Related papers: The 1/N Expansion in Noncommutative Quantum Mechan…
We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method,…
A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $\hbar$-expansions and suitable quantization conditions, the recursion formulae obtained…
Proceeding from nonlinear realizations of (super)conformal symmetries, we explicitly demonstrate that adding the harmonic oscillator potential to the action of conformal mechanics does not break these symmetries but modifies the…
The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the…
A systematic expansion in 1/N is constructed for baryons in QCD. Predictions of the 1/N expansion at leading and subleading order for baryon axial current coupling constant ratios such as F/D, baryon masses and magnetic moments are derived.…
An extended Holstein-Primakoff mapping which incorporates both single- and double boson mappings is used in the context of O(N+1) anharmonic oscillator with the global symmetry broken down to O(N) to study the next-to-leading order of the…
It is shown how nonlinear versions of quantum mechanics can be refolmulated in terms of a (linear) C*-algebraic theory. Then also their symmetries are described as automorphisms of the correspondong C*-algebra. The requirement of…
Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant…
Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse…
We propose an non-standard method to calculate non-equilibrium physical observables. Considering the generic example of an anharmonic quantum oscillator, we take advantage of the fact that the commutator algebra of second order polynomials…
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of $1/c^2$ terms representing (transverse) current-current interaction. For its derivation we…
The 1/N expansion of the two-particle irreducible (2PI) effective action is employed to compute universal properties at the second-order phase transition of an O(N)-symmetric N-vector model directly in three dimensions. At next-to-leading…
We present a brief summary of exact results on the non-perturbative effective superpotential of N=1 supersymmetric gauge theories based on generalized Konishi anomaly equations. In particular we consider theories with classical gauge groups…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
We generalize a recently proposed small-energy expansion for one-dimensional quantum-mechanical models. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present…
In this paper, we found new q-binomial formula for Q-commutative operators. Expansion coefficients in this formula are given by q-binomial coefficients with two bases (q,Q), determined by Q-commutative q-Pascal triangle. Our formula…
Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…