Related papers: A quantum mechanical version of Price's theorem fo…
Weyl's formulation of quantum mechanics opened the possibility of studying the dynamics of quantum systems both in infinite-dimensional and finite-dimensional systems. Based on Weyl's approach, generalized by Schwinger, a self-consistent…
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
Quantum Mechanics (QM) is a very special probabilistic theory, yet we don't know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical nature. Here I will analyze the…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…
Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and…
We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
The generalized Weyl transform of index $\alpha$ is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation…
The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum…