Related papers: A Parafermionic Generalization of the Jaynes Cummi…
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…
We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed…
We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural, well-known…
We analyze the possible types of ordering in a boson--fermion model. The Hamiltonian is inherently related to the Bose--Hubbard model for vector two-species bosons in optical lattices. We show that such model can be reduced to the…
We consider the quantum analog of the generalized Zernike systems given by the Hamiltonian: $$\hat{\mathcal{H}}_N =\hat{p}_1^2+\hat{p}_2^2+\sum_{k=1}^N \gamma_k (\hat{q}_1 \hat{p}_1+\hat{q}_2 \hat{p}_2)^k ,$$ with canonical operators…
This work presents a pedagogical and self-contained derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime. A perturbative unitary transformation removes nonresonant atom-field…
We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify…
Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, $\pi$-mesons, excitons, Cooper pairs are not ideal bosons, and,…
Generalized Z_k^(r/2) parafermionic theories - characterized by the dimension (r/2)(1-1/k) of the basic parafermionic field - provide potentially interesting quantum-Hall trial wavefunctions. Such wavefunctions reveal a W_k structure. This…
A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically…
Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…
Parafermions are fractional excitations which can be regarded as generalizations of Majorana bound states, but in contrast to the latter they require electron-electron interactions. Compared to Majorana bound states, they offer richer…
We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum…
We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to…
A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces…
We recently derived the Hamiltonian of fermionic composites by an exact procedure of bosonization. In the present paper expand this Hamiltonian in the inverse of the number of fermionic states in the composite wave function and give the…
We analyse parafermionic operators in the Q-state Potts model from three different perspectives. First, we explicitly construct lattice holomorphic observables in the Fortuin-Kasteleyn representation, and point out some special simplifying…
We study the generalized Jaynes-Cummings model of quantum optics at the inversion-symmetry-breaking and in the ultrastrong coupling regime. With the help of a generalized multiphoton rotating-wave approximation, we study the stationary…
Generalized quantum statistics, such as paraboson and parafermion statistics, are characterized by triple relations which are related to Lie (super)algebras of type B. The correspondence of the Fock spaces of parabosons, parafermions as…