Related papers: Classical dilations \`a la Hudson-Parthasarathy of…
The classical Landau-Lifshitz equation with damping term has been derived from the time evolution of a quantum mechanical wave function under the assumption of a non-hermitian Hamilton operator. Further, the trajectory of a classical spin…
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying uniqueness) for this class. In the second part, we establish…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an…
We show that the discrete-time evolution of an open quantum system generated by a single quantum channel $T$ can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e. we construct a unitary dilation of the…
Mixed quantum-classical dynamics is a set of methods often used to understand systems too complex to treat fully quantum mechanically. Many techniques exist for full quantum mechanical evolution on quantum computers, but mixed…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial (based on Kullback-Leibler distances between phase-space attractors)…
In literature on imprecise probability little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical…
We study classical and quantum scattering properties in the ballistic regime of particles in two-dimensional chaotic billiards that are models of electron- or micro- waveguides. To this end we construct the purely classical counterparts of…
We analyze the estimation of a time dependent perturbation acting on a continuously monitored quantum system. We describe the temporal fluctuations of the perturbation by a Hidden Markov Model, and we combine quantum measurement theory and…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…