Spontaneous Resonances and the Coherent States of the Queuing Networks

We present an example of a highly connected closed network of servers, where the time correlations do not vanish in the infinite volume limit. The limiting interacting particle system behaves in a periodic manner. This phenomenon is similar to the continuous symmetry breaking at low temperatures in statistical mechanics, with the average load playing the role of the inverse temperature.     

Wigner Functions and Tomograms of?the?Klauder-Perelomov Coherent States for?the?Pseudoharmonic Oscillator

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the Klauder-Perelomov coherent states (KP-CSs) for the pseudoharmonic oscillator (PHO) are obtained and the variations of the Wigner functions with the parameters k and z are discussed. Moreover, the tomograms of the KP-CSs for the PHO are calculated by virtue of intermediate coordinate-momentum representation in quantum optics. Project 10574060 supported by the National Natural Science Foundation of China and project X071049 supported by Science Foundation of Liaocheng University.     

Reply to the Comments of Sharipov on “Symmetry of the Linearized Boltzmann Equation”

This is a reply to the comments by Sharipov on the papers published in J. Stat. Phys. 136:751 (2009) and in J. Stat. Phys. 136:945 (2009). The present reply will show that the comments do not apply to the papers.     

Quantum Key Distribution Based on Coherent States

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Comments on the “Method for observation of neutrinos and antineutrinos”

It is shown that a mechanism of coherent enhancement of the cross section of the neutrino scattering in a periodic structure, suggested by Weber could be excluded by the present neutron scattering experiments.     

On Lieb's Conjecture for the Wehrl Entropy¶of Bloch Coherent States

Lieb@s conjecture for the Wehrl entropy of Bloch coherent states is proved for spin 1 and spin 3/2. Using a geometric representation we solve the entropy integrals for states of arbitrary spin and evaluate them explicitly in the cases of spin 1, 3/2, and 2. We also give a group theoretic proof for all spin of a related inequality. Received: 2 March 1999 / Accepted: 7 May 1999     

Solution of the Crow-Kimura and Eigen Models for Alphabets of Arbitrary Size by Schwinger Spin Coherent States

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an h-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary h and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler’s theorem for homogeneous functions is used to derive this ‘thermodynamic’ formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine h=2 alphabet and the nucleic acid h=4 alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the h=4 and h=20 cases. We also derive the maximum principle for the Eigen model for general h. The general result for the Eigen model reduces to a known result for h=2. Examples are presented for the nucleic acid h=4 and the amino acid h=20 alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.     

Entangled Finite Dimensional Pair Coherent States and Their Applications

Intermediate states of electromagnetic field are reviewed. It is a type of the correlated two-mode states (converter state). Based on the resonant ion-cavity interaction, we propose a scheme to generate these states revealing their connection with the converter state. The practical feasibility of this method is also discussed. We discuss nonclassicality of a finite dimensional pair coherent states in terms of sub-Poissonian photon statistics as well as the negativity of the Wigner function after deriving the analytic expression for the Wigner function. We explore a superposition of two finite dimensional pair coherent states. We show that such states possess inherent nonclassical properties such as sub-Poissonian distribution, anti-correlation between the two modes and violation of Cauchy-Schwarz inequalities. The s-parameterized characteristic function (CF) is considered. The phase distribution in the framework of Pegg and Barnett formalism, W-function and Q-function are discussed. Furthermore, a two-level atom in interaction with a two-mode quantized electromagnetic fields besides a frequency converter interaction initially prepared in an entangled two-mode coherent state is presented. Exact solution of the wave function in the Schrödinger picture is obtained. Some statistical aspects of this model are presented. The results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy squeezing and variance squeezing. General conclusions reached are illustrated by numerical results.     

Coupling Between the Group—Related Coherent States

When two representations of the Lie algebra are coupled,the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states,These kernels have a connection with usual coupling coefficients.The explicit expressions of these kernels for SU(2),SO(4) and SUq(2) are given.When the direct product of three representations is formed in two ways,the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced,and the relations between these kernels and the general recoupling coefficients are obtained.The properties of these kerels are discussed.     

Comments on “role of impurities on the primary process for f-coloring in alkali halides”

Growth of the V₄ centers during and after pulsed electron irradiation of KBr was measured between 77K and 200K. It is found that the growth during pulsed irradiation is clearly different from that due to the thermal motion of the H centers. Critical discussions on the mechanism of the interstitial interaction in the primary step of the Frenkel-pair creation were made.     

