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Here, homogeneous and heterogeneous catalysts have advantages and disadvantages. Molecular catalysts supported on heterogeneous materials have the potential to combine the advantages of both fields. Jabbour et al. report a detailed study of the 3D structure of an Ir-catalyst on silica.
Here, 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.
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Below are all of the pictures for the CNEC and CVT measurements performed at the DAF in July 2016. In total there are 165 pictures. The photos on pages 2-105 were taken during the first week of measurements and the photos on pages 106-165 were taken during the second week of measurements. Many photos are applicable to both sets, which is why it is best to keep the entire set together. For most configurations, a description of the configuration was written on a white board; photos of the measurement setup were taken, then a photo of the white board was taken. For example, the pictures on pages 6-19 (which precede a white board picture on page 20) are of the configuration with Rocky Flats Shells 1-2 surrounded by 4 AmLi sources, which is listed on the white board picture on page 20. In some cases, the white board picture precedes the configuration pictures.
The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact N-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC (IP-DMQMC) method that overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation, thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.
Gas hydrate formation is rarely an issue during continuous production conditions. Unplanned and/or extended shut-downs comprise the majority of scenarios where overlapping concern and uncertainty for gas hydrate blockages exist. To date, most experimental studies and theoretical analysis of gas hydrate formation derive from the steady-state conceptual picture. Yet, significant distinctions induced by phase separation and prolonged cooling suggest an altered conceptual picture is required for transient shut-in/restart operations. To address this outstanding issue, this work presents a conceptual picture for the base case of a non-surface active hydrocarbon undergoing cold restart without enacted mitigation efforts. First, phase separation upon shut-in leads to the localization of gas hydrate ingredients due to fluids density differences and pipeline inclination. Cooling to the seafloor temperature, then, induces gas hydrate film formation at the hydrocarbon interface and maximizes subcooling, resulting in rapid and confined gas hydrate growth occurring upon restart. Furthermore, this ultimately leads to plugging dominated by the deposition of porous, low conversion gas hydrate masses. Direct visual observations and results from Raman spectroscopy, hydrate contact angle and film growth, micromechanical force apparatus, rocking cell, and flow loop studies support the mechanisms outlined within each step. Similar to the influence provided by the original Colorado School of Mines steady-state conceptual picture that was introduced about 15 years ago, this transient counterpart builds a foundation that could inspire new directions of hydrate research and analysis in areas where uncertainty abounds.
Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schrödinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can be achieved explicitly in the equations of motion by "gauging" the global unitary invariance of quantum mechanics into a local gauge invariance. That is, expectation values $\langle \psi|A|\psi \rangle$ are invariant under a global unitary transformation acting on the wavefunction $|\psi\rangle \to U |\psi\rangle$ and operators $A \to U A U^\dagger$, and we show that it is possible to gauge this global invariance into a local gauge invariance. To do this, we replace the wavefunction with a collection of local wavefunctions $|\psi_J\rangle$, one for each patch of space $J$. The collection of spatial patches is chosen to cover the space; e.g. we could choose the patches to be single qubits or nearest-neighbor sites on a lattice. Local wavefunctions associated with neighboring pairs of spatial patches $I$ and $J$ are related to each other by dynamical unitary transformations $U_{IJ}$. The local wavefunctions are local in the sense that their dynamics are local. That is, the equations of motion for the local wavefunctions $|\psi_J\rangle$ and connections $U_{IJ}$ are explicitly local in space and only depend on nearby Hamiltonian terms. (The local wavefunctions are many-body wavefunctions and have the same Hilbert space dimension as the usual wavefunction.) We call this picture of quantum dynamics the gauge picture since it exhibits a local gauge invariance. The local dynamics of a single spatial patch is related to the interaction picture, where the interaction Hamiltonian consists of only nearby Hamiltonian terms. We can also generalize the explicit locality to include locality in local charge and energy densities.
In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron–electron correlations and might give a bound on the correlation energy. Furthermore, the results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron–electron correlations.
