Related papers: On the Quantization Procedure in Classical Mechani…
A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…
We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The dynamics averaged over the noise is described by an…
We provide here an explicit example of Khinchin's idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics. This point of view is supported by extensive numerical…
Recently, it has been shown that the quantum equilibrium distribution in the original Bohm's model is unstable and so it isn't a tenable physical theory [Proc. R. Soc. A 470 20140288 (2014)]. In this paper we show that a natural…
The ontological aspect of Bohmian mechanics, as a hidden-variable theory that provides us with an objective description of a quantum world without observers, is widely known. Yet its practicality is getting more and more acceptance and…
In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as…
With the goal of giving evidence for the theoretical consistency of the Horava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order…
We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…
It is often argued that measurable predictions of Bohmian mechanics cannot be distinguished from those of a theory with arbitrarily modified particle velocities satisfying the same equivariance equation. By considering the wave function of…
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…
The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by…
We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the…
The dynamics of quantized vortices in weakly interacting superfluids are often modeled by a nonlinear Schr\"odinger equation. In contrast, we show that quantized vortices in fact obey a non-Hamiltonian evolution equation, which enhances…
It is shown how the essentials of quantum theory, i.e., the Schroedinger equation and the Heisenberg uncertainty relations, can be derived from classical physics. Next to the empirically grounded quantisation of energy and momentum, the…
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…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable…
We derive the Gross Pitaevskii equation (GPE) for condensate of bosons obeying deformed statistics under external potential and inter-particle interaction. First, we obtain the well-known Schrodinger equation. Using a suitable Hamiltonian…
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…