Self-calibrated 3D differential phase contrast microscopy with optimized illumination.

3D phase imaging recovers an object's volumetric refractive index from intensity and/or holographic measurements. Partially coherent methods, such as illumination-based differential phase contrast (DPC), are particularly simple to implement in a commercial brightfield microscope. 3D DPC acquires images at multiple focus positions and with different illumination source patterns in order to reconstruct 3D refractive index. Here, we present a practical extension of the 3D DPC method that does not require a precise motion stage for scanning the focus and uses optimized illumination patterns for improved performance. The user scans the focus by hand, using the microscope's focus knob, and the algorithm self-calibrates the axial position to solve for the 3D refractive index of the sample through a computational inverse problem. We further show that the illumination patterns can be optimized by an end-to-end learning procedure. Combining these two, we demonstrate improved 3D DPC with a commercial microscope whose only hardware modification is LED array illumination.

Asymmetric temperature equilibration with heat flow from cold to hot in a quantum thermodynamic system.

A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to "thermal equilibrium" at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. A description is given in which a recently defined quantum entropy S_{univ}^{Q} for a pure state "universe" continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account ΔS_{univ}^{Q}≥0 holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease ΔS^{vN}<0 on the way to the asymmetric equilibrium.

Soft Mode Metal-Linker Dynamics in Carboxylate MOFs Evidenced by Variable-Temperature Infrared Spectroscopy.

Through comprehensive analysis of carboxylate-based metal-organic frameworks (MOFs), we present general evidence that challenges the common perception of MOF metal-linker bonds being static. Structural dynamics in MOFs, however, typically refers to the "breathing" behavior of cavities, where pores open and close in response to guest molecules, and to the transient binding of guest molecules, but dynamic bonding would explain important MOF phenomena in catalysis, postsynthetic exchange, negative thermal expansion, and crystal growth. Here, we demonstrate, through use of variable-temperature diffuse reflectance infrared Fourier transform spectroscopy (VT-DRIFTS) aided by ab initio plane wave density functional theory, that similar evidence for melting behavior in zeolitic imidazolate frameworks (ZIFs), i.e., reversible metal-linker bonding, driven by specific vibrational modes, can be observed for carboxylate MOFs by monitoring the red-shifts of carboxylate stretches coupled to anharmonic metal-carboxylate oscillators. To demonstrate the generality of these findings, we investigate a wide class of carboxylate MOFs that includes iconic examples with diverse structures and metal-linker chemistry. As the very vibrations invoked in ZIF melting but heretofore unobserved for carboxylate MOFs, these metal-linker dynamics resemble the ubiquitous soft modes that trigger important phase transitions in diverse classes of materials while offering a fundamentally new perspective for the design of next-generation metal-organic materials.

Simulating quantum thermodynamics of a finite system and bath with variable temperature.

We construct a finite bath with variable temperature for quantum thermodynamic simulations in which heat flows between a system S and the bath environment E in time evolution of an initial SE pure state. The bath consists of harmonic oscillators that are not necessarily identical. Baths of various numbers of oscillators are considered; a bath with five oscillators is used in the simulations. The bath has a temperaturelike level distribution. This leads to definition of a system-environment microcanonical temperature T_{SE}(t) which varies with time. The quantum state evolves toward an equilibrium state which is thermal-like, but there is significant deviation from the ordinary energy-temperature relation that holds for an infinite quantum bath, e.g., an infinite system of identical oscillators. There are also deviations from the Einstein quantum heat capacity. The temperature of the finite bath is systematically greater for a given energy than the infinite bath temperature, and asymptotically approaches the latter as the number of oscillators increases. It is suggested that realizations of these finite-size effects may be attained in computational and experimental dynamics of small molecules.

Quantum Microcanonical Entropy, Boltzmann's Equation, and the Second Law.

A recent proposal for a quantum entropy S univ Q for a pure state of a system-environment "universe" is developed to encompass a much more realistic temperature bath. Microcanonical entropy is formulated in the context of the idea of a quantum microcanonical shell. The fundamental relation that holds for the classical microcanonical ensemble - TΔ S univ = Δ F sys is tested for the quantum entropy Δ S univ Q in numerical simulations. It is found that there is "excess entropy production" Δ S x due to quantum time-energy uncertainty and spreading of states in the zero-order basis. The excess entropy production is found numerically to become small as the magnitude of the system-environment coupling nears zero, as one would hope for in the limit of the classical microcanonical ensemble. The quantum microcanonical ensemble and the new "universe entropy" thereby appear as well-founded concepts poised to serve as a point of departure for time-dependent processes in which excess entropy production is physically significant.

