Computer simulation of quantum dynamics in a classical spin environment

Harnessing a static magnetic field to drive molecular vibrations presents a promising avenue for controlling chemical processes. However, the coupling of nuclear dynamics with an external magnetic field has largely been explored only through classical approximations. In this work, we introduce a time-dependent quantum dynamics formalism based on London nuclear-electronic orbitals, enabling the simulation of magnetic field-driven quantum dynamics. Through simulations of HCN and H2CO molecules, we provide a detailed analysis of how the relative orientation of the magnetic field and vibrational symmetry influence the resulting quantum dynamics. Our findings reveal field-induced mode couplings and symmetry-dependent effects, offering new insights into the role of magnetic fields in vibrational control. This work establishes a quantum mechanical framework for understanding and manipulating vibrational dynamics using external magnetic fields, paving the way for novel applications in spectroscopy, reaction dynamics, and quantum control.

The adiabatic control is a powerful technique for many practical applications in quantum state engineering, light-driven chemical reactions and geometrical quantum computations. This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls. The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels. In a parametric Hilbert space, the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path. The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters. The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system. The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions. When the upper bound is adiabatically controlled, the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.

The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.

In recent years, quantum walks have been proposed as promising resources for the simulation of physical quantum systems. In fact it is widely adopted to simulate quantum dynamics. Up to now single particle quantum walks have been experimentally demonstrated by different approaches, while only few experiments involving many-particle quantum walks have been realized. Here we simulate the 2-particle dynamics on a discrete time quantum walk, built on an array of integrated waveguide beam splitters. The polarization independence of the quantum walk circuit allowed us to exploit the polarization entanglement to encode the symmetry of the two-photon wavefunction, thus the bunching-antibunching behavior of non interacting bosons and fermions has been simulated. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.

We investigate the ecient computation of a few of the lowest eigenvalues of a symmetric eigenvalue problem occurring in quantum dynamical molecular simulations. The large sparse system of order n 3 is highly structured such that its multiplication with a vector costs O(n 3 logn) oating point operations only. We compare a number of eigensolvers: subspace iteration, two variants of the restarted Lanczos algo- rithm, among them ARPACK, the Jacobi-Davidson algorithm and the classical algorithms from LAPACK for full matrices. Some of them are applied with a shift-and-invert spectral transformation. The arising systems of equations are solved by the preconditioned conjugate gradient method for which new ecient ADI-type preconditioners are proposed and analyzed.

Based on the principle of equivalence of the general theory of relativity and the definition of the non-Euclidean metric of space in a non-inertial frame of reference associated with rotation, a geometric (topological) phase is found that occurs when traversing any closed loop. This approach made it possible to establish a deep physical analogy between various wave effects (both classical and quantum) in closed waveguides that arise under the conditions of their rotation. Due to the coherence of the wave function of spinless charge carriers (Cooper pairs of conduction electrons with oppositely directed spins) in superconductors in the ground quantum state (superconducting state), the appearance of a geometric phase in closed loops under rotation conditions can lead to interference effects in the presence of weak bonds in the loop. To register interference effects, it was proposed to use superconducting quantum interferometers placed in the electric field of a cylindrical or spherical capacitor. In accordance with the general theory of the geometric phase of rotation, the study obtained the basic relations between the geometric phase of rotation and the phase of the wave function induced by an external magnetic field, and an estimate of their values was obtained for acceptable values of the angular velocity of rotation, dimensions of superconducting quantum interferometers, and voltages on the capacitor. The errors in measuring the magnetic flux during the rotation of the measuring complex are determined. Taking into account the dependence of the magnitude of the geometric phase of rotation on the voltage across the capacitor and the size of the superconducting quantum interferometers, and also taking into account the specific range of angular velocities of rotation, the sensitivity of superconducting quantum interferometers to the angular velocity can be regulated by a rational choice of these parameters. Based on the results obtained, a new method for measuring magnetic fields was proposed using two superconducting quantum interferometers with different values of areas bounded by closed contours under conditions of rotational movements, which makes it possible to compensate for the disturbing influence of rotations on magnetic measurements, as well as to simultaneously determine the magnetic induction and angular velocity of rotation.

