相关论文: On q-deformed quantum stochastic calculus
The canonical operator $\hat{a}^{\dagger}$ ($\hat{a}$) represents the ideal process of adding (subtracting) an {\it exact} amount of energy $E$ to (from) a physical system in both elementary quantum mechanics and quantum field theory. This…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
We propose an approach to the quantum-classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics. Making use of the factorization method, we construct classical versions of the momentum and…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…
A simple version of the q-deformed calculus is used to generate a pair of q-nonlocal, second-order difference operators by means of deformed counterparts of Darboux intertwining operators for zero factorization energy. These deformed…
Generalized numbers, arithmetic operators and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of $q$-logarithm/$q$-exponential inverse functions. Some of the…
The recently introduced two- and three-parameter ($p,q$)- and ($p,q,\mu$)-deformed extensions of the Heisenberg algebra were explored under the condition of their connectedness with the respective nonstandard (other than known ones)…
We extend to quantum mechanics the technique of stochastic subordination, by means of which one can express any semi-martingale as a time-changed Brownian motion. As examples, we considered two versions of the q-deformed Harmonic oscillator…
A generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and dimensionality form in terms of Malliavin derivative on a projective Fock space, and their uniform continuity with…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a…
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory, for the case when the…
In this letter, we define the homodyne $q$-deformed quadrature operator. Analytic expression for the wavefunctions of $q$-deformed oscillator in the quadrature basis are found. Furthermore, we compute the explicit analytical expression for…
The quantum deformation concept is applied to a study of pairing correlations in nuclei with mass 40<A<100. While the nondeformed limit of the theory provides a reasonable overall description of certain nuclear properties and fine structure…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…