Related papers: Open Systems in Classical Mechanics
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
Can certain degrees of freedom of a closed physical system, described by a time-independent Hamiltonian, become more and more classical as they evolve from some state? This question is important because our universe seems to have done just…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian…
In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie…
The prospect of AGI instantiated on quantum substrates motivates the development of mathematical frameworks that enable direct comparison of their operation in classical and quantum environments. To this end, we introduce a Hamiltonian…
The development of supersymmetric (SUSY) quantum mechanics has shown that some of the insights based on the algebraic properties of ladder operators related to the quantum mechanical harmonic oscillator carry over to the study of more…
We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced…
We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics…
Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra.…
In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…
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…
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
This work conducts a Hamilton-Jacobi analysis of classical dynamical systems with internal constraints. We examine four systems, all previously analyzed by David Brown: three with familiar components (point masses, springs, rods, ropes, and…
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
There is a lack of formalism for some key foundational concepts in systems engineering. One of the most recently acknowledged deficits is the inadequacy of systems engineering practices for engineering intelligent systems. In our previous…