相关论文: The energy operator for infinite statistics
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We scrutinize the possibility of extending the result of \cite{ccr} to the case of q-deformed oscillator for $q$ real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two…
The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…
We clarify that an ideal gas obeying infinite statistics cannot undergo condensation. Then we derive the dynamic equation for an identical particle system obeying infinite statistics under external potential and inter-particle interaction.…
Using Ursell operators for the study of the poperties of dilute degenerate gases
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root…
We compute the statistical potential between two particles in the coherent state formalism on the deformed configuration space. The result obtained by using the coherent states having a further degree of freedom (proposed in \cite{rohwer})…
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…
We discuss many-body states and the algebra of creation and annihilation operators for particles obeying exclusion statistics.
Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying…
We describe new $q$-deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra $\mathfrak{sl}_2$ and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to…
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
Concerning the energy of harmonic oscillator, a prescription is proposed for making the original form unchanged even after q-deformation. Applicability of the prescription is limited, but, it can be applied to various cases which are well…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…
A decomposition of the level-one $q$-deformed Fock representations of $\uqn$ is given. It is found that the action of $\upqn$ on these Fock spaces is centralized by a Heisenberg algebra, which arises from the center of the affine Hecke…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
Corresponding to two ways of realizing the q-deformed Heisenberg algebra by the undeformed variables there are two q-perturbative Hamiltonians with the additional momentum-dependent interactions, one originates from the perturbative…