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We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
Particles interacting with a prescribed quasimonochromatic gravitational wave (GW) exhibit secular (average) nonlinear dynamics that can be described by Hamilton's equations. We derive the Hamiltonian of this "ponderomotive" dynamics to the…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
A realist description of our universe requires a twofold concept of locality. On one hand, there are the strictly Einstein-local interactions which generate the time evolution. On the other hand, the quantum state space calls for a…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
Possibly, the most general action in the background of isotropic and homogeneous space-time has been considered to study the quantum evolution of the early universe, apart from a cosmological constant. The hermiticity of the effective…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
In recent years, the non-relativistic quantum dynamics derived from three assumptions; i) probability current conservation, ii) average energy conservation, and iii) an epistemic momentum uncertainty [A. Budiyono and D. Rohrlich,…
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…
Inspired by Mott's (1929) analysis of particle tracks in a cloud chamber, we consider a simple model for quantum cosmology which includes, in the total Hamiltonian, model detectors registering whether or not the system, at any stage in its…
For a quantum field living on a non - static spacetime no instantaneous Hamiltonian is definable, for this generically necessitates a choice of inequivalent representation of the canonical commutation relations at each instant of time. This…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…
Classical constrained Hamiltonian theory assumes complete observability of system states, but in reality only partial state information is often available. This paper establishes a complete geometric theoretical framework for handling such…
We propose a way of defining Hamiltonians for quantum field theories without any renormalization procedure. The resulting Hamiltonians, called IBC Hamiltonians, are mathematically well-defined (and in particular, ultraviolet finite) without…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. We identify two…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
We derive photon counting statistics for an output field of a single-photon wave packet interacting with a quantum system (e.g. a quantum harmonic oscillator or a two-level atom). We determine the exclusive probability densities for the…