Related papers: Quantum Diffusion, Measurement and Filtering
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is…
It is argued that Feynman's rules for evaluating probabilities, combined with von Neumann's principle of psycho-physical parallelism, help avoid inconsistencies, often associated with quantum theory. The former allows one to assign…
A fundamental principle of quantum theory, clearly manifested in the two-slit experiment, is that for any alternatives that cannot be distinguished by measurement physical predictions are obtained by summation of their amplitudes. In…
We propose a new structure of ensembles in quantum theory, based on the recently introduced intrinsic properties of electrons and photons. On this statistical basis the spreading of a wave-packet, collapse of the wave function, the quantum…
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the…
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…
Inhomogeneous Nelson's diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold with this tensor of diffusion as a metric tensor. The influence of matter to the energy density of…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
We outline a fundamentally quantum description of bosonic dark matter (DM) from which the conventional classical-wave picture emerges in the limit $m \ll 10~\textrm{eV}$. As appropriate for a quantum system, we start from the density matrix…
A new, realist interpretation of the quantum measurement processes is given. In this scenario a quantum measurement is a non-equilibrium phase transition in a ``resonant cavity'' formed by the entire physical universe including all its…
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be…
The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each…
The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $\beta \in (0,1)$. The fundamental solution for the Cauchy problem is…
Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria…
Quantum optical fields offer numerous control knobs which are not available with classical light and may be used for monitoring the properties of matter by novel types of spectroscopy. It has been recently argued that such quantum…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…