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We consider the family of 3x3 operator matrices H(K), K ∈ T³ := (-π; π]³ associated with the lattice systems describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles. We find a finite set Λ ⊂ T³ to prove the existence of infinitely many eigenvalues of H(K) for all K ∈ ⊂ when the associated Friedrichs model has a zero energy resonance. It is found that for every K ∈ ⊂, the number N(K, z) of eigenvalues of H(K) lying on the left of z, z < 0, satisfies the asymptotic relation ... with 0 < U0 < ∞, independently on the cardinality of ... . Moreover, we prove that for any K ∈ ⊂ the operator H(K) has a finite number of negative eigenvalues if the associated Friedrichs model has a zero eigenvalue or a zero is the regular type point for positive definite Friedrichs model. [ABSTRACT FROM AUTHOR]

We construct exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene with a small potential. [ABSTRACT FROM AUTHOR]

Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation. In this paper, we study linear stochastic Schrödinger equations (LSSEs) associated with QBN in the space of square integrable complex-valued Bernoulli functionals. We first rigorously prove a formula concerning the number operator N on Bernoulli functionals. And then, by using this formula as well as Mora and Rebolledo's results on a general LSSE [C. M. Mora and R. Rebolledo, Infinite. Dimens. Anal. Quantum Probab. Relat. Top. 10, 237-259 (2007)], we obtain an easily checking condition for a LSSE associated with QBN to have a unique Nr-strong solution of mean square norm conservation for given r ≥ 0. Finally, as an application of this condition, we examine a special class of LSSEs associated with QBN and some further results are proven. [ABSTRACT FROM AUTHOR]

We study the special features of vacuum particle creation in an external classical field for two simple external field models in standard QED. Our investigation is based on a kinetic equation that is a nonperturbative consequence of the fundamental QED equations of motion. We identify the special features of system evolution that apply qualitatively also for other systems and are therefore rather general. The common basis for a description of these systems is formed by kinetic equations for vacuum particle creation belonging to the class of integro-differential equations of non-Markovian type with fastly oscillating kernel. This allows us to characterize the processes of this type as belonging to the class of field-induced phase transitions. Examples range from condensed matter physics to cosmology. [ABSTRACT FROM AUTHOR]

We study the wave part of a localized solution of the linear systemof shallow water equations. Given a relationship between initial conditions, the relationship between the corresponding solutions is found. [ABSTRACT FROM AUTHOR]

We consider the problem of remote two-qubit state creation using the two-qubit excitation pure initial state of the sender. The communication line is based on the optimized boundary-controlled chain with two pairs of properly adjusted coupling constants. We show that the communication line can be characterized by a set of parameters independent of the initial state of the sender. These parameters are permanent attributes of a communication line and can be either calculated theoretically or measured in experiment. In particular, they determine the creatable subregion of the receiver's state space. The creation of a particular state within the creatable region is achieved by a proper choice of the independent parameters of the sender's initial state (control parameters) and reduces to the solvability of a certain system of algebraic equations. The creation of the two-qubit Werner state is considered as an example. We also study the effects of imperfections of the chain on the state creation. [ABSTRACT FROM AUTHOR]

We deduce the canonical brackets for a two (1+1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime. [ABSTRACT FROM AUTHOR]

Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. In this paper, we first present some new results concerning quantum Bernoulli noises, which themselves are interesting. Then, based on these new results, we construct a time-dependent quantum walk with infinitely many degrees of freedom. We prove that the walk has a unitary representation and hence belongs to the category of the so-called unitary quantum walks. We examine its distribution property at the vacuum initial state and some other initial states and find that it has the same limit distribution as the classical random walk, which contrasts sharply with the case of the usual quantum walks with finite degrees of freedom. [ABSTRACT FROM AUTHOR]

