Negative Binomial States of the Radiation Field and their Excitations are Nonlinear Coherent States

We show that the well-known negative binomial states of the radiation field and their excitations are nonlinear coherent states. Excited nonlinear coherent state are still nonlinear coherent states with different nonlinear functions. We finally give exponential form of the nonlinear coherent states and remark that the binomial states are not nonlinear coherent states.Comment: 10 pages, no figure

Study of a model for the distribution of wealth

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of an iterated nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.Comment: 12 pages, 2 figure

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

Representation-theoretic derivation of the Temperley-Lieb-Martin algebras

Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making explicit use of the Hecke algebra representation theory. Similar techniques are used to construct the algebras whose representations do not contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.

Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^\dag$ are boson annihilation and creation operators, satisfying $[a,a^\dag]=1$. This consequently provides the solution for the exponential $e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics "Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005), Myczkowce, Poland. 13 pages, 31 reference

Modeling the impact of white-plague coral disease in climate change scenarios

Coral reefs are in global decline, with coral diseases increasing both in prevalence and in space, a situation that is expected only to worsen as future thermal stressors increase. Through intense surveillance, we have collected a unique and highly resolved dataset from the coral reef of Eilat (Israel, Red Sea), that documents the spatiotemporal dynamics of a White Plague Disease (WPD) outbreak over the course of a full season. Based on modern statistical methodologies, we develop a novel spatial epidemiological model that uses a maximum-likelihood procedure to fit the data and assess the transmission pattern of WPD. We link the model to sea surface temperature (SST) and test the possible effect of increasing temperatures on disease dynamics. Our results reveal that the likelihood of a susceptible coral to become infected is governed both by SST and by its spatial location relative to nearby infected corals. The model shows that the magnitude of WPD epidemics strongly depends on demographic circumstances; under one extreme, when recruitment is free-space regulated and coral density remains relatively constant, even an increase of only 0.5 degrees C in SST can cause epidemics to double in magnitude. In reality, however, the spatial nature of transmission can effectively protect the community, restricting the magnitude of annual epidemics. This is because the probability of susceptible corals to become infected is negatively associated with coral density. Based on our findings, we expect that infectious diseases having a significant spatial component, such as Red-Sea WPD, will never lead to a complete destruction of the coral community under increased thermal stress