Related papers: A Primary Unified Geometric Framework of Molecular…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
Molecular dynamics is based on solving Newton's equations for many-particle systems that evolve along complex, highly fluctuating trajectories. The orbital instability and short-time complexity of Newtonian orbits is in sharp contrast to…
We present a new formulation for the mean-field propagation part of the relativistic quantum molecular dynamics, simulating an $N$-body system of interacting Gaussian wave packets via Lorentz scalar and vector potentials. Covariant…
Finding optimal reaction coordinates and predicting accurate kinetic rates for activated processes are two of the foremost challenges of molecular simulations. We introduce an algorithm that tackles the two problems at once: starting from a…
We discuss nuclear dynamics at molecule-metal interfaces including non-equilibrium molecular junctions. Starting from the many-body states (pseudoparticle) formulation of the molecule-metal system in the molecular vibronic basis, we…
We consider the radiation reaction to the motion of a point-like particle of mass $m$ and specific spin $S$ traveling on a curved background. Assuming $S=O(Gm)$ and $Gm\ll L$ where $L$ is the length scale of the background curvature, we…
We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time…
Traditionally, gravity is generally considered to exert an extremely weak effect in chemistry because the Newtonian gravitation is typically negligible compared to the dominant Coulomb potentials in a molecular system. In this work, we…
We present the variational action principle for initial value problems in classical, conservative-force point particle mechanics. We rigorously derive this formulation by taking the classical limit of the Schwinger-Keldysh expression for…
In this paper we propose an ab initio method to solve quantum many-body problems of molecular dynamics where both the electronic and the nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both…
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this…
Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We…
A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically,…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…
Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…
A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear…
Quantum geometrical molecular dynamics provides a quantum geometric picture for understanding reactive dynamics, especially excited-state conical intersection dynamics, and also a numerically exact method for strongly correlated…
An approach to correlated dynamics of quantum nuclei and electrons both in dynamical interaction with external environments is presented. This stochastic quantum molecular dynamics rests on a theorem that establishes a one-to-one…