Creation and annihilation operators for Nielsen-Olesen vortices in the coherent state approximation

Using the standard techniques of canonical quantization, we construct approximate expressions for the creation and annihilation operators for Nielsen-Olesen vortices. The forms for the creation and annihilation operators are appropriate to situations where large-scale vortex condensation takes place. In particular, a phenomenon such as this is basic in the quark confinement schemes of Mandelstam and 't Hooft.     

谐振子产生算符和湮没算符的逆算符

本引入谐振子产生算符和湮没算符的逆算符，导出它们在Ｆｏｃｋ空间的表达式，并给出了一些简单应用。     

Controllability of pure states for the Pöschl-Teller potential with a dynamical group SU(2)

The controllability of a quantum system for the modified Pöschl-Teller (MPT) potential with the discrete bound states is investigated. The creation and annihilation operators of this potential are constructed directly from the normalized wave function with the factorization method and associated to an su(2) algebra. It is shown that this quantum system with the nondegenerate discrete bound states can, in principle, be strongly completely controllable, i.e., the system eigenstates can be guided by the external field to approach arbitrarily close to a target state, which could be theoretically realized by the actions of the creation and annihilation operators on the ground state.     

Holevo-Ordering and the Continuous-Time Limit for Open Floquet Dynamics

We consider an atomic beam reservoir as a source of quantum noise. The atoms are modelled as two-state systems and interact one-at-a-time with the system. The Floquet operators are described in terms of the Fermionic creation, annihilation and number operators associated with the two-state atom. In the limit where the time between interactions goes to zero and the interaction is suitably scaled, we show that we may obtain a causal (that is, adapted) quantum stochastic differential equation of Hudson—Parthasarathy type, driven by creation, annihilation and conservation processes. The effect of the Floquet operators in the continuous limit is exactly captured by the Holevo ordered form for the stochastic evolution     

Theory of two-photon lasers I

We start from the microscopic Hamiltonian formulated by means of creation and annihilation operators for the field modes, and creation and annihilation operators for the electrons. The virtual transitions via the intermediate atomic level are eliminated by second order perturbation theory so that an effective Hamiltonian results which describes two-photon creation or annihilation. In the next step Heisenberg equations of motion are derived for the field amplitudes, the atomic dipole moments, and the inversion. The effect of heatbaths is taken into account by means of damping terms and fluctuating forces. In the present paper these equations are averaged over the fluctuating forces and the resulting semiclassical equations are solved for the stationary state. We treat the degenerate and nondegenerate case including detuning and atomic levels with homogeneous and inhomogeneous broadening. The field modes may be either running or standing waves. A detailed discussion of the laser condition is given.     

Time-dependent formulation of the linear unitary transformation and the time evolution of general time-dependent quadratic Hamiltonian systems

A time-dependent closed-form formulation of the linear unitary transformation for harmonic-oscillator annihilation and creation operators is presented in the Schrödinger picture using the Lie algebraic approach. The time evolution of the quantum mechanical system described by a general time-dependent quadratic Hamiltonian is investigated by combining this formulation with the time evolution equation of the system. The analytic expressions of the evolution operator and propagator are found. The motion of a charged particle with variable mass in the time-dependent electric field is considered as an illustrative example of the formalism. The exact time evolution wave function starting from a Gaussian wave packet and the operator expectation values with respect to the complicated evolution wave function are obtained readily.     

Drinfeld twists of the open XXZ chain with non-diagonal boundary terms

The Drinfeld twists or factorizing F-matrices for the open XXZ spin chain with non-diagonal boundary terms are constructed. It is shown that in the F-basis the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. The explicit and completely symmetric expressions of the two sets of Bethe states of the model are obtained.     

New Application of Noncanonical Maps in Quantum Mechanics

One invertible and one unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. The original annihilation and creation operators are mapped into new operators, not conjugate to each other, whose standard commutator equals the identity plus a correction proportional to the original number operator. The consistency condition for the existence of this new set of operators is derived, by exploiting the Stone theorem on 1-parameter unitary groups. The above scheme leads to modified equations of motion which do not preserve the properties of the original first-order set for annihilation and creation operators. Their relation with commutation relations is also studied.     