Kinetic Model of Translational Autoregulation.

We investigate the dynamics of a kinetic model of inhibitory autoregulation as exemplified when a protein inhibits its own production by interfering with its mRNA, known in molecular biology as translational autoregulation. We first show how linear models without feedback set the stage with a nonequilibrium steady state that constitutes the target of the regulation. However, regulation in the simple linear model is far from optimal. The negative feedback mechanism whereby the protein "jams" the mRNA greatly enhances the effectiveness of the control, with response to perturbation that is targeted, rapid, and metabolically efficient. Understanding the full dynamics of the system phase space is essential to understanding the autoregulation process.

Motion-resolved quantitative phase imaging.

The temporal resolution of quantitative phase imaging with Differential Phase Contrast (DPC) is limited by the requirement for multiple illumination-encoded measurements. This inhibits imaging of fast-moving samples. We present a computational approach to model and correct for non-rigid sample motion during the DPC acquisition in order to improve temporal resolution to that of a single-shot method and enable imaging of motion dynamics at the framerate of the sensor. Our method relies on the addition of a simultaneously-acquired color-multiplexed reference signal to enable non-rigid registration of measurements prior to phase retrieval. We show experimental results where we reduce motion blur from fast-moving live biological samples.

Node-Pore Coded Coincidence Correction: Coulter Counters, Code Design, and Sparse Deconvolution.

We present a novel method to perform individual particle (e.g. cells or viruses) coincidence correction through joint channel design and algorithmic methods. Inspired by multiple-user communication theory, we modulate the channel response, with Node-Pore Sensing, to give each particle a binary Barker code signature. When processed with our modified successive interference cancellation method, this signature enables both the separation of coincidence particles and a high sensitivity to small particles. We identify several sources of modeling error and mitigate most effects using a data-driven self-calibration step and robust regression. Additionally, we provide simulation analysis to highlight our robustness, as well as our limitations, to these sources of stochastic system model error. Finally, we conduct experimental validation of our techniques using several encoded devices to screen a heterogeneous sample of several size particles.

BARKER-CODED NODE-PORE RESISTIVE PULSE SENSING WITH BUILT-IN COINCIDENCE CORRECTION.

A resistive pulse sensing device is able to extract quantities such as concentration and size distribution of particles, e.g. cells or microspheres, as they flow through the device's sensor region, i.e. channel, in an electrolyte solution. The dynamic range of detectable particle sizes is limited by the channel dimensions. In addition, signal interference from multiple particles transiting the channel simultaneously, i.e. coincidence event, further hinder the dynamic range. Coincidence data is often considered unusable and is discarded, reducing the throughput and introducing possible biases and errors into the distributions. Here, we propose a two-step solution. We code the channel such that the system response results in a Manchester encoded Barker-Code sequence, allowing us to take advantage of the code's pulse compression properties. We pose the parameter estimation problem as a sparse inverse problem, which enables estimation of particle sizes and velocities while resolving coincidences, and solve it with a successive interference cancellation algorithm. We introduce modifications to the algorithm to account for device fabrication variations and natural stochastic variations in flow. We demonstrate the ability to resolve coincidences and possible increases in the device's dynamic range by screening particles of different size through a Barker encoded device.

Time dependent quantum thermodynamics of a coupled quantum oscillator system in a small thermal environment.

Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.

Isotope effect in normal-to-local transition of acetylene bending modes.

The normal-to-local transition for the bending modes of acetylene is considered a prelude to its isomerization to vinylidene. Here, such a transition in fully deuterated acetylene is investigated using a full-dimensional quantum model. It is found that the local benders emerge at much lower energies and bending quantum numbers than in the hydrogen isotopomer HCCH. This is accompanied by a transition to a second kind of bending mode called counter-rotator, again at lower energies and quantum numbers than in HCCH. These transitions are also investigated using bifurcation analysis of two empirical spectroscopic fitting Hamiltonians for pure bending modes, which helps to understand the origin of the transitions semiclassically as branchings or bifurcations out of the trans- and cis-normal bend modes when the latter become dynamically unstable. The results of the quantum model and the empirical bifurcation analysis are in very good agreement.

