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The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics…
We propose quantum algorithms for complex-valued nonlinear partial differential equations in the strongly nonlinear regime, where the dynamics is governed by vortex cores, phase singularities, and nonlinear vortex interactions. Examples…
We show that the natural motion of particles in continuous space-time (CSTM) is not classical continuous motion (CCM), but one kind of essentially discontinuous motion, the wave function in quantum mechanics is the very mathematical complex…
Electronic coherences are key to understanding and controlling photo-induced molecular transformations. We identify a crucial quantum-mechanical feature of electron-nuclear correlation, the projected nuclear quantum momenta, essential to…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
General molecular dynamic approach, making possible direct calculation of eigen values and eigen functions for a quantum-mechanical system of an arbitrary symmetry is proposed. The method is based on analogy between discrete representation…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
We discuss the problem of consistency of quantum mechanics as applied to low energy nucleon dynamics with the symmetries of QCD. It is shown that the dynamics consistent with these symmetries is not governed by the Schrodinger equation. We…
The first exact quantum simulation of a real molecular system (HD$^+$) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled…
Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schr\"odinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization.…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach…
Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary and electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular…
Basic problems of the semiclassical microscopic modelling of strongly interactingsystems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…
With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the…
We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and…
At present, there are many methods of quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of…
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…
Quantum Chromodynamics and Quantum Electrodynamics, both renormalizable quantum field theories with a small number of precisely constrained input parameters, dominate the dynamics of the quarks and gluons - the underlying building blocks of…