Bose Operators Research Articles

Construction of Bose and Fermi operators in terms of q=0 quon operators

Bose and Fermi operators are constructed manifestly by using q=0 quon operators as standard building blocks as suggested by Greenberg. This confirms the assertion that quons with qϵ(−1, 1), q=1, q=−1, obey Boltzmann, Bose, Fermi statistics respectively.

Integration within an ordered product for q-deformed bosons

We introduce a newly developed technique of integration within an ordered product (IWOP) of Bose operators for the q-deformed boson case. In so doing, some new q-boson operator identities can be derived. A q-series formula is presented to derive the power series expansion of the vacuum projection operator in terms of the q-creation and q-annihilation operators.

Generalized SU(1,1) coherent-state theory and quantum characteristics of a weakly interacting Bose system.

We expand the Hamiltonian of a weakly interacting Bose system to second order in the Bose operators of the elementary excitations and use the mean-field approximation to linearize it. It is found that the dynamical algebra of the pairing'' approximated Hamiltonian is SU(1,1) algebra. By using the generalized SU(1,1) coherent-state theory we show that both the condensate states and the weakly excited states are generalized SU(1,1) coherent states. Based on these states, the quantum fluctuations and the second-order correlation functions of the Bose system are calculated and discussed.

Mixed correlation functions in systems interacting with Bose fields

For a large class of systems interacting with Bose fields, exact expressions are found for correlation functions containing products of Bose operators with evolution law of the free field and operators of the “medium”. Hierarchical equations describing the evolution of the system are constructed by means of these expressions. The Born—Markov approximation is investigated. A “causality principle” associated with the absence of an influence on the evolution of the system of stochastic forces due to the free field at short times is established.

New boson realization ofSU(1,1) algebra and its coherent state in the three-mode fock space

A new three-mode boson realization of theSU(1, 1) Lie algebra is found, on the basis of which a new unitary operatorU generating a normalizableSU(1, 1) coherent state from the vacuum is derived. The transformation properties of bose operators under theU transformation are obtained, which exhibit squeezing.

SOLITARY WAVES IN A SPIN CHAIN UNDER A SUPER-LONG-WAVE APPROXIMATION

Solitary waves in a spin chain with biquadratic anisotropic exchange interaction are investigated by means of the Holstein-Primakoff bosonic representation of spin operators. It is argued that the modified terms of the nonlinear Schrödinger equation are restricted strongly by the relative ratio of two small parameters η and ε used in long wave approximation and semiclassical approximation respectively. When assuming that η and ε2 have the same order (η−ε2, the so-called “super-long wave approximation”), after retaining terms of the equivalent order O(ε8), we find that the motion of Bose operator in the anisotropic case satisfies Schrödinger equation with high-order nonlinear term α|α|4. Its solitary wave solution and relevant physical results are discussed.

On a Concept of Quasiparticles with Parastatistics

AbstractA possibility of description of some physical models in solids in terms of quasiparticles with parastatistics is considered. These quasiparticles can be introduced both by Green's generalized second quantization and by means of a nonlinear operator transformation for Bose and/or Fermi operators. Several examples of the nonlinear transformations are given. Some physical properties of the superconducting models are discussed.

Exact energy spectrum and thermodynamics of one-dimensional bose system

For a one-dimensional many boson system with delta-functional repulsive potential, the total Hamiltonian H can be diagonalized U∗HU= 1 2m ∑ p þ 2a p∗a p+ 1 2m φℏ L ∑ p,q |þ−q|a p∗a pa q∗a q+ 1 2m φℏ L 2 1 3 [( ∑ p a p∗a p) 3− ∑ p a p∗a p] and cast into a compact form by a unitary operator U in the case of an infinitely large coupling constant, where a p and a p∗ are the annihilation and creation bose operators. We also expand the eigenenergy in a power-series of the inverse coupling constant, and obtain thermodynamic functions of this system up to the second order of the series.

Boson Hamiltonians and stochasticity for the vorticity equation

The evolution of the vorticity in time for 2D inviscid flow and in Lagrangian time for 3D viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise.

Nonlinear dynamical systems, first integrals, Bose operators, and Lie algebras

A connection between nonlinear autonomous systems of ordinary differential equations, first integrals, Bose operators and Lie algebras is described. An extension to nonlinear partial differential equations is given.

Solitonlike excitations in a spin chain with a biquadratic anisotropic exchange interaction.

Nonlinear solitonlike excitations in a spin chain with a biquadratic anisotropic exchange interaction are investigated using the coherent-state method combined with the Holstein-Primakoff bosonic representation of the spin operators. It is argued that the modified terms of the nonlinear Schr\odinger equation are strongly restricted by the relation between the continuum approximation (\ensuremath{\eta}=d/\ensuremath{\lambda}, the degree of the long-wavelength approximation, where d is the lattice constant and \ensuremath{\lambda} is the characteristic wavelength of excitation) and the semiclassical approximation (\ensuremath{\epsilon}=1/ \ensuremath{\surd}S , the degree of the truncation of the operator expansion, where S is the spin length). When assuming that \ensuremath{\eta} and \ensuremath{\epsilon} have the same order (\ensuremath{\eta}\ensuremath{\sim}\ensuremath{\epsilon}) after retaining terms of equivalent order O(${\mathrm{\ensuremath{\epsilon}}}^{6}$), the motion of the Bose operator for the anisotropic case satisfies the nonlinear Schr\odinger equation with cubic nonlinearity, and solitonlike excitations are obtained. The other two cases of the relations between \ensuremath{\eta} and \ensuremath{\epsilon}(\ensuremath{\eta}\ensuremath{\sim}${\mathrm{\ensuremath{\epsilon}}}^{3/2}$ and \ensuremath{\eta}\ensuremath{\sim}${\mathrm{\ensuremath{\epsilon}}}^{2}$) are also discussed.

