Related papers: The substructure of a Quantum Oscillator field
Requirements of a conjugate operator are emphasized, especially in its role in uncertainty relations.It is argued that in many contexts it is necessary to extend the Hilbert space in order to define a conjugate operator as in gauge…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
In this paper, we propose an approach based on the theory of an axiomatic $S$ matrix and partially switching on an interaction, which is extremely suitable for describing the phenomenon of oscillations within the framework of quantum field…
Spectra of the position and momentum operators of the Biedenharn-Macfarlane q-oscillator (with the main relation aa^+-qa^+a=1) are studied when q>1. These operators are symmetric but not self-adjoint. They have a one-parameter family of…
A new concept of the constitution of Nature is proposed. The constructed submicroscopic quantum mechanics is deterministic and is characterised by elementary excitations of the space net that is treated as the tessellation of balls, or…
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…
Due to their simultaneous optimization for radial and parallel neoclassical transport, quasi-isodynamic fields have been the main choice of stellarator magnetic configuration for most fusion reactor candidates in recent years. However,…
Fock representations are constructed for a free scalar field in the closed and quasi-Euclidean isotropic cosmological models. Invariance of their cyclic vector (vacuum) under isometries and the correspondence principle single out a class of…
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
In the bilayer quantum Hall system, a spontaneously charge imbalance state appears at the ground energy level. Gap in the collective excitation energy makes it stable against decoherence in macroscopic level. This state behaves as a spin…
The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In…
The spin and orbital angular momentum carried by different quark flavors in the nucleon are calculated in the SU(3) chiral quark model with symmetry-breaking. The similar calculation is also performed for other octet and decuplet baryons.…
We propose a quantum matrix oscillator as a model that provides the construction of the quantum Hall states in a direct way. A connection of this model to the regularized matrix model introduced by Polychronakos is established . By…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
Neutrino oscillations occur within the frame of the Standard Model, assuming that a neutrino is composed of a left handed and a right handed mass less fermion. Neutrino oscillations proceed via the 4-component Higgs field as intermediate…
We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the…
We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the…
Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables phi in R mod 2 pi and I > 0. But the symplectic transformation (\phi,I) to (q,p) is singular for (q,p) = (0,0). Globally {(q,p)} has…
It is shown that response properties of a quantum harmonic oscillator are in essence those of a classical oscillator, and that, paradoxical as it may be, these classical properties underlie all quantum dynamical properties of the system.…
We present a control-theoretic analysis of the system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that by applying external fields with just two resonant frequencies, any desired unitary operator can…