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic advantages for some Hamiltonians, but incurs prohibitive constant factors and is incompatible with methods like qubitization. We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations over known algorithms. These approaches show asymptotic improvements over the individual methods that comprise them and further make interaction picture simulation methods practical in the near term. Physical applications of these hybridized methods yield a gate complexity scaling as log 2 ⁡ Λ in the electric cutoff Λ for the Schwinger Model and independent of the electron density for collective neutrino oscillations, outperforming the scaling for all current algorithms with these parameters. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter λ used to impose an energy cost on time-evolution into an unphysical subspace.
They say a picture is worth a thousand words. My response to that? A picture is also worth a thousand data points! However, not all pictures are created equal: a good visualization tells a story and helps the viewer to understand the data. A polished visualization can help you In the first half of this workshop, I will discuss the seven sins of visualization, and how to avoid them. I will introduce guidelines on how to make excellent visualization choices. In the second half of the workshop, I will guide the participants in an interactive session on creating meaningful visualizations with just a few lines of code.
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Atomic Bose–Einstein condensates (BECs) can be viewed as macroscopic objects where atoms form correlated atom clusters to all orders. Therefore, the presence of a BEC makes the direct use of the cluster-expansion approach–lucrative e.g. in semiconductor quantum optics–inefficient when solving the many-body kinetics of a strongly interacting Bose. An excitation picture is introduced with a nonunitary transformation that describes the system in terms of atom clusters within the normal component alone. The nontrivial properties of this transformation are systematically studied, which yields a cluster-expansion friendly formalism for a strongly interacting Bose gas. Its connections and corrections to the standard Hartree–Fock–Bogoliubov approach are discussed and the role of the order parameter and the Bogoliubov excitations are identified. The resulting interaction effects are shown to visibly modify number fluctuations of the BEC. Even when the BEC has a nearly perfect second-order coherence, the BEC number fluctuations can still resolve interaction-generated non-Poissonian fluctuations. - Highlights: • Excitation picture expresses interacting Bose gas with few atom clusters. • Semiconductor and BEC many-body investigations are connected with cluster expansion. • Quantum statistics of BEC is identified in terms of atom clusters. • BEC number fluctuations show extreme sensitivity to many-body correlations. • Cluster-expansion friendly framework is established for an interacting Bose gas.
We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this “difference self-consistent field (dSCF)” picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TERACHEM SCF implementation.
The multilayer multiconfiguration time-dependent Hartree method is applied in an interaction picture to simulate dynamics of the spin-boson model in the reaction-coordinate representation. The use of the interaction picture allows a more effective description of correlation effects, especially when the coupling strength between the reaction coordinate and the bath is very strong. Examples show that in most physical regimes the efficiency is improved significantly, in some cases up to several orders of magnitude. This opens up new avenues for studying quantum dynamical problems.
A consistent and unified picture for critical phenomena of charged AdS black holes in f ( R ) gravity is drawn in this paper. Firstly, we investigate the phase transition in canonical ensemble. We derive the explicit solutions corresponding to the divergence of C {sub Q} . The two solutions merge into one when the condition Q {sub c} =√(−1/3 R {sub 0}) is satisfied. The curve of specific heat for Q < Q {sub c} has two divergent points and can be divided into three regions. Both the large radius region and the small radius region are thermodynamically stable with positive specific heat while the medium radius region is unstable with negative specific heat. However, when Q > Q {sub c} , the specific heat is always positive, implying the black holes are locally stable and no phase transition will take place. Secondly, both the T − r {sub +} curve and T − S curve f ( R ) AdS black holes are investigated and they exhibit Van der Vaals like behavior as the P − v curve in the former research. Critical physical quantities are obtained and they are consistent with those derived from the specific heat analysis. We carry out numerical check of Maxwell equal area law for the cases Q =0.2 Q {sub c} , 0.4 Q {sub c} , 0.6 Q {sub c} , 0.8 Q {sub c} . The relative errors are amazingly small and can be negligible. So the Maxwell equal area law holds for T − S curve of f ( R ) black holes. Thirdly, we establish geometrothermodynamics for f ( R ) AdS black hole to examine the phase structure. It is shown that the Legendre invariant scalar curvature R would diverge exactly where the specific heat diverges. To summarize, the above three perspectives are consistent with each other, thus providing a unified picture which deepens the understanding of critical phenomena of f ( R ) AdS black holes.