Related papers: Lagrangian formalism and classical statistical ens…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…
We present a general method to derive the classical mechanics of a system of identical particles in a way that retains information about quantum statistics. The resulting statistical mechanics can be interpreted as a classical version of…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is…
We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a…
Lagrangian properties obtained from a Particle Tracking Velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation,…
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…
The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical…
These notes grew out of a lecture course on mathematical methods of classical physics for students of mathematics and mathematical physics at the master's level. Also, physicists with a strong interest in mathematics may find this text…
We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential collection with application to the Transformer and its token space. Our methods are catered to the…
We study the reduction of non-autonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of the system $Q\times\real\to\real$. These kind of symmetries…
The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for…
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…