Related papers: Statistical approach to quantum mechanics II: Nonr…
We initiate a research program for the systematic investigation of quantum superintegrable systems involving the interaction of two non-relativistic particles with spin $1/2$ moving in the three-dimensional Euclidean space. In this paper,…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the…
We formulate incomplete classical statistics for situations where the knowledge about the probability distribution outside a local region is limited. The information needed to compute expectation values of local observables can be collected…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
The measurement of a spin-$\half$ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement,…
Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to…
In the literature on quantum reference frames, the internal (relative) properties of a system are defined as those which are preserved under an arbitrary change of reference frame. For a system of quantum spins, these are all properties…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive…
In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the…
Coherent states offer a promising path for near-term quantum computing due to their inherent protection against bit-flip noise. However, their large photon numbers can be challenging for numerical simulation. This paper introduces an…
We consider the statics and dynamics of distinguishable spin-1/2 systems on an arbitrary graph G with N vertices. In particular, we consider systems of quantum spins evolving according to one of two hamiltonians: (i) the XY hamiltonian…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
Relativistic arbitrary spin Hamiltonians are shown to obey the algebraic structure of supersymmetric quantum system if their odd and even parts commute. This condition is identical to that required for the exactness of the Foldy-Wouthuysen…
We construct a $\mathcal{PT}$-symmetric Richardson--Gaudin models for spin-$\tfrac{1}{2}$ systems by deforming the closed integrable Hamiltonian through complex-valued transverse magnetic fields and coupling constants. By defining parity as…