Bose Operators Research Articles

ORDINARY DIFFERENTIAL EQUATIONS, FIRST INTEGRALS, CONFORMAL INVARIANTS, BOSE OPERATORS, COHERENT STATES AND ENTANGLEMENT

Autonomous systems of first order ordinary differential equations can be embedded into a Hilbert space description by using Bose operators and Glauber coherent states. The first integrals and conformal invariants of the autonomous system can be represented by states in a Hilbert space. Thus the embedding in a Hilbert space allows us to study entanglement of the states. We apply it here to first integrals and conformal invariants which are expressed as states.

A KIND OF NONLINEAR COHERENT-ENTANGLED STATE AND SQUEEZING PROPERTY

Based on the technique of integration within an ordered product of nonlinear Bose operators, a new kind of nonlinear coherent entangled state, which exhibits both the property of coherent state and quantum entanglement, is constructed and its application in squeezing is discussed.

Bose Operators as Linear Combination of Fermi Operators. Correlated Electron Pairs Formation

Bose Operators as Linear Combination of Fermi Operators. Correlated Electron Pairs Formation

Entanglement, Bose operators, coherent states and classical dynamical systems

Classical dynamical systems can be embedded into a Hilbert space description by using Bose operators and Glauber coherent states. Thus the embedding in a Hilbert space allows us to study entanglement of the states. We apply it here to first integrals which are expressed as states.

On Bosonic Magnetic Flux Operator and Bosonic Faraday OperatorFormula

In the literature about mesoscopic Josephson devices the magneticflux is considered as an operator, the fundamental commutative relationbetween the magnetic flux operator and the Cooper-pair charge operator isusually preengaged. In this paper we show that such a relation can be deducedfrom the basic Bose operators' commutative relation through the entangled staterepresentation. The Faraday formula in bosonic form is then equivalent tothe second Josephson equation. The current operator equation for LCmesoscopic circuit is also derived.

Collective modes for an array of magnetic dots in the vortex state

The dispersion relations for collective magnon modes for square-planar arrays of vortex-state magnetic dots, having closure magnetic flux are calculated. The array dots have no direct contact between each other, and the sole source of their interaction is the magnetic dipolar interaction. The magnon formalism using Bose operators along with translational symmetry of the lattice, with the knowledge of mode structure for the isolated dot, allows the diagonalization of the system Hamiltonian giving the dispersion relation. Arrays of vortex-state dots show a large variety of collective mode properties, such as positive or negative dispersion for different modes. For their description, not only dipolar interaction of effective magnetic dipoles, but non-dipolar terms common to higher multipole interaction in classical electrodynamics can be important. The dispersion relation is shown to be non-analytic as the value of the wavevector approaches zero for all dipolar active modes of the single dot. For vortex-state dots the interdot interaction is not weak, because, the dynamical part (in contrast to the static magnetization of the vortex state) dot does not contain the small parameter, the ratio of vortex core size to the dot radius. This interaction can lead to qualitative effects like the formation of modes of angular standing waves instead of modes with definite azimuthal number known for the insolated vortex state dot.

Generating Generalized Bessel Equations by Virtue ofBose Operator Algebra and Entangled State Representations

With the help of Bose operator identities and entangledstate representation and based on our previous work[Phys. Lett. A 325 (2004) 188]we derive some new generalized Bessel equations which also haveBessel function as their solution. It means that for these intricatehigher-order differential equations, we can get Bessel function solutionswithout using the expatiatory power-series expansion method.

Fractional Hankel transform gained via non-unitary bosonic operator realization of angular momentum generators

By proposing new non-unitary Bose operator realization of angular momentum generators ( J − , J + , J 0 ) and finding that the charge-amplitude entangled states (CAES) introduced in [H.-y. Fan, Phys. Lett. A 313 (2003) 343] carry the representative space of them, we derive the integral kernel of optical fractional Hankel transform (FHT) by calculating the matrix element of exp { i θ ( J + + J − ) } in the CAES.

Statistical properties of the Cooper pair operators

AbstractThe Cooper pair has the total spin S = 0. So, in accordance with the Pauli principle, the wave functions describing the Cooper pair system should have the boson permutation symmetry, but the pairon operators (Cooper's pair operators) do not obey the boson commutation relations. The pairon operators may not be considered neither as the Bose operators, nor as the Fermi operators. In this work, we analyze the statistical properties and the commutation relations for the pairon operator and reveal that they correspond to the modified parafermi statistics of rank p = 1. Two different expressions for the Cooper pair number operator are presented. We demonstrate that the calculations with a Hamiltonian expressed via pairon operators is more convenient using the commutation properties of these operators without presenting them as a product of fermion operators. This allows to study problems in which the interactions between Cooper's pair are also included. The problem of two interacting Cooper's pairs is discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Infinite statistics and theSU(1, 1) phase operator

A few years ago, Agarwal (1991 Phys. Rev. A 44 8398) showed that the Susskind–Glogower phase operators, expressible in terms of Bose operators, provide a realization of the algebra for particles obeying infinite statistics. In this paper we show that the SU(1, 1) phase operators, constructed in terms of the elements of the su(1, 1) Lie algebra, also provide a realization of the algebra for infinite statistics. There are many realizations of the su(1, 1) algebra in terms of single or multimode bose operators, three of which are discussed along with their corresponding phase states. The Susskind–Glogower phase operator is a special case of the SU(1, 1) phase operator associated with the Holstein–Primakoff realization of su(1, 1).