Based on the principle of equivalence of the general theory of relativity and the definition of the non-Euclidean metric of space in a non-inertial frame of reference associated with rotation, a geometric (topological) phase is found that occurs when traversing any closed loop. This approach made it possible to establish a deep physical analogy between various wave effects (both classical and quantum) in closed waveguides that arise under the conditions of their rotation. Due to the coherence of the wave function of spinless charge carriers (Cooper pairs of conduction electrons with oppositely directed spins) in superconductors in the ground quantum state (superconducting state), the appearance of a geometric phase in closed loops under rotation conditions can lead to interference effects in the presence of weak bonds in the loop. To register interference effects, it was proposed to use superconducting quantum interferometers placed in the electric field of a cylindrical or spherical capacitor. In accordance with the general theory of the geometric phase of rotation, the study obtained the basic relations between the geometric phase of rotation and the phase of the wave function induced by an external magnetic field, and an estimate of their values was obtained for acceptable values of the angular velocity of rotation, dimensions of superconducting quantum interferometers, and voltages on the capacitor. The errors in measuring the magnetic flux during the rotation of the measuring complex are determined. Taking into account the dependence of the magnitude of the geometric phase of rotation on the voltage across the capacitor and the size of the superconducting quantum interferometers, and also taking into account the specific range of angular velocities of rotation, the sensitivity of superconducting quantum interferometers to the angular velocity can be regulated by a rational choice of these parameters. Based on the results obtained, a new method for measuring magnetic fields was proposed using two superconducting quantum interferometers with different values of areas bounded by closed contours under conditions of rotational movements, which makes it possible to compensate for the disturbing influence of rotations on magnetic measurements, as well as to simultaneously determine the magnetic induction and angular velocity of rotation.

Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here we use a programmable integrated photonic chip to simulate a model comprised of twin pairs of $PT$-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behaviour that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.

The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence-the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state-and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrodinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.

The dynamics of chemical reactions in solution are of paramount importance in fields ranging from biology to materials science. Because the hydrogen-bond network and proton dynamics govern the behavior of aqueous solutions, they have been the subject of numerous studies over the years. Here, we report the observation of a previously unknown associative state in the hydroxide ion that forms when a proton from a neighboring water molecule approaches the hydroxide ion, utilizing resonant inelastic soft X-ray scattering (RIXS) and quantum dynamical simulations. State-of-the-art theoretical analysis reveals state mixing in the electronically excited states between aqueous hydroxide ions and the solvent. Our results give new insights into chemical bonding and excited-state dynamics in the aqueous environment. This investigation of associative states opens up new pathways for spectroscopic studies of chemical reaction dynamics and lays the foundation for directly accessing dynamic proton exchange in solution.

We show how geometric phases may be used to fully describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of its Hilbert space. We find a direct relation between geometric phases and von Neumann algebras. In particular, we show that a vanishing geometric phase implies the existence of a well-defined trace functional on the algebra. We discuss how this is realised within the AdS/CFT correspondence for the eternal black hole. On the other hand, a non-vanishing geometric phase indicates missing information for a local observer, associated to reference frames covering only parts of the quantum system considered. We illustrate this with several examples, ranging from a single spin in a magnetic field to Virasoro Berry phases and the geometric phase associated to the eternal black hole in AdS spacetime. For the latter, a non-vanishing geometric phase is tied to the presence of a centre in the associated von Neumann algebra.

Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator

In this paper, we compare and contrast basis set sampling techniques recently developed for use in the ab initio multiple cloning method, a direct dynamics extension to the multiconfigurational Ehrenfest approach, used recently for the quantum simulation of ultrafast photochemistry. We demonstrate that simultaneous use of basis set cloning and basis function trains can produce results which are converged to the exact quantum result. To demonstrate this, we employ these sampling methods in simulations of quantum dynamics in the spin boson model with a broad range of parameters and compare the results to accurate benchmarks.

Processes of electron photoinjection into water and electron tunneling through water layers are considered. The thermalization process in bulk water and transmission probability through thin water films of photoinjected electrons are described within classical molecular dynamics simulations. Electron tunneling through thin water layer is studied using quantum dynamical simulations.

The transport of components in liquid media under the influence of an applied electric field can be described with the continuity equation. It represents a nonlinear conservation law that is based upon the balance laws of continuous transport processes and can be solved in time and space numerically. This procedure is referred to as dynamic computer simulation. Since its inception four decades ago, the state of dynamic computer simulation software and its use has progressed significantly. Dynamic models are the most versatile tools to explore the fundamentals of electrokinetic separations and provide insights into the behavior of buffer systems and sample components of all electrophoretic separation methods, including moving boundary electrophoresis, CZE, CGE, ITP, IEF, EKC, ACE, and CEC. This article is a continuation of previous reviews (Electrophoresis 2009, 30, S16–S26 and Electrophoresis 2010, 31, 726–754) and summarizes the progress and achievements made during the 2010 to 2020 time period in which some of the existing dynamic simulators were extended and new simulation packages were developed. This review presents the basics and extensions of the three most used one‐dimensional simulators, provides a survey of new one‐dimensional simulators, outlines an overview of multi‐dimensional models, and mentions models that were briefly reported in the literature. A comprehensive discussion of simulation applications and achievements of the 2010 to 2020 time period is also included.