Related papers: Derivation of the Euler Equations from Quantum Dyn…
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to…
Recent theoretical work has developed the Hamilton's-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: (1) Euler-Poincar\'e equations (the Lagrangian analog of…
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
We present a new way of deriving classical mechanics from quantum mechanics. A key feature of the method is its compatibility with the standard approach used to derive transition rates between quantum states due to interactions. We apply…
Transport equations for autonomous driven Fermionic quantum systems are derived with the help of statistical assumptions and of the Markov approximation. The statistical assumptions hold if the system consists of subsystems within which…
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total…
We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge…
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 amplitudes, Born rule,…
Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels…
Using the general framework of quantum field theory, we derive basic equations of quantum field kinetics. The main goal of this approach is to compute the observables associated with a quark-gluon plasma at different stages of its…
In this paper, we review two related aspects of field theory: the modeling of the fields by means of exterior algebra and calculus, and the derivation of the field dynamics, i.e., the Euler-Lagrange equations, by means of the stationary…
In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…