相关论文: On quantum and relativistic mechanical analogues i…
Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Using quantum-classical analogies, we find that dynamical pictures of quantum mechanics have precise counterparts in classical mechanics. In particular, the Eulerian and Lagrangian descriptions of fluid dynamics in classical mechanics are…
Friction incorporates the close connection between classical mechanics in irreversible thermodynamics. The translation to a quantum mechanical foundation is not trivial and requires a generalization of the Lagrange function. A change to…
In classical physics there is a well-known theorem in which it is established that the energy per degree of freedom is the same. However, in quantum mechanics due to the non-commutativity of some pairs of observables and the possibility of…
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…
For any classical statistical-mechanics model with a discrete state space, and endowed with a dynamics satisfying detailed balance, it is possible to generalize the Rokhsar-Kivelson point for the quantum dimer model. That is, a quantum…
We observe that the Schrodinger equation may be written as two real coupled Hamilton-Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing the quantum state through exact…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
We consider the Hamiltonian and Lagrangian formalism describing free \k-relativistic particles with their four-momenta constrained to the \k-deformed mass shell. We study the modifications of the formalism which follow from the introduction…
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…
In the frames of classical mechanics the generalized Langevin equation is derived for an arbitrary mechanical subsystem coupled to the harmonic bath of a solid. A time-acting temperature operator is introduced for the quantum Klein-Kramers…
Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
A simple real-space model for the free-electron wavefunction with spin is proposed, based on coherent vortices on the scale of h/mc, rotating at mc^2/h. This reproduces the proper values for electron spin and magnetic moment. Transformation…
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…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
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…