相关论文: On quantum and relativistic mechanical analogues i…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schr\"odinger representation. This additional information specifies the microstate of $\psi$ that is incorporated into the…
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…
This work presents a unified perspective on thermal equilibrium and quantum dynamics by examining the simplest quantum system, a qubit, as a minimal model. We show that both the thermal partition function and the Loschmidt amplitude can be…
The hydrodynamic interpretation of quantum mechanics treats a system of particles in an effective manner. In this work, we investigate squeezed coherent states within the hydrodynamic interpretation. The Hamiltonian operator in question is…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
The quantum theory of relativistic particles, based on the first quantization technique similar to that used by Schroedinger and Dirac in formulating quantum mechanics, is reconsidered on the basis of a photon-like dispersion relation…
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle that endows every classical system with an intrinsic environment. Decomposing the action into conservative and…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…
The aim of this paper is to understand the relation between the canonical Hamilton-Jacobi equation for Maxwell's electrodynamics, which is an equation with variational derivatives for a functional of field configurations, and the covariant…
We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation.…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
We show that the Schr\"odinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…