Slave-Fermion Mean Field Theory of the Hubbard Model

Square lattice Hubbard model is investigated near half-filled in the limit of large U. A slave-fermion scheme is used, where electron operators are replaced by bose operators with auxiliary fermi operators. The ground state by a mean field approximation with RVB order parameter for spin shows long-range antiferromagnetic order, which is incommensurate except for half-filled case.

Kinetics of two-photon superradiance in the case of damped polarization

A Dicke type model with interaction bilinear in the field operators is considered. An exact hierarchy of kinetic equations in which the dynamical Bose operators formally do not occur is constructed. The Bose operators are eliminated by means of the conservation law inherent in the model and a theorem on nonequilibrium mean values of special form. The theorem is proved under general conditions and is valid for both Bose and Fermi operators. It is shown that the nonequilibrium operator which occurs in these mean values is arbitrary and may be either explicitly dependent on the time or be a many-time operator. The solution of the hierarchy of kinetic equations in the case of damped polarization shows that the pulse of two-photon superradiance of a concentrated system can have two comparable maxima. It is well known that the pulse of single-photon superradiance of a concentrated system can have only one maximum.

Solitons in the anisotropic Heisenberg chain in the Holstein-Primakoff representation

It is shown that the Holstein-Primakoff boson representation of spin operators leads to the same soliton excitations, in the anisotropic Heisenberg chain, as the classical treatment of spins, if one retains the terms up to products of six Bose operators.

On the theory of dense exciton systems

Abstract A rigorous reformulation of the Hamiltonian describing a dense exciton system is given in terms of ideal Bose operators. The kinematic implications of the Pauli exclusion principle are treated consistently. It is shown that as a consequence of the fermionic nature of the elementary constituents macroscopic occupation of single pair states cannot occur. A variational approach for the study of Off-Diagonal Long-Range Order (ODLRO) is outlined and the incorporation of the subsidiary condition is discussed.

Theory of Ferromagnetic State of HCP Solid 3He for Pair, Triple and Quadruple Spin Exchange Interaction. I Spin Wave Theory

There are two sublattices in hcp solid 3He in spite of the ferromagnetic state, because the hexagonal close-packed structure consists of two interpenetrating simple hexagonal Bravais lattices. The spins in each sublattice, and the multiple-exchange Hamiltonian including the most important two, three and four-particle exchange processes for the hcp phase of solid 3He are expressed in terms of Bose operators al, and bm by the method of Holstein and Primakoff. The eigen-energies of the spin wave obtained and we find an optical magnon branch besides the acoustic magnon branch. We calculate the temperature dependence of the order parameter <Sz>, the specific heat, and other physical quantities by the method of the spin wave theory.

Multiboson Holstein-Primakoff squeezed states for SU(2) and SU(1,1).

We define a new set of squeezed states using group-theoretical methods. The definition is based on the Holstein-Primakoff realization of both SU(2) and SU(1,1). Generalizations of these realizations are presented, connected with the Brandt-Greenberg generalized Bose operators. The new states exhibit interesting squeezing properties, depending in a characteristic way on the dimension of the irreducible unitary representation adopted. We also discuss the asymptotic behavior and present a set of relevant numerical results. Unexpected and interesting scaling behavior appears.

Kinematical and dynamic interactions do not change properties of two-particle solitons

The system of Frenkel excitons interacting with phonons is treated in the Agranovich-Toshich bosonic representation of Pauli operators up to terms with four Bose operators, comprising both kinematic and dynamic interaction. Equations of motion are formulated for the two-particle soliton wavefunction and it is shown that they are completely identical with those obtained previously with the hamiltonian quadratic in Bose operators.

Bosonization of a two-level system with dissipation.

We summarize in this work the relations of the spin-boson Hamiltonian, which was recently studied in connection with the phenomenon of quantum coherence in the presence of dissipation, to three different fermionic Hamiltonians. These relations were obtained through well-known equivalences between Fermi and Bose operators in one dimension. The fermionic Hamiltonians correspond to (a) a two-level system coupled linearly with a fermionic bath, (b) the resonant-level model, and (c) the anisotropic Kondo model. For the first Hamiltonian we reobtain and discuss the relationship between the dimensionless dissipation coefficient \ensuremath{\alpha} and the phase shift of the fermions. The resonant-level model allows us to study the properties of the two-level system for values of \ensuremath{\alpha} around (1/2). At \ensuremath{\alpha}=(1/2) the model reduces to the Toulouse limit, where the Hamiltonian is exactly soluble. A pure exponential decay is obtained for the relaxation of P(t)=〈${\ensuremath{\sigma}}_{z}$(t)〉 for tg0, given that for tl0 the system is known to be localized in one of the two states. The comparison with the Kondo model gives the long-time-limit behavior of the system for (1/2)1 and provides a connection between universal numbers obtained previously for the spin-boson Hamiltonian and the Kondo model.

Method of the spin hamiltonian diagonalization

A nonlinear unitary transformation is proposed which permits one to remove nondiagonal terms in the spin hamiltonian. The diagonalization procedure is based on solution of linear differential equations with bonds. This method allows one to simplify the theoretical description of spin systems both in magneto-ordered and in paramagnetic states. It may be also employed for Bose and Fermi operators.