Related papers: Quantum dynamics in the self-consistent quadratic …
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
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…
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The…
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is…
The time dependent quantum variational principle is emerging as an important means of studying quantum dynamics, particularly in early universe scenarios. To date all investigations have worked within a Gaussian framework. Here we present…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
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…
We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
In order to study quantum dynamics of the FRW-universe of closed type, definitions of velocity, Hubble function and duration of the evolved universe are introduced into cosmology. The proposed definitions are characterized by high stability…
We show that the quantum dynamics of a real scalar field for a large class of potentials in the symmetric Gaussian state, where the nonperturbative quantum contributions are taken into account, can be described equivalently by a…