Effect of Cavity Decay on the Coherent Control of Atomic Tunneling

In this paper we study the influence of cavity decay on the atomic tunneling and entanglement dynamics in a cavity QED system. The system consists of an atom in a double-well potential and a cavity. The results show that the cavity decay affects significantly the tunneling and the entanglement dynamics. The tunneling behaves as a damping-oscillating function of time in this case, while the entanglement shared between the internal and external degree of freedom of the atom exhibits the so-called entanglement sudden death (ESD).     

Generalized Spin Coherent States: Construction and Some Physical Properties

A generalized deformation of the su(2) algebra and a scheme for constructing associated spin coherent states is developed. The problem of resolving the unity operator in terms of these states is addressed and solved for some particular cases. The construction is carried using a deformation of Holstein-Primakoff realization of the su(2) algebra. The physical properties of these states is studied through the calculation of Mandel’s parameter.     

Squeezing in the Real and Imaginary Spin Coherent States

We study spin squeezing properties in the real and imaginary spin coherent states. We obtain analytical expressions of two spin squeezing parameters via a novel ladder operator formalism of the spin coherent state and the generation function method. Numerical results of the spin squeezing properties are discussed in detail, and the rea/and imaginary spin coherent state can be spin squeezed over a large range of parameters.     

Coherent π Electroproduction on the Deuteron

A general analysis of polarization phenomena for coherent pion electroproduction on deuterons is presented. The spin and isospin structures of the γ*+d→d+P⁰ amplitudes (where γ* is a virtual photon) are established and relationships between meson electroproduction on deuterons and on nucleons are given in the framework of the impulse approximation. The reaction e+d→e+d+π⁰ is investigated in detail, for a relatively large value of momentum transfer, 0.5 GeV²≤−k²≤2 GeV², both at threshold and in the region of Δ-isobar excitation. Special attention is devoted to the sensitivity of different contributions to the exclusive cross section for d(e, eπ⁰)d, as the γ*πω form factor or the NN-potential. The predicted k²-dependence of the cross section agrees well with the available experimental data.     

Law of Large Numbers for Non-Local Functions on Probabilistic Cellular Automata

We prove a multi-dimensional version of the law of large numbers for invariant measures of a large class of probabilistic cellular automata, whose transition probabilities satisfy some inequalities, which are known to assure their ergodicity. In some non-ergodic cases analogous results have been obtained for local functions. We deal with a larger class of functions, which includes some non-local ones.     

Coherent states for the Kepler–Coulomb problem on a sphere

An algebraic approach to Kepler problem in a curved space is introduced. By using this approach, the creation and annihilation operators associated to this system and their algebra are calculated. These operators satisfy a deformed Weyl–Heisenberg algebra which can be assumed as a deformed su(2)$\mathfrak{s}\mathfrak{u}\left(2\right)$ algebra. By using this fact, the nonlinear coherent states of this system are constructed. The scalar product and Bargmann representation of this family of nonlinear coherent states are constructed. The present contribution shows that these nonlinear coherent states possess some non-classical features which strongly depend on the Kepler coupling constant and space curvature. Depending on the non-classical measures, the smaller the curvature parameter, the more the non-classical features. Moreover, the stronger Kepler constant provides more non-classical features.     

Noncrossing Normal Ordering for Functions of Boson Operators

Normally ordered forms of functions of boson operators are important in many contexts in particular concerning Quantum Field Theory and Quantum Optics. Beginning with the seminal work of Katriel (Lett. Nuovo Cimento 10(13):565–567, 1974), in the last few years, normally ordered forms have been shown to have a rich combinatorial structure, mainly in virtue of a link with the theory of partitions. In this paper, we attempt to enrich this link. By considering linear representations of noncrossing partitions, we define the notion of noncrossing normal ordering. Given the growing interest in noncrossing partitions, because of their many unexpected connections (like, for example, with free probability), noncrossing normal ordering appears to be an intriguing notion. We explicitly give the noncrossing normally ordered form of the functions (a ^r (a ^† ) ^s ) ⁿ ) and (a ^r +(a ^† ) ^s ) ⁿ , plus various special cases. We are able to establish for the first time bijections between noncrossing contractions of these functions, k-ary trees and sets of lattice paths.     

Comments on the F-factor approximation for HF(1∑)

Using a linear dipole moment function, the analytical vibrational-rotational transition moment matrix elements of Herman and Rubin, and their simplified formulation, the so-called F-factor approximation, of Herman, Rothery and Rubin are compared for the HF molecule in its ¹∑ electronic ground state. The comparison reveals that, both for the v′ = 1, J′ →v″ = 0, J″ and the v′ = 2, J′ →v″ = 1, J″ transitions, the F-factor approximation gives a better than 5 per cent agreement with the HR theory for J″ up to 25, but becomes rapidly worse thereafter.