相关论文: Classical representation of the dynamics of quantu…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
This paper contributes an in-depth study of properties of continuous time Markov chains (CTMCs) on non-negative integer lattices $\N_0^d$, with particular interest in one-dimensional CTMCs with polynomial transitions rates. Such stochastic…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
The continuous-time quantum walks (CTQWs) are a fundamental tool in the development of quantum algorithms. Recently, it was shown that discretizations of p-adic Schr\"odinger equations give rise to continuous-time quantum Markov chains…
This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…
We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
Understanding thermalisation in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e. whether thermalisation…
We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…
We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose…
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…