Related papers: Statistics and Nos\'e formalism for Ehrenfest dyna…
The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct.…
Mixed quantum-classical methods, such as surface hopping and Ehrenfest dynamics, have proven useful for describing molecular processes involving multiple electronic states. These methods require propagating many independent trajectories,…
On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
Imagine a freely rotating rigid body. The body has three principal axes of rotation. It follows from mathematical analysis of the evolution equations that pure rotations around the major and minor axes are stable while rotation around the…
A recent proposal for mixed dynamics of classical and quantum ensembles is shown, in contrast to other proposals, to satisfy the minimal algebraic requirements proposed by Salcedo for any consistent formulation of such dynamics. Generalised…
Einstein conjectured long ago that much of quantum mechanics might be derived as a statistical formalism describing the dynamics of classical systems. Bell's Theorem experiments have ruled out complete equivalence between quantum field…
We consider an Ehrenfest approximation for a particle in a double-well potential in the presence of an external environment schematized as a finite resource heat bath. This allows us to explore how the limitations in the applicability of…
We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
We consider a coupled system of Schr\"odinger equations, arising in quantum mechanics via the so-called time-dependent self-consistent field method. Using Wigner transformation techniques we study the corresponding classical limit dynamics…
The two-dimensional electron-nuclear Schr\"odinger equation using soft-core Coulomb potentials has been a cornerstone for modeling and predicting the behavior of one-active-electron diatomic molecules, particularly for processes where both…
We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and R\"ossler systems as examples. The Schr\"odinger equation for the corresponding quantum statistical ensemble is…
In closed quantum systems, wavepackets can spread exponentially in time due to chaos, forming long-range superpositions in just seconds for ordinary macroscopic systems. A weakly coupled environment is conjectured to decohere the system and…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
We investigate detailed balance for a quantum system interacting with thermal radiation within mixed quantum-classical theory. For a two-level system coupled to classical radiation fields, three semiclassical methods are benchmarked: (1)…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for…