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In deterministic theories, one can start from a set of ontological states to formulate the dynamical laws, but these may not be directly observable. Observable are only equivalence classes of states, and these will span a basis of…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
A new family of one-dimensional quantum models is proposed in terms of new potentials with a Gaussian asymptotic behavior but approaching to the potential of the harmonic o scillator when $x\to 0$. It is shown that, in the energy basis of…
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems…
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…
Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete…
We study the work distribution of a single particle moving in a harmonic oscillator with time-dependent strength. This simple system has a non-Gaussian work distribution with exponential tails. The time evolution of the corresponding moment…
This work prolongs, using an operator method, the investigations started in our recent paper J. Math. Phys. 51., 102108 on the spectrum and states of the harmonic oscillator on twisted Moyal plane, where rather a Moyal-star-algebraic…
What can we learn about quantum gravity from a simple toy model, without actually quantizing it? The toy model consists of a finite number of point particles, coupled to three dimensional Einstein gravity. It has finitely many physical…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
Based on Newton's laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed oscillating universe. We find that the behaviour of the…
The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally…
Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability…
We compute the particle creation of a harmonic oscillator using the classical stochastic method. This recently constructed method reproduces all the vacuum expectation values in quantum theory. We prepare the vacuum state at the initial…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
For want of a more natural proposal, it is generally assumed that the back-reaction of a quantised matter field on a classical metric is given by the expectation value of its energy-momentum tensor, evaluated in a specified state. This…
Toy models are highly idealized and deliberately simplified models that retain only the essential features of a system in order to explore specific theoretical questions. Long used in physics and other sciences, they have recently begun to…
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…