A lossless, exact compaction of the time-evolved state of the quantum dynamical system of a perturbed anharmonic molecule is demonstrated using dynamical symmetries. The density matrix of the anharmonic molecule is a linear combination of these symmetries, and it remains so as a time-dependent perturbation is applied. Accurate, unitary-but-approximate, and thereby irreversible compaction is further shown using fewer symmetries, and the fidelity of this lossy compaction is quantified. Perturbations are typically linear in the operators of a Lie algebra. For a Hamiltonian that is also linear, one knows well how to reversibly compact the state of a dynamical system. However, anharmonic vibrations have a finite number of unequally spaced energy levels, and a good description of their spectra typically requires an algebraic-type Hamiltonian that is bilinear in the operators of a Lie algebra. For a bilinear Hamiltonian we show how a matrix-based approach allows us to compact both the populations and the coherences, either exactly reversibly or inexactly irreversibly, with fewer symmetries. A forced Morse oscillator is used as an explicit analytical and numerical example covering the entire range of dynamics from the sudden to the adiabatic limits.

We show that the quantum force that the electrons in a molecule exert on the nuclei remains local even in the presence of strong nonadiabatic interactions. At every geometry, the total force is the sum of a potential gradient term driven by the local population and a nonclassical, nonadiabatic force driven by the local electronic coherence. On the nonadiabatic seams, the nonadiabatic force competes effectively with the potential terms. Following a sudden photoionization, we show how the nonadiabatic component of the local force drives the dynamics of the structural Jahn–Teller rearrangement of the methane cation toward the C 2 v geometry using 2 effective nuclear coordinates and 3 coupled electronic states for either CH 4 + or CD 4 + . Toward the progress in reaching shorter femtosecond resolution in time-resolved x-ray and electron diffraction experiments, our work provides a quantitative understanding and pictorial visualization of the local forces that drive ultrafast molecular rearrangement and chemical reactivity with a special reference to the role of electronic coherences and nonadiabatic couplings.

An attosecond optical pulse can entangle coherently related states of different characters, such as electronic and vibrational, in a molecular system. Using a quantum information theoretic approach, we explicitly define and discuss the surprisal of such a system in the maximal entropy formalism and identify the constraints and their conjugate Lagrange multipliers. Surprisal analysis shows how these constraints become fewer and simpler in the sudden approximation of the dynamics, a limit often valid for an ultrafast excitation. The optically accessible lower electronic states of N2 are used as a numerical example to show the compaction of the dynamics from On2 down to On constraints, where n is the number of vibronic states. The von Neumann entropy is used to confirm the fidelity of the compaction.

Abstract Glioblastoma (GBM) is a highly heterogeneous and invasive brain tumor in which complex interactions among tumor cells, immune cells, and neurons shape disease progression and therapeutic resistance. Resolving spatial patterns programs in glioblastoma (GBM) requires analytical approaches that go beyond variance-driven embeddings. Here, we applied thermodynamic surprisal analysis, an information-theoretic decomposition framework, to spatial transcriptomic sequencing from human GBM specimens to identify orthogonal constraint modes that capture dominant and previously hidden spatial programs. Surprisal analysis revealed structured patterns in the data that are not highlighted by standard approaches such as PCA or cell type deconvolution, including immune-activation–associated signatures as well as spatial programs consistent with synapse remodeling. Coupling surprisal decomposition with spatial ligand–receptor interaction analysis, NICHES, along with multiplexed protein imaging connected these spatial hidden modes to reveal potential communication networks. Together, these results position surprisal analysis as a powerful, complementary strategy for interrogating spatial tumor architecture, enabling discovery of non-obvious spatial programs and interactions that are obscured by variance-based methods.

The connection between the maximum entropy (MaxEnt) formalism and restricted Boltzmann machines (RBMs) is natural as both give rise to a Boltzmann-like distribution with constraints enforced by Lagrange multipliers, which correspond to RBM parameters. We integrate RBMs into quantum state tomography by using them as probabilistic models to approximate quantum states while satisfying MaxEnt constraints. Additionally, we employ polynomially efficient quantum sampling techniques to enhance RBM training, enabling scalable and high-fidelity quantum state reconstruction. This approach provides a computationally efficient framework for applying RBMs to MaxEnt-based quantum tomography. Furthermore, our method applies to the general and previously unaddressed case of reconstructing arbitrary mixed quantum states from incomplete and potentially noncommuting sets of expectations of observables while still ensuring maximal entropy.

When exciting an ensemble of initially randomly oriented molecules, a linearly polarized few cycle, few femtosecond, or UV or NIR pulse entangles the molecular degrees of freedom with the orientations of the molecule during the fast excitation step. We show, using fully quantum dynamical studies of an ensemble of initially randomly oriented LiH molecules, that the entanglement is not maximal and varies significantly with the pulse parameters. For a few-cycle NIR multiphoton excitation, a dozen dominant orientations suffice to describe the ensemble coherent dynamics, while only a few are needed for a one-photon UV process. Each principal orientation is correlated with a principal molecular vector made of a superposition of Σ or Π electronic states because of the cylindrical symmetry. For each principal molecular vector, the oscillation of specific electronic coherences drives charge migration and forces on the nuclei.

