Self-Adjointness criterion for operators in Fock spaces

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.Comment: 20 page

Cylindrical Wigner measures

In this paper we study the semiclassical behavior of quantum states acting on the C*-algebra of canonical commutation relations, from a general perspective. The aim is to provide a unified and flexible approach to the semiclassical analysis of bosonic systems. We also give a detailed overview of possible applications of this approach to mathematical problems of both axiomatic relativistic quantum field theories and nonrelativistic many body systems. If the theory has infinitely many degrees of freedom, the set of Wigner measures, i.e. the classical counterpart of the set of quantum states, coincides with the set of all cylindrical measures acting on the algebraic dual of the space of test functions for the field, and this reveals a very rich semiclassical structure compared to the finite-dimensional case. We characterize the cylindrical Wigner measures and the \emph{a priori} properties they inherit from the corresponding quantum states.Comment: 59 page

Classical limit of the Nelson model with cut off

In this paper we analyze the classical limit of the Nelson model with cut off, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum observables to the solutions of classical equations, and find the evolution of quantum fluctuations around the classical solution. Furthermore we analyze the convergence of transition amplitudes of normal ordered products of creation and annihilation operators between different types of initial states. In particular the limit of normal ordered products between states with a fixed number of both relativistic and non-relativistic particles yields an unexpected quantum residue: instead of the product of classical solutions we obtain an average of the product of solutions corresponding to varying initial conditions.Comment: 42 page

Concentration of cylindrical Wigner measures

In this note we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide conditions at the quantum level sufficient to prove the concentration of all the corresponding cylindrical Wigner measures as Radon measures on suitable topological vector spaces. The analysis is motivated by variational and dynamical problems in the semiclassical study of bosonic quantum field theories.Comment: 23 page

Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy

We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein-Gordon-Schr\"odinger equation. Also, we show that the ground state energy level of $N$ nucleons, when $N$ is large and the meson field approaches its classical value, is given by the infimum of the classical energy functional at a fixed density of particles. Our study relies on a recently elaborated approach for mean field theory and uses Wigner measures.Comment: 37 page

AGGREGATION OVER CONSUMERS AND THE ESTIMATION OF A DEMAND SYSTEM FOR U.S. FOOD

This paper estimates a complete demand system for food for the United States using an extension of the Almost Ideal Demand System (AIDS) with household and aggregate data. The major purpose is to explore the implications of aggregation over consumers. Empirical evidence, based on data from the 1980-87 Continuing Consumer Expenditure Surveys, shows that the regression results and demand elasticities of the household and aggregate models and data can be very similar. Further results reveal factors which affect the similarity of the household and aggregate estimates.Consumer/Household Economics, Demand and Price Analysis,

Magnetic Schr\"odinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models

We study the quasi-classical limit of the Pauli-Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the degrees of freedom of the field, and consider the classical limit of the latter. We prove that the partial trace of the full Hamiltonian converges, in resolvent sense, to an effective Schr\"odinger operator with magnetic field and a corrective electric potential that depends on the field configuration. Furthermore, we prove the convergence of the ground state energy of the microscopic system to the infimum over all possible classical field configurations of the ground state energy of the effective Schr\"odinger operator.Comment: 26 pages, pdfLatex. Final version to appear in J. Spectr. Theor