Related papers: From classical to quantum dynamics at Rokhsar-Kive…
Conceptual analogies among statistical mechanics and classical (or quantum) mechanics often appeared in the literature. For classical two-body mean field models, an analogy develops into a proper identification between the free energy of…
We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time…
It is shown that the classical dynamics of 1:1 resonance interaction between two identical linearly coupled Duffing oscillators is equivalent to the symmetric (non-biased) case of `macroscopic' quantum dynamics of two weakly coupled…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of…
We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
In this paper, we address the problem how to represent a classical data distribution in a quantum system. The proposed method is to learn quantum Hamiltonian that is such that its ground state approximates the given classical distribution.…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
We have studied the emergence of classical states in the perturbative interaction model. The states which interact with many other degrees of freedom, such as the center of mass of a macro-object, play important role. Although the random…
We study the spreading of a quantum-mechanical wavepacket in a one-dimensional tight-binding model with a noisy potential, and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite…
Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing the Hilbert space formulation of classical statistical…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
In general, classical fully-connected systems are known to undergo violent relaxation. This phenomenon refers to the relaxation of observables to stationary, non-thermal, values on a finite timescale, despite their long-time dynamics being…