费密共振和甲烷的振动能谱

用局域模模型来解释甲烷的伸展和弯曲振动能谱，其中伸展振动和弯曲振动间的相互作用用费密共振项来描写，它由一个伸展振子的玻色产生（或湮没）算子和两个弯曲振子的玻色湮没（或产生）算子乘积的T_d不变组合构成．这模型包含10个参数，与已发表的甲烷振动能谱的实验数据比较，得到能量的方均根偏差为12.38cm^－1． 关键词：     

标量算符本征值对g壳层LSQ耦合态的完全分类计算

按（Ｕ,Ｄ）Ｌ－ＬＳＱ格式构造ｌ壳层ＬＳＱ耦合态,这里Ｕ（Ｄ）是自旋向上（向下）电子的轨道角动量,Ｌ、Ｓ、Ｑ是总轨道角动量、总自旋和准旋。由４个产生－湮灭算符构造与轨道、自旋准旋算符均为易的标量算符并用基本征值对ＬＳＱ耦合态进上步分类,实现了对ｆ、ｇ壳层耦合态的完全分类,列出了ｇ壳层耦合态完全分类的主要结果。     

Many-electron exchange Hamiltonian in the theory of ferromagnetism

A Hamiltonian describing effects of many-electron interatomic exchange in magnetic crystals is derived by application of an appropriate unitary transformation to the many-electron, many-nucleus Hamiltonian. It is expressed in terms of atomic annihilation and creation operators and j-fold exchange matrix elements for 1 ? j ? N, where N is the number of electrons localized on each crystal site. Explicit formulas are derived for the case of not more than half-filled shells with Hund's rule factorization. An appropriate spin algebra is introduced and the coefficient of the bilinear (Heisenberg) and biquadratic interactions evaluated in terms of single and double-exchange matrix elements. The relative magnitudes of such matrix elements are roughly estimated using determinantal wave functions.     

Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator

Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.     

A free-algebraic solution for the planar approximation

An explicit solution for the generating functional of n-point functions in the planar approximation is given in terms of two sets of free-algebraic annihilation and creation operators.     

Invariants and coherent states for a nonstationary fermionic forced oscillator

Invariant creation and annihilation operators and related Fock states and coherent states are built up for the system of nonstationary fermionic forced oscillator.     

Dobiński relations and ordering of boson operators

We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations.     

Exact analytical solution for quantum spins mixing in spin-1 Bose--Einstein condensates

This paper solves exactly a set of fully quantized coupled equations describing the quantum dynamics of quantum spins mixing in spin-1 Bose-Einstein condensates by deriving the exact explicit analytical expressions for the evolution of creation and annihilation operators.     

Angular momenta and eigenvectors of the weakly coupled T ⊗ t Jahn‐Teller system

The eigenvalues of the weakly coupled T ? t Jahn‐Teller problem are known for several decades, and the same holds also true for the eigenstates. These, however, are only given in the traditional position representation, which proves inconvenient if one attempts to extend the weak‐coupling treatment into the region of stronger coupling. Here the solution of the T ? t eigenvalue problem at weak coupling is derived in terms of creation and annihilation operators. This reformulation of the problem is nontrivial, since the algebraic form of the oscillator eigenvectors, being simultaneous angular‐momentum eigenstates, has been worked out only recently and is probably still widely unknown. The electronic and oscillator eigenstates are then coupled to form eigenvectors of the total angular momentum. Finally, in preparation for an extension of the weak‐coupling treatment, the action of the boson creation and annihilation operators on the oscillator eigenvectors is calculated, thus completing the algebraic approach to the weakly coupled T ? t system.     

Power Series Expansions for Vacuum Projection Operator of Paraparticles

Some power series expansions for the vacuum projection operator of paraboson and parafermion are derived. A recursion method is essential to these derivations of the power series expansion in terms of creation and annihilation operators of the paraparticles.     

Phase space theory of Bose–Einstein condensates and time-dependent modes

A phase space theory approach for treating dynamical behaviour of Bose–Einstein condensates applicable to situations such as interferometry with BEC in time-dependent double well potentials is presented. Time-dependent mode functions are used, chosen so that one, two,…highly occupied modes describe well the physics of interacting condensate bosons in time dependent potentials at well below the transition temperature. Time dependent mode annihilation, creation operators are represented by time dependent phase variables, but time independent total field annihilation, creation operators are represented by time independent field functions. Two situations are treated, one (mode theory) is where specific mode annihilation, creation operators and their related phase variables and distribution functions are dealt with, the other (field theory) is where only field creation, annihilation operators and their related field functions and distribution functionals are involved. The field theory treatment is more suitable when large boson numbers are involved. The paper focuses on the hybrid approach, where the modes are divided up between condensate (highly occupied) modes and non-condensate (sparsely occupied) modes. It is found that there are extra terms in the Ito stochastic equations both for the stochastic phases and stochastic fields, involving coupling coefficients defined via overlap integrals between mode functions and their time derivatives. For the hybrid approach both the Fokker–Planck and functional Fokker–Planck equations differ from those derived via the correspondence rules, the drift vectors are unchanged but the diffusion matrices contain additional terms involving the coupling coefficients.Results are also presented for the combined approach where all the modes are treated as one set. Here both the Fokker–Planck and functional Fokker–Planck equations are exactly the same as those derived via the correspondence rules. However, although the Ito stochastic field equations are also unchanged, the Ito equations for the stochastic phases contain an extra classical term involving the coupling coefficients.