Ultrafast pumping displaces both electrons and nuclei from equilibrium so that the wave function is a double sum of separable terms for the dynamics of the electrons and nuclei. We convert the double sum into a single one by a matricization of the wave function, that is equivalent to the Schmidt decomposition. If more than one term needs to be included in this sum, the wave functions exhibit entanglement of electrons and nuclei. We discuss generating the best exact separable expression for the entangled molecular wave function. Then an approximation with a minimum number of single terms is obtained via Singular Value Decomposition, SVD. Two contrasting examples, LiH and N2, are used as an illustration. In the energy range accessible by a UV excitation, the two differ in their adiabatic electronic dynamics. During the nuclear motion the singlet states of N2 remain bound while the states of LiH are dissociative.

A quantitative expression for the value of information within the framework of information theory and of the maximal entropy formulation is discussed. We examine both a local, differential measure and an integral, global measure for the value of the change in information when additional input is provided. The differential measure is a potential and as such carries a physical dimension. The integral value has the dimension of information. The differential measure can be used, for example, to discuss how the value of information changes with time or with other parameters of the problem.

Stable isotope ratio measurements provide valuable insights into a broad range of natural processes, from planetary atmospheres and climate to interstellar chemistry. Nitrogen, which has two stable isotopes, exhibits varying isotope ratios across the solar system. To model these observations, the isotope fraction as a function of energy is essential. At the Advanced Light Source (ALS), we measured the photodissociation of molecular nitrogen (N2) with vacuum UV photons where a single photon is sufficiently energetic to dissociate the strong bond. The nitrogen atoms produced are scavenged with H2 to form ammonia, whose isotopic makeup is determined. Blending the experiments with dynamical computations that include the shielding of light, we examine the isotopic composition and electronic atomic states produced. The measured photodissociation of N2 at a natural isotopic composition with a frequency broad light beam exceptionally strongly favors the formation of the heavier nitrogen isotope, 15N. Computations concur and suggest that the maximum in the quantum yield reflects significant variations in the specific electronic quantum states of the product N atoms that have quite different reactivities. Our quantum computations show that at similar energies, photodissociation of 14N14N and 15N14N can lead to different product channels. The computed dynamics include extensive state-selective spin-orbit and nonadiabatic couplings affecting the light absorption and dissociation pathways that proceed via the triplet manifold of states. Our results are relevant for future exploration missions, both in situ and sample-return and for other molecules such as O2 and CO.

A practical approach is put forward for a compact representation of the time evolving density matrix of the forced Morse oscillator. This approach uses the factorized product form of the unitary time evolution operator, à la Wei-Norman. This product form casts the time evolution operator in the basis of operators that form a closed Lie algebra. The further requirement that the Hamiltonian of the system be closed within this Lie algebra is satisfied by restricting the dynamics to its sudden limit. One is thereby able to propagate in time both pure and mixed quantum states. As an example, for a thermal initial state, the time-evolved density matrix of maximum entropy is derived, and it is compacted to be described by only three explicit constraints: one time-dependent constraint, which is a dynamical symmetry, and two constants of the motion, with corresponding time-independent coefficients. This representation is a significant reduction from O(j2) constraints down to just three, where j is the number of bound states of the Morse oscillator.

Attopulses have an energy bandwidth broad enough to coherently excite several electronic states of molecules. Towards the control of chemical reactivity by attopulses we derive the quantum mechanical expression for the force exerted on the nuclei in such a vibronic wave packet both during and after the exciting pulse. Tuning the pulse parameters allows accessing specific electronic coherences that determine the force strength and direction during and after the pulse. Following the pulse, the force due to the non adiabatic interactions accelerates or slows down the motion of the vibronic wave packet on the excited electronic states and its sign controls the direction of population transfer. Computational results for the LiH and LiT molecules and the probing by the emission dipole are discussed.

We report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Σ and Π states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters.

Atto pulses allow controlling the charge migration and the spatio-temporal beating of the electronic density on a purely electronic time scale by tailoring the parameters of the pump pulse to excite specific electronic coherences. As the nuclei begin to move, the electronic and nuclear motions are entangled and the engineered electronic coherences can be usefully exploited for steering the vibronic density to specific products through the network of non adiabatic interactions. Three recent examples for which we demonstrate such a control by fully quantum dynamical computations are discussed. Two diatomic molecules, LiH and N 2 excited by a 2 fs deep UV pulse and the ultrafast structural Jahn-Teller rearrangement in CH 4 + . The entanglement between electronic and nuclear degrees of freedom arises from the optical excitation and from non adiabatic coupling induced by the nuclear motion. We provide insight of the coherence control mechanism by analyzing the time evolution of the entanglement using a singular valued decomposition (SVD) of the matricized wave function.

Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent operators with time-dependent coefficients. There are possible applications to the dynamics of systems of coupled coherent two-state systems, such as qubits, pumped by optical excitation and other addressing inputs. Thereby, the interaction of the system with the excitation is bilinear in the coherence between the two states and in the strength of the time-dependent excitation. The total Hamiltonian is a sum of such bilinear terms and of terms linear in the populations. The terms in the Hamiltonian form a basis for Lie algebra, which can be represented as coupled individual two-state systems, each using the population and the coherence between two states. Using the factorization approach of Wei and Norman, we construct a unitary quantum mechanical evolution operator that is a factored contribution of individual two-state systems. By that one can accurately propagate both the wave function and the density matrix with special relevance to quantum computing based on qubit architecture. Explicit examples are derived for the electronic dynamics in coupled semi-conducting nanoparticles that can be used as hardware for quantum technologies.

The development of drug resistance is a nearly universal phenomenon in patients with glioblastoma multiforme (GBM) brain tumors. Upon treatment, GBM cancer cells may initially undergo a drug-induced cell-state change to a drug-tolerant, slow-cycling state. The kinetics of that process are not well understood, in part due to the heterogeneity of GBM tumors and tumor models, which can confound the interpretation of kinetic data. Here, we resolve drug-adaptation kinetics in a patient-derived in vitro GBM tumor model characterized by the epithelial growth factor receptor (EGFR) variant(v)III oncogene treated with an EGFR inhibitor. We use radiolabeled 18F-fluorodeoxyglucose (FDG) to monitor the glucose uptake trajectories of single GBM cancer cells over a 12 h period of drug treatment. Autocorrelation analysis of the single-cell glucose uptake trajectories reveals evidence of a drug-induced cell-state change from a high- to low-glycolytic phenotype after 5-7 h of drug treatment. Information theoretic analysis of a bulk transcriptome kinetic series of the GBM tumor model delineated the underlying molecular mechanisms driving the cellular state change, including a shift from a stem-like mesenchymal state to a more differentiated, slow-cycling astrocyte-like state. Our results demonstrate that complex drug-induced cancer cell-state changes of cancer cells can be captured via measurements of single cell metabolic trajectories and reveal the extremely facile nature of drug adaptation.

Nonadiabatic quantum dynamics sheds light on the non-monotonic energy dependence of the branching fractions of N 2 .

Charge migration in LiH molecule and its isotopomers LiD and LiT is examined by quantum dynamics including the non-adiabatic effects of nuclear motions. Upon excitation by an ultrafast UV pulse, mass-independent charge migration occurs between the ground and first excited sigma states. The opposite polarity of these states and a relatively small energy gap between them allow the charge to oscillate at early time of the dynamics during 2 fs after the pulse is over. When the nuclei move, a mass-dependent revival of coherence is computed with a period of 80, 107, 123 fs for LiH, LiD, and LiT, respectively.

Vacuum ultraviolet (UV) light at a well-defined wavelength excites N2 to different vibronic levels of the singlet electronic states that strongly interact through nonadiabatic coupling. Each discrete vibronic state acts as an isolated resonance: it is weakly coupled to a dissociative continuum of triplet states via a weak spin-orbit coupling. Here, we seek to compare this decay to that of a coherent superposition of bound singlets pumped by a broad in energy - ultrafast pulse. Despite the strong intersinglets and intertriplets nonadiabatic couplings, the coherent set of states decays as a mixture of the isolated vibronic states with essentially their individual lifetimes as determined separately in a sharp wavelength excitation. The vibrational quantum number of the vibronic states is a nearly good one when the spin-orbit coupling is as weak as is the case for N2. Numerically converged dynamical computations valid for longer times show that for nonrotating molecules the individual vibronic resonances overlap and interfere only upon an artificially order of magnitude increase of the strength of the spin-orbit coupling. The resonances strongly overlap only at an even stronger coupling to the dissociative continuum.

Following a single photon VUV absorption, the N2 molecule dissociates into distinct channels leading to N atoms of different reactivities. The optically accessible singlets are bound, and dissociation occurs through spin-orbit induced transfer to the triplets. There is a forest of coupled electronic states, and we here aim to trace a path along the nonadiabatic couplings toward a particular exit channel. To achieve this, we apply a time-reversed quantum dynamical approach that corresponds to a dissociation running back. It begins with an atom-atom relative motion in a particular product channel. Starting with a Gaussian wave packet at the dissociation region of N2 and propagating it backward in time, one can see the population transferring among the triplets due to a strong nonadiabatic interaction between these states. Simultaneously, the optically active singlets get populated because of spin-orbit coupling to the triplets. Thus, backward propagation traces the nonradiative association of nitrogen atoms.