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Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…

Quantum theory depends on an external classical time, and there ought to exist an equivalent reformulation of the theory which does not depend on such a time. The demand for the existence of such a reformulation suggests that quantum theory…

This paper concerns the homogenization of Schrodinger equations for non-crystalline matter, that is to say the coefficients are given by the composition of stationary functions with stochastic deformations. Two rigorous results of so-called…

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…

These lectures address the dynamics of phase ordering out of equilibrium in condensed matter and in quantum field theory in cosmological settings, emphasizing their similarities and differences. In condensed matter we describe the…

We prove that a single-jump quantum stochastic unitary evolution is equivalent to a Dirac boundary value problem on the half line in one extra dimension. It is shown that this exactly solvable model can be obtained from a Schroedinger…

In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…

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…

Recently a model of metric fluctuations has been proposed which yields an effective Schr\"odinger equation for a quantum particle with a modified inertial mass, leading to a violation of the weak equivalence principle. The renormalization…

We derive the probabilities of measurement results from Schroedinger's equation plus a definition of macroscopic as a particular kind of thermodynamic limit. Bohr's insight that a measurement apparatus must be classical in nature and…

The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is…

Distinguishability plays a major role in quantum and statistical physics. When particles are identical their wave function must be either symmetric or antisymmetric under permutations and the number of microscopic states, which determines…

This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schr\"odinger equation allows to construct quantum trajectories describing the dynamics of the system…

In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…

A localized free particle is represented by a wave packet and its motion is discussed in most quantum mechanics textbooks. Implicit in these discussions is the assumption of zero temperature. We discuss how the effects of finite temperature…

A deterministic model with a large number of continuous and discrete degrees of freedom is described, and a statistical treatment is proposed. The model exactly obeys a Schrodinger equation, which has to be interpreted exactly according to…

Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…

The Schrodinger equation based on the de Broglie wave is the most fundamental equation of the quantum mechanics. There can be no doubt about it's prediction validity. However, the probabilistic interpretation on the quantum mechanics has…

The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also…

It is well-known that the coordinate as a continuous variable, consisting of a set of all points between 0 and $L$ contradicts the observability of measurement. In other words there might exist a fundamental length in nature, such as the…