Static spin susceptibility in the <Emphasis Type="Italic">t</Emphasis>-<Emphasis Type="Italic">J</Emphasis> model

Based on the equation-of-motion method for the relaxation function expressed in terms of Hubbard operators, we evaluate the static spin susceptibility and correlation functions in the two-dimensional t-J model. We show that at zero temperature, a long-range antiferromagnetic order exists in the lattice for the hole concentration δ < δ_c ≃ 0.018. The calculated dependences of the spin susceptibility and correlation length on the temperature and hole concentration agree qualitatively with the experiment. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 538–550, September, 2007.     

<Emphasis Type="Italic">N</Emphasis>=1 supersymmetric conformal block recursion relations

We present explicit recursion relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 476–487, September, 2007.     

Statistical theory of nonlinear hydrodynamic fluctuations in ionic systems

A system of equations for time correlation functions in ionic systems is obtained and solved on the basis of the Fokker-Planck equation for the distribution function of coarse-grained dynamic variables such as mass density, charge density, momentum density, current density, and total energy. Statistical weight, thermodynamic forces and hydrodynamic velocities are calculated both in Gaussian and higher approximations. Expressions for generalized transfer coefficients depending onk andw, with separate fluctuation contributions, are found.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 3, pp. 448–464, September, 1996.     

Smoothness of Correlations in the Anderson Model at Strong Disorder

We study the higher-order correlation functions of covariant families of observables associated with random Schr?dinger operators on the lattice in the strong disorder regime. We prove that if the distribution of the random variables has a density analytic in a strip about the real axis, then these correlation functions are analytic functions of the energy outside of the planes corresponding to coincident energies. In particular, this implies the analyticity of the density of states, and of the current-current correlation function outside of the diagonal. Consequently, this proves that the current-current correlation function has an analytic density outside of the diagonal at strong disorder. Submitted: October 8, 2005; Accepted: February 15, 2006     

Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II

We calculate the pair correlation function and the magnetic susceptibility in the anisotropic Ising model on the lattice with one infinite and one finite dimension with periodic boundary conditions imposed along the second dimension. Using the exact expressions for lattice form factors, we propose formulas for arbitrary spin matrix elements, thus providing a possibility to calculate all multipoint correlation functions in the anisotropic Ising model on cylindrical and toroidal lattices. We analyze passing to the scaling limit.     

An Analytic Approach to <Emphasis Type="Italic">Q</Emphasis>-Balls

We present the analytic approach for constructing Q-ball solutions in the general case of a sixth-order potential. In particular, we show that the symmetrized Woods-Saxon function describes the Q-ball profile function. The energy and charge can therefore be evaluated explicitly. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 342–347, August, 2005.     

Système de Yang-Mills-Vlasov pour des Particules avec Densité de Charge de Jauge Non-Abélienne sur un Espace-Temps Courbe

. We prove local in time existence theorems of solutions of the Cauchy problem for the Yang-Mills system in temporal gauge, with current generated by a distribution function that satisfies a Vlasov equation, and an unknown non-abelian charge density subject to a conservation equation.     

Explicit solutions of the one‐dimensional Vlasov–Poisson system with infinite mass

A collisionless plasma is modelled by the Vlasov–Poisson system in one dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge as |x| → ∞ is considered. Thus, the total positive charge and the total negative charge are infinite. In this paper, the charge density of the system is shown to be compactly supported. More importantly, both the electric field and the number density are determined explicitly for large values of |x|. Copyright © 2007 John Wiley & Sons, Ltd.     

Steady spatial asymptotics for the Vlasov–Poisson system

A collisionless plasma is modelled by the Vlasov–Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as ∣x∣ tends to infinity is considered. Hence, the total positive charge and the total negative charge are infinite. Smooth solutions with appropriate asymptotic behaviour were shown to exist locally in time in a previous work. This paper studies the time behaviour of the net charge and a natural quantity related to energy, and shows that neither is constant in time in general. Also, neither quantity is positive definite. When the background density is a decreasing function of ∣v∣, a positive definite quantity is constructed which remains bounded. A priori bounds are obtained from this. Copyright © 2003 John Wiley & Sons, Ltd.     

Critical Asymptotic Behavior of Correlations in a Simple Liquid

We consider a representation of the total and the direct correlation functions in a liquid in terms of the corresponding spectral densities. Analysis of the spectral density properties reveals a mechanism responsible for changing the analytic properties of the Fourier transform of the correlation function and its asymptotic behavior in the critical domain. We show that the well-known restrictions imposed on possible values of the critical asymptotic exponent follow from this mechanism.     

A general control variate method for option pricing under Lévy processes

We present a general control variate method for simulating path dependent options under Lévy processes. It is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation of the payoff of the original option and the payoff of a similar option under geometric Brownian motion. The method is applicable for all types of Lévy processes for which the probability density function of the increments is available in closed form. Numerical experiments confirm that our method achieves considerable variance reduction for different options and Lévy processes. We present the applications of our general approach for Asian, lookback and barrier options under variance gamma, normal inverse Gaussian, generalized hyperbolic and Meixner processes.     

The two-time Green’s function and the diagram technique

Based on constructing the equations of motion for the two-time Green’s functions, we discuss calculating the dynamical spin susceptibility and correlation functions in the Heisenberg model. Using a Mori-type projection, we derive an exact Dyson equation with the self-energy operator in the form of a multiparticle Green’s function. Calculating the self-energy operator in the mode-coupling approximation in the ferromagnetic phase, we reproduce the results of the temperature diagram technique, including the correct formula for low-temperature magnetization. We also consider calculating the spin fluctuation spectrum in the paramagnetic phase in the framework of the method of equations of motion for the relaxation function.     

On asymptotic properties of the empirical correlation matrix of a homogeneous vector-valued Gaussian field

We investigate properties of the empirical correlation matrix of a centered stationary Gaussian vector field in various function spaces. We prove that, under the condition of integrability of the square of the spectral density of the field, the normalization effect takes place for a correlogram and integral functional of it.     

Nonstationary probabilities and time correlation functions for an asymmetric exclusion process

We give the complete solution of the master equation for a system of interacting particles with finite density. We obtain the solution using a new form of the Bethe ansatz for an asymmetric simple exclusion process on the ring. We first find the one-point time correlation function for the discrete version of the process. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 499–508, March, 2006.     

Stieltjes representation of the 3D Bruggeman effective medium and Padé approximation

The paper deals with Bruggeman effective medium approximation (EMA) which is often used to model effective complex permittivity of a two-phase composite. We derive the Stieltjes integral representation of the 3D Bruggeman effective medium and use constrained Padé approximation method introduced in [39] to numerically reconstruct the spectral density function in this representation from the effective complex permittivity known in a range of frequencies. The problem of reconstruction of the Stieltjes integral representation arises in inverse homogenization problem where information about the spectral function recovered from the effective properties of the composite, is used to characterize its geometric structure. We present two different proofs of the Stieltjes analytical representation for the effective complex permittivity in the 3D Bruggeman effective medium model: one proof is based on direct calculation, the other one is the derivation of the representation using Stieltjes inversion formula. We show that the continuous spectral density in the integral representation for the Bruggeman EMA model can be efficiently approximated by a rational function. A rational approximation of the spectral density is obtained from the solution of a constrained minimization problem followed by the partial fractions decomposition. We show results of numerical rational approximation of Bruggeman continuous spectral density and use these results for estimation of fractions of components in a composite from simulated effective permittivity of the medium. The volume fractions of the constituents in the composite calculated from the recovered spectral function show good agreement between theoretical and predicted values.     

Monge–Ampère of Pac-Man

We show that the Monge–Ampère density of the extremal function $$V_P$$ for a non-convex Pac-Man set $$P\subset {{\mathbb {R}}}^2$$ tends to a finite limit as we approach the vertex p of P along lines but with a value that may vary with the line. On the other hand, along a tangential approach to p, the Monge–Ampère density becomes unbounded. This partially mimics the behavior of the Monge–Ampère density of the union of two quarter disks S of Sigurdsson and Snaebjarnarson (Ann Pol Math 123:481–504, 2019). We also recover their formula for $$V_S$$ by elementary methods.     

Specific heat and mean energy of a Heisenberg ferromagnet in the Green's function method

A system of equations that permits calculation of the longitudinal correlation function in terms of the correlation functions of the transverse spin components is proposed. In the Green's function method, the system permits calculation of the susceptibility, mean energy, and specific heat in the same approximation as the magnetization. The experimental data on the specific heat in Gd and EuS agree qualitatively with the conclusions of the theory.Ural State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 127–134, April, 1993.     

Dynamical magnetic susceptibility of the periodic anderson model in the chaotic phase approximation

Using the diagram technique in the atomic representation in the generalized chaotic phase approximation, we solve the problem of calculating the dynamical magnetic susceptibility of the periodic Anderson model in the strong electron correlation regime. We express the dynamical magnetic susceptibility in terms of four Matsubara Green’s functions describing partial contributions, which are calculated based on exact solutions of integral equations.     

JOINTLY‐DETERMINED ECOLOGICAL THRESHOLDS AND ECONOMIC TRADE‐OFFS IN WILDLIFE DISEASE MANAGEMENT

ABSTRACT. We investigate wildlife disease management, in a bioeconomic framework, when the wildlife host is valuable and disease transmission is density‐dependent. Disease prevalence is reduced in density‐dependent models whenever the population is harvested below a host‐density threshold a threshold population density below which disease prevalence declines and above which a disease becomes epidemic. In conventional models, the threshold is an exogenous function of disease parameters. We consider this case and find a steady state with positive disease prevalence to be optimal. Next, we consider a case in which disease dynamics are affected by both population controls and changes in human‐environmental interactions. The host‐density threshold is endogenous in this case. That is, the manager does not simply manage the population relative to the threshold, but rather manages both the population and the threshold. The optimal threshold depends on the economic and ecological trade‐offs arising from the jointly‐determined system. Accounting for this endogene‐ity can lead to reduced disease prevalence rates and higher population levels. Additionally, we show that ecological parameters that may be unimportant in conventional models that do not account for the endogeneity of the host‐density threshold are potentially important when host density threshold is recognized as endogenous.