Visualizing the zero order basis of the spectroscopic Hamiltonian.

Recent works have shown that a generalization of the spectroscopic effective Hamiltonian can describe spectra in surprising regions, such as isomerization barriers. In this work, we seek to explain why the effective Hamiltonian is successful where there was reason to doubt that it would work at all. All spectroscopic Hamiltonians have an underlying abstract zero-order basis (ZOB) which is the "ideal" basis for a given form and parameterization of the Hamiltonian. Without a physical model there is no way to transform this abstract basis into a coordinate representation. To this end, we present a method of obtaining the coordinate space representation of the abstract ZOB of a spectroscopic effective Hamiltonian. This method works equally well for generalized effective Hamiltonians that encompass above-barrier multiwell behavior, and standard effective Hamiltonians for the vicinity of a single potential minimum. Our approach relies on a set of converged eigenfunctions obtained from a variational calculation on a potential surface. By making a one-to-one correspondence between the energy eigenstates of the effective Hamiltonian and those of the coordinate space Hamiltonian, a physical representation of the abstract ZOB is calculated. We find that the ZOB basis naturally adjusts its complexity depending on the underlying nature of phase space, which allows spectroscopic Hamiltonians to succeed for systems sampling multiple stationary points.

Effective Hamiltonian for femtosecond vibrational dynamics.

Time propagation of zero-order states of an effective spectroscopic Hamiltonian is tested against femtosecond time dependent dynamics of adiabatic wavepackets evolving on a model potential energy surface for two coupled modes of the radical HO(2) with multiple potential wells and above barrier motion. A generalized Hamiltonian which breaks the usual conserved polyad action by including extra resonance couplings (V(2:1) and V(3:1)) successfully describes the time evolution after the further addition of two "ultrafast" couplings. These new couplings are a nonresonant coupling a(1)a(2)+a(1)(†)a(2)(†) and a resonant coupling V(1:1) that functions as an ultrafast term because the system is far from 1:1 frequency resonance.

Detailed analysis of polyad-breaking spectroscopic Hamiltonians for multiple minima with above barrier motion: isomerization in HO2.

We present a two-dimensional model for isomerization in the hydroperoxyl radical (HO(2)). We then show that spectroscopic fitting Hamiltonians are capable of reproducing large scale vibrational structure above isomerization barriers. Two resonances, the 2:1 and 3:1, are necessary to describe the pertinent physical features of the system and, hence, a polyad-breaking Hamiltonian is required. We further illustrate, through the use of approximate wave functions, that inclusion of additional coupling terms yields physically unrealistic results despite an improved agreement with the exact energy levels. Instead, the use of a single diagonal term, rather than "extra" couplings, yields good fits with realistic results. Insight into the dynamical nature of isomerization is also gained through classical trajectories. Contrary to physical intuition the bend mode is not the initial "reaction mode," but rather isomerization requires excitation in both the stretch and bend modes. The dynamics reveals a Farey tree formed between the 2:1 and 3:1 resonances with the prominent 5:2 (2:1 + 3:1) feature effectively dividing the tree into portions. The 3:1 portion is associated with isomerization, while the 2:1 portion leads to "localization" and perhaps dissociation at higher energies than those considered in this work. Simple single resonance models analyzed on polyad phase spheres are able to account in a qualitative way for the spectral, periodic orbit, and wave function patterns that we observe.

Communication: Effective spectroscopic Hamiltonian for multiple minima with above barrier motion: Isomerization in HO(2).

We present a two-dimensional potential surface for the isomerization in the hydroperoxyl radical HO(2) and calculate the vibrational spectrum. We then show that a simple effective spectroscopic fitting Hamiltonian is capable of reproducing large scale vibrational spectral structure above the isomerization barrier. Polyad breaking with multiple resonances is necessary to adequately describe the spectral features of the system. Insight into the dynamical nature of isomerization related to the effective Hamiltonian is gained through classical trajectories on the model potential. Contrary to physical intuition, the bend mode is not a "reaction mode," but rather isomerization requires excitation in both stretch and bend. The dynamics reveals a Farey tree formed from the 2:1 and 3:1 resonances, corresponding to the resonance coupling terms in the effective Hamiltonian, with the prominent 5:2 (2:1+3:1) feature dividing the tree into parts that we call the 3:1 and 2:1 portions.