In this article, we obtain a regularized trace formula for magic Gribov operator H = λ ″ G + H μ , λ acting on Bargmann space where G = a ⁎ 3 a 3 and H μ , λ = μ a ⁎ a + i λ a ⁎ ( a + a ⁎ ) a Here a and a ⁎ are the standard Bose annihilation and creation operators and in Reggeon field theory, the real parameters λ ″ is the magic coupling of Pomeron, μ is Pomeron intercept, λ is the triple coupling of Pomeron and i 2 = − 1 . By applying some abstract results of Sadovnichii–Podol'skii (2002) [23] , we give the number of corrections sufficient for the existence of finite formula of the trace of concrete magic Gribov's operator. [ABSTRACT FROM AUTHOR]

An experimentally realizable scheme is considered for manipulating quantum states using a general superposition (SUP) of products of interacting annihilation and creation operators. Application of such an operation on states with classical features introduces strong nonclassicality. This provides the possibility of engineering quantum states with nonclassical features. [ABSTRACT FROM AUTHOR]

In previous works, we studied the problem of constructing a basis in the space of local operators for an anisotropic XXZ spin chain with spin 1/2 such that the vacuum expectation values have a simple form. For this, we introduced fermionic creation operators. Here, we extend this construction to the spin- 1 case. Using a certain version of the fusion procedure, we find two doublets of fermionic creation operators and one triplet of bosonic creation operators. We prove that the basis obtained by the action of these operators satisfies the dual reduced quantum Knizhnik-Zamolodchikov equation. [ABSTRACT FROM AUTHOR]

A short description, analysis, and comparison of four different methods used for calculation of the Green's functions for the Hubbard model in the approximation of static fluctuations are presented. The Green's functions in the approximation of static fluctuations are calculated for fullerene С, and three main optical С absorption bands are interpreted. [ABSTRACT FROM AUTHOR]

Anewrepresentation-which is similar to the Bargmann representation-of the creation and annihilation operators is introduced, in which the operators act like 'multiplication with' and like 'derivation with respect to' a single real variable. The Hilbert space structure of the corresponding states space is produced and the relations with the Schroedinger representation are derived. Possible connections of this new representation with the asymptotic wavefunctions of the gauge-fixed quantum Chern-Simons field theory and (2+1) gravity are pointed out. It is shown that the representation of the field operator algebra of the Chern-Simons theory in the Landau gauge is not a *-representation; the consequences on the evolution of the states in the semiclassical approximation are discussed. [ABSTRACT FROM AUTHOR]

We study the exact Bethe ansatz solution of the Hamiltonian in a form whereby quantum numbers of states refer to hole-pairs, rather than particle-pairs used in previous studies. We find an asymmetry between these approaches. For an attractive system states in the strong pairing regime take the form of a partial condensate involving two distinct hole-pair creation operators. An analogous feature is not observed in the particle-pair picture of an attractive system. [ABSTRACT FROM AUTHOR]

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS. [ABSTRACT FROM AUTHOR]

The family {∂k,∂k*}k≥0 of annihilation and creation operators acting on square integrable functionals of a Bernoulli process Z = (Zk)k>=0 can be interpreted as quantum Bernoulli noises. In this note we consider the operator family {ℓk,ℓk*}k≥0, where ℓk=∂kEk with Ek being the conditional expectation (operator) given σ-field σ(Zj; 0 <= j <= k). We show that ℓk (resp. ℓk*) is essentially a kind of localization of the annihilation operator ∂k (resp. creation operator ∂k*). We examine properties of the family {ℓk,ℓk*}k≥0 and prove, among other things, that ℓk and ℓk* satisfy a local canonical anti-communication relation and (ℓk*)k≥0 forms a mutually orthogonal operator sequence although each ℓk is not a projection operator. We find that the operator series ∑k=0∞ℓk*Xℓk converges in the strong operator topology for each bounded operator X acting on square integrable functionals of Z. In particular we get an explicit sum of the operator series ∑k=0∞ℓk*ℓk. A useful norm estimate on ∑k=0∞ℓk*Xℓk is also obtained. Finally we show applications of our main results to quantum dynamical semigroups and quantum probability. [ABSTRACT FROM AUTHOR]