Neimark–Sacker bifurcation. We also consider numerical characteristics of dissipative quantum chaos. The largest quantum Lyapunov exponent, which is based on analyzing the divergence rate of the initially close quantum trajectories, allows one to numerically study the structure of the regular and chaotic domains of various open quantum systems. Numerical characteristics of dissipative quantum chaos, which can be observed in a physical experiment, are also considered. It is shown that the qualitatively different statistics of the distribution of times between the successive emissions of individual photons by the system take place for the regular and chaotic regimes in an open quantum cavity. [ABSTRACT FROM AUTHOR]

We present universal statistical relations between the center of mass of a quantum ensemble and its sub-ensembles when the Bohmian trajectories of the particles are distorted. These relations break the additivity property of the expectation into subadditivity of the distorted expectation, which obtains an evident difference between the various ways to infer quantum expectations. The results do not depend on the form of the Hamiltonian, and do not have a classical parallel. While an experimentalist can arrange the distortion of the trajectories to produce the proposed relations, such distortion may naturally appear in standard experimental setups. [ABSTRACT FROM AUTHOR]

We present qLEET, an open-source Python package for studying parameterized quantum circuits (PQCs), which are widely used in various variational quantum algorithms (VQAs) and quantum machine learning (QML) algorithms. qLEET enables computation of properties such as expressibility and entangling power of a PQC by studying its entanglement spectrum and the distribution of parameterized states produced by it. Furthermore, it allows users to visualize the training trajectories of PQCs along with high-dimensional loss landscapes generated by them for different objective functions. It supports quantum circuits and noise models built using popular quantum computing libraries such as Qiskit, Cirq, and PyQuil. In our work, we demonstrate how qLEET provides opportunities to design and improve hybrid quantum-classical algorithms by utilizing intuitive insights from the ansatz capability and structure of the loss landscape. [ABSTRACT FROM AUTHOR]

We study the evolution of a quantum particle in a harmonic potential whose position and momentum are repeatedly monitored. A back-action of measuring devices is accounted for. Our model utilizes a generalized measurement corresponding to the positive operator-valued measure. We assume that upon measurement, the particle’s wavefunction is projected onto one of the possible detector states depending on the observed result. We chose these post-measurement states to be moving Gaussian wavepackets. The wavefunction quantum Monte Carlo formalism is used to simulate single quantum trajectories of the particle. We show how classical trajectories emerge in the course of observation and study in detail the dispersion of position and momentum of the particle. [ABSTRACT FROM AUTHOR]

In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of nonlinear, coupled partial differential equations simultaneously. We opt for a fundamentally different route. We first derive a general closed form expression for the Path Integral propagator valid for any general potential as a functional of the corresponding classical path. The method is exact and is applicable in many dimensions as well as multi-particle cases. This, then, is used to compute the Quantum Potential, which, in turn, can generate the Quantum Trajectories. As a model application to illustrate the method, we solve for the double-well potential, both analytically (using a perturbative approach) and numerically (exact solution). Using this we delve into seeking insight into Quantum Tunnelling. The work formally bridges the Path Integral approach with Quantum Fluid Dynamics, an issue of fundamental importance. [ABSTRACT FROM AUTHOR]