Bifurcation phase diagram for C(2)H(2) bending dynamics has a tetracritical point with spectral patterns.

Critical points and bifurcations are considered for the acetylene effective Hamiltonian in the polyad space of total bend and vibrational angular momentum quantum numbers [N(b), [Formula: see text]]. A "phase diagram" is constructed for the surface of minimum energy critical points. The phases denote vibrational modes of different character, including new types of anharmonic modes born in bifurcations from the ordinary normal modes. A tetracritical point is the outstanding feature of the diagram. Patterns in the energy levels are considered. We start with a search for "defects" in the lattice of energy levels, similar to what is found with quantum monodromy in integrable systems. No such pattern is found. Instead, patterns are predicted in the first and second derivatives of the energy with respect to the quantum numbers, by close analogy to the theory of phase transitions. The tetracritical point finds striking manifestation in these patterns. This may be amenable to experimental test. Moreover, the minimum energy path, analogous to the reaction path, has derivative patterns that can already be compared with experiment. Agreement of theory and experiment is found within experimental error.

Spectral intensity patterns and vibrational phase space structure.

We examine patterns of absorption intensity in two-mode systems with a 2:1 Fermi resonance in an intensity model based on the effective fitting Hamiltonian. We relate these patterns to the Fermi resonance phase space structure and catastrophe map. Each of the four zones of the catastrophe map has a phase sphere structure with a certain number of distinct regions. For each zone, we find that for every region on the sphere, there is a distinct region in the intensity pattern.

Catastrophe map and the role of individual resonances in C2H2 bending dynamics.

A catastrophe map analysis is presented of the birth of new modes in bifurcations of the normal modes of the acetylene pure bending system using a spectroscopic fitting Hamiltonian that is nonseparable with multiple resonances. The map splits into two independent maps for subspaces defined by the resonance frequency conditions. Nonetheless, both resonance couplings act on each of the resonance subspaces, since the system is nonseparable. With this generalized notion of independent resonances, the map accounts for partial resemblances to single resonance models but maintains the full complexity inherent in the nonseparable Hamiltonian. This suggests a way to extend both the generalized Fermi resonance and the catastrophe map analysis to systems with higher degrees of freedom.

Critical points bifurcation analysis of high-l bending dynamics in acetylene.

The bending dynamics of acetylene with pure vibrational angular momentum excitation and quantum number l not = 0 are analyzed through the method of critical points analysis, used previously [V. Tyng and M. E. Kellman, J. Phys. Chem. B 110, 18859 (2006)] for l = 0 to find new anharmonic modes born in bifurcations of the low-energy normal modes. Critical points in the reduced phase space are computed for continuously varied bend polyad number N(b) = n(4) + n(5) as l = l(4) + l(5) is varied between 0 and 20. It is found that the local L, orthogonal O, precessional P, and counter-rotator CR families persist for all l. In addition, for l > or = 8, there is a fifth family of critical points which, unlike the previous families, has no fixed relative phase ("off great circle" OGC). The concept of the minimum energy path in the polyad space is developed. With restriction to l=0 this is the local mode family L. This has an intuitive relation to the minimum energy path or reaction mode for acetylene-vinylidene isomerization. With l > or = 0 included as a polyad number, the l = 0 minimum energy path forms a troughlike channel in the minimum energy surface in the polyad space, which consists of a complex mosaic of L, O, and OGC critical points. There is a division of the complete set of critical points into layers, the minimum energy surface forming the lowest.

Effective Hamiltonian for chaotic coupled oscillators.

A generalized effective fitting Hamiltonian is tested against a model system of highly excited coupled Morse oscillators. At energies approaching dissociation, a very few resonance couplings in addition to the standard 1:1 and 2:2 couplings of the Darling-Dennison Hamiltonian suffice to fit the spectrum and match the large-scale features of the mixed regular and chaotic phase spaces, consisting of resonance zones organized around periodic orbits of low order that break the total polyad action.