function for the squeezed atomic coherent state in entangled state representation and some of its applications

Based on the Einstein, Podolsky, and Rosen (EPR) entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state (SACS), which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.     

Wave function for the squeezed atomic coherent state in entangledstate representation and some of its applications

Based on the Einstein, Podolsky, and Rosen (EPR) entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state (SACS), which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.     

Generation of a new bipartite coherent-entangled state and its applications

A new bipartite coherent-entangled state is introduced in the two-mode Fock space, which exhibits the properties of both a coherent state and an entangled state. The set of coherent-entangled states makes up a complete and partly nonorthogonal representation. A simple experimental scheme to produce the coherent-entangled state using an asymmetric beamsplitter is proposed. Some applications of the coherent-entangled state in quantum optics are also presented.     

Generation of a new bipartite coherent-entangled state and its applications

A new bipartite coherent-entangled state is introduced in the two-mode Fock space,which exhibits the properties of both a coherent state and an entangled state.The set of coherent-entangled states makes up a complete and partly nonorthogonal representation.A simple experimental scheme to produce the coherent-entangled state using an asymmetric beamsplitter is proposed.Some applications of the coherent-entangled state in quantum optics are also presented.     

Commutation superoperator of a state and its applications to the noncommutative statistics

For a normal state on a von Neumann algebra the space of square-integrable operators is introduced. As distinct from the L² space in the classical probability theory, it possesses an additional skew-symmetric form and the associated superoperator, which is a convenient tool to describe commutation properties in L². It is shown that a state on the algebra of canonical commutation relations is Gaussian (quasi-free) iff the space of canonical observables is an invariant subspace of the corresponding commutation superoperator. Basing on these ideas a new approach to some problems in the noncommutative statistic is developed.     

On a new method of quantisation and some of its applications

Any quantum-mechanical problem withO(2,1) as SGA (spectrum-generating algebra) is considered as a single oscillator related to a new quantisation. In the case of small interactions the problems can be solved within essentially Fock representations while in the case of strong attractive potentials they can be solved only within the essentially non-Fock representations of the new commutation relations. Explicit realisations of a system ofn oscillators through para-Bose operators have been constructed.On leave of absence from the Institute of Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria.     

Dynamics of the even-binomial state in some quantum system

The effect of the even-binomial state (the state which interpolates between the even-number state and the even-coherent state) on the Jaynes-Cummings model and resonance fluorescence for a single atom and for many cooperative atoms is discussed. The study of two quantum optical systems in such a state provides more insight into the continuous passage from the even-number state to the even-coherent state. The squeezing phenomenon and the correlation functions are examined.     

Representation of the coherent state for a beam splitter operator and its applications

A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.     

Langevin dynamics simulations of phase separation in a one-component system

Langevin dynamics computer simulations have been performed for a two-dimensional Lennard-Jones fluid quenched into the coexistence region of its liquid-vapor phase diagram. For late stages of the phase-separation process, the average radius of the liquid clusters is found to grow proportional to (time)^1/4. This growth law is analyzed theoretically and compared to recent molecular dynamics and Monte Carlo results. Details of the different simulation methods are critically discussed.     

The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving, at any order, certain symmetries of the exact solution.The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion, in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.     

Equilibrium equation of small-size phases and some its applications

The equilibrium equation of small-size phases for a one-component system, taking into account the size dependences of the pressure, temperature, and interface energy at the phase boundaries in the highly dispersed state, is presented. It is shown that the phase-transition and ternary-point temperatures decrease with a decrease in the particle size. Expressions are derived, which relate the surface tensions at the solid-vapor and solid-liquid interfaces (which are difficult to experimentally determine) to the liquid-vapor surface tension and other physical quantities, which can be experimentally determined with high accuracy. There is satisfactory agreement between the obtained results and experimental data.     

On the equation of state of classical one-component systems with long-range forces

Several definitions of the pressure are introduced for one-component systems and shown to be nonequivalent in the presence of a rigid neutralizing background. Relations between these pressures are derived for finite and infinite systems; these relations depend on the asymptotic behavior of the force at infinity, with the Coulomb force at the borderline between different properties. It is argued that only one of those definitions is physically acceptable and its properties are discussed in relation to the asymptotic behavior of the force. It is seen in particular that a knowledge of the state of the infinite system is not sufficient to determine its thermodynamic properties. The results are illustrated by some typical examples.For example, for two-dimensional systems with three-dimensional Coulomb interaction see refs. 2–4.     

Interfacial tension of a crystalline nanoparticle in the liquid mother phase in a one-component metallic system

The expressions for the interfacial tension on plane and curved solid-liquid boundaries and for the distance between the equimolecular separating surface and the separating surface corresponding to a zero excess free energy of the system have been obtained in terms of a thermodynamic approach using two separating surfaces. For 50 metals, the numerical calculations have been performed for plane boundaries and solid spherical nanoparticles in their own melts in the dependence on their sizes at the melting temperatures.     

Equation of state of a real gas

It is shown using 28 gases as an example that the Van der Waals equation in the form $$\left[ {P + \frac{a}{{(V + c)^k T^m }}} \right](V - b) = RT$$ correctly expresses quantitative relations between parameters P, V, and T for real gases. Here, a, b, and c are constants; k is a number close to 2; and m varies in the range 0.2–2.17 for different gases. The critical parameters of most gases calculated by this formula are found to be close in value to the experimental parameters.     

Structure factor of liquid metals in one-component plasma system

We present the analytical expression to determine the static structure factorS(q) of liquid alkali metals based on the semi-analytic theory of Baus and Hansen. The calculations were motivated to point out the anomalies exhibited by one-component plasma system (ocp) in describing the structure factor. The numerical example of Na illustrates our results.ocp structure factor is also compared with those obtained by the hard sphere system.     

Algebraic aspects of the Hirzebruch signature operator and applications to transitive Lie algebroids

The index of the classical Hirzebruch signature operator on a manifold M is equal to the signature of the manifold. The examples of Lusztig ([10], 1972) and Gromov ([4], 1985) present the Hirzebruch signature operator for the cohomology (of a manifold) with coefficients in a flat symmetric or symplectic vector bundle. In [6], we gave a signature operator for the cohomology of transitive Lie algebroids. In this paper, firstly, we present a general approach to the signature operator, and the above four examples become special cases of a single general theorem.     

Equation of state for a hard-sphere mixture

The equation of state for a multicomponent hard-sphere system is derived using the method of accelerated convergence of the perturbation series. In the asymptotic limit of small densities, this equation reproduces the virial coefficients known for the systems in question. In the case of a one-component system, the equation transforms into a form that adequately describes both the stable and metastable phases of the substance.     

New bipartite coherent-entangled state in two-mode Fock space and its applications

A new bipartite coherent-entangled state (CES) is found which exhibits both coherent state and entangled state properties. The set of CESs constitute a complete and partly nonorthogonal representation. Using an asymmetric beamsplitter a experimental scheme to produce the CES is proposed. Applications of CESs in quantum optics are also presented.