Correlations between Kondo clouds in nearly antiferromagnetic Kondo lattices

Abstract We discuss a novel fluctuational mechanism explaining the physics of nearly antiferromagnetic Kondo lattices (KL). The effective action for KL model is expressed in terms of Bose operators responsible for paramagnetic excitations and semi-bosonic fields describing the dynamic Kondo clouds created by conduction electrons around local spin. The gauge invariant resonance valence bond theory of interacting Kondo clouds describes the spin liquid with strong critical fluctuations imitating itinerant fluctuation magnetism of Moriya type.

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra**The project supported by National Natural Science Foundation of China under Grant No. 10175057 and the President Foundation of the Chinese Academy of Sciences

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation describing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some Hamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.

Chaotic Maps, Invariants, Bose Operators, and Coherent States

We first show how an autonomous system of ordinary first-order difference equations can be embedded into a Hilbert space description by using Bose operators and coherent states. Then we describe how an invariant can be expressed using Bose operators. Two examples are given.

Deformed CliffordClq(n m) and orthosymplecticUq[osp(2n 1 2m)] superalgebras and their root of unity representations

It is shown that the Clifford superalgebra Cl(n|m) generated by m pairs of Bose operators (odd elements) anticommuting with n pairs of Fermi operators (even elements) can be deformed to Clq(n|m) such that the latter is a homomorphic image of the quantum superalgebra Uq[osp(2n + 1|2m)]. The Fock space F(n|m) of Clq(n|m) is constructed. For q being a root of unity (q = exp(i?l/k)) q-bosons (and q-fermions) are operators acting in a finite-dimensional subspace Fl/k(n|m) of F(n|m). Each Fl/k(n|m) is turned through the above-mentioned homomorphism into an irreducible (root of unity) Uq[osp(2n + 1|2m)] module. For q being a primitive root of unity (l = 1) the corresponding representation is unitary. The module F1/k(n|m) is decomposed into a direct sum of irreducible Uq[sl(m|n)] submodules. The matrix elements of all Cartan?Weyl elements of Uq[sl(m|n)] are given within each such submodule.

New Bose Operator Realization of SU(2) Algebra and Its Application in Optical Propagation**The project supported by National Natural Science Foundation of China under Grant No. 10175057

We introduce a new Bose operator realization of SU(2) Lie algebra and applied it to optical propagation in GRIN media or some lens-setup.

-representation, positive -representation, and antinormally ordering expansion of density matrices in nonlinear coherent states

Based on the newly constructed overcompleteness relation of the nonlinear coherent states (NLCSs) and corresponding -representation we derive: (1) a new antinormally ordered expansion of density matrices; and (2) the corresponding positive -representation. Our derivation employs the technique of integration within an ordered product of nonlinear Bose operator functions. A relationship between the positive -representation and the generalized characteristic function in the context of NLCSs is also obtained.

Random-phase approximation study of collective excitations in the Bose-Fermi mixed condensate of alkali-metal gases

We perform Random Phase Approximation (RPA) study of collective excitations in the bose-fermi mixed degenerate gas of Alkali-metal atoms at T=0. The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of bose and fermi multipole ($L$) operators with $L=0,1,2,3$. Transition densities and dynamical structure factors are calculated for collective excitations. Comparison with the sum rule prediction for the collective frequency is given. Time dependent behavior of the system after an external impulse is studied.

The P-representation on Nonlinear Coherent State Basis**The project supported by National Natural Science Foundation of China

Using the technique of integration within an ordered product of nonlinear Bose operators and by composing the nonlinear coherent state's over-completeness relation, we construct the corresponding P-representation theory. The generalized P-representation for some nonlinear Bose operators can be established.

Self-and cross-phase modulation of ultrashort light pulses in an inertial Kerr medium: spectral control of squeezed light

Quantum theory of self-phase and cross-phase modulation of ultrashort light pulses in the Kerr medium is developed, taking into account the response time of an electronic nonlinearity. The corresponding algebra of time-dependent Bose operators is elaborated. It is established that the spectral region of the pulse where the quadrature fluctuation level is lower than the shot-noise one depends on the value of the nonlinear phase shift, the intensity of another pulse and the relaxation time of the nonlinearity. It is shown that the frequency of the pulse spectrum at which the suppression of fluctuations is maximum can be controlled by adjusting the other pulse intensity.

BOSE OPERATOR HAMILTONIAN MODEL FOR ROTATING ELECTRIC DIPOLE AND GENERALIZED EHRENFEST'S THEOREM

We present a Bose operator Hamiltonian model for totally quantum mechanically describing energy and eigenfunctions of a rotating dipole in the presence of electric field. The corresponding Heisenberg equations of motion are derived which leads us to the generalized Ehrenfest theorem for rotating system. Remarkably, a zero-point angular momentum ℏ/2 appears in the generalized Ehrenfest theorem corresponding to the classical equation Iω=L.