Related papers: Topics in quantum statistical mechanics and operat…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we have picked out two 2-dim billiard systems. Both systems are…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states…
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
The recent progresses in Machine Learning opened the door to actual applications of learning algorithms but also to new research directions both in the field of Machine Learning directly and, at the edges with other disciplines. The case…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
The basic physical problems that necessitated the emergence of quantum physics are summarized, along with the elements of wave mechanics and its traditional statistical interpretation. Alternative interpretations to the statistical one,…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
The chiral algebra of tetrahedral molecules, derived from Fischer projections, is discussed in the framework of quantum mechanics. A quantum chiral algebra is obtained whose operators, acting as rotations or inversions, commute with the…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
Koopman operator based models emerged as the leading methodology for machine learning of dynamical systems. But their scope is much larger. In fact they present a new take on modeling of physical systems, and even language. In this article…
The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum…