Rendiconti di Matematica di Sapienza Università di Roma

	Rendiconti di Matematica e delle sue Applicazioni
ISSN 1120-7183 (print) ISSN 2532-3350 (online) Home Editorial Board Latest articles Published Volumes Historical Notes Editorial Policy Publication Ethics Instructions for Authors Copyright Subscription Information Editorial Office rendmat@mat.uniroma1.it	Latest Articles Once a paper is accepted it goes immediately into production. It is a policy of the journal to publish papers online within four weeks of acceptance. Expansion of the resolvent in a Feshbach model. Raffaele Carlone, Domenico Finco PDF download, published online 7 december 2018. Abstract. In this paper we extend the results proved in [7] about Feshbach resonances in a multichannel Hamiltonian H, proving a low energy expansion of the resolvent (H-k²)^-1 as k --> 0 in the resonant case. Recent advances in symmetry of stochastic differential equations. Giuseppe Gaeta, Claudia Lunini, Francesco Spadaro PDF download, published online 3 december 2018. Abstract. We discuss some recent advances concerning the symmetry of stochastic differential equations, and on particular the interrelations between these and the integrability -- complete or partial -- of the equations. Regularized Quadratic Forms for a Three Boson System with Zero-Range Interactions. Giulia Basti, Rodolfo Figari, Alessandro Teta PDF download, published online 3 december 2018. Abstract. We present two possible strategies to obtain a lower bounded Hamiltonian for three bosons interacting through zero-range interactions. First, we investigate a family of zero-range Hamiltonians defined in a Hilbert space of tensorial wave functions. Then, we examine the regularizing effect of an ultraviolet cutoff on the boundary conditions satisfied by functions in the form domain of zero-range Hamiltonians of a three boson system. One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid. Riccardo Adami, Simone Dovetta PDF download, published online 3 december 2018. Abstract. We investigate the existence of ground states for the focusing Nonlinear Schrödinger Equation on the infinite three-dimensional cubic grid. We extend the result found for the analogous two-dimensional grid by proving an appropriate Sobolev inequality giving rise to a family of critical Gagliardo-Nirenberg inequalities that hold for every nonlinearity power from 10/3 to 6, namely, from the L²-critical power for the same problem in R³ to the critical power for the same problem in R. Given the Gagliardo-Nirenberg inequality, the problem of the existence of ground state can be treated as already done for the two-dimensional grid. A note on the infrared problem in model field theories. Massimo Bertini, Diego Noja, Andrea Posilicano PDF download, published online 29 november 2018. Abstract. In this note we critically re-examine the usual procedure of quantization of classical wave equations with static sources. We point out that the origin of infrared difficulties in the so called van Hove model is related to the complex Hilbert space structure one puts on the classical phase space and the corresponding unitarization of the classical symplectic evolution. Whereas in the usual framework the condition of infrared regularity forces the total charge of the external source to vanish, in our setting the infrared regularity condition is equivalent to having a source with a finite (electrostatic) energy. A similar analysis could be applied to models of field-particle interaction such as the Nelson model. Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis. Alessandro Michelangeli, Giuseppe Pitton PDF download, published online 28 november 2018. Abstract. We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. Locally invertible σ--harmonic mappings. Giovanni Alessandrini, Vincenzo Nesi PDF download, published online 22 november 2018. Abstract. We extend a classical theorem by H. Lewy to planar σ-harmonic mappings, that is mappings U whose components u¹ and u² solve a divergence structure elliptic equation div (σ∇ uⁱ)=0, for i=1,2. A similar result is established for pairs of solutions of certain second order non--divergence equations. Hamiltonians for Two-Anyon Systems. Michele Correggi, Luca Oddis PDF download, published online 22 november 2018. Abstract. We study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for non-interacting anyons and prove their closedness and boundedness from below. We then show that the corresponding self-adjoint operators give rise to a one-parameter family of extensions of the naive two-anyon Schrödinger operator. We finally extend the results in presence of a two-body radial interaction. On inverses of Krein's Q-functions. Claudio Cacciapuoti, Davide Fermi, Andrea Posilicano PDF download, published online 22 november 2018. Abstract. Not availabe in HTML format, see the PDF file.

Latest Articles

Once a paper is accepted it goes immediately into production. It is a policy of the journal to publish papers online within four weeks of acceptance.

Expansion of the resolvent in a Feshbach model.
Raffaele Carlone, Domenico Finco
PDF download, published online 7 december 2018.

Abstract. In this paper we extend the results proved in [7] about Feshbach resonances in a multichannel Hamiltonian H, proving a low energy expansion of the resolvent (H-k²)^-1 as k --> 0 in the resonant case.

Recent advances in symmetry of stochastic differential equations.
Giuseppe Gaeta, Claudia Lunini, Francesco Spadaro
PDF download, published online 3 december 2018.

Abstract. We discuss some recent advances concerning the symmetry of stochastic differential equations, and on particular the interrelations between these and the integrability -- complete or partial -- of the equations.

Regularized Quadratic Forms for a Three Boson System with Zero-Range Interactions.
Giulia Basti, Rodolfo Figari, Alessandro Teta
PDF download, published online 3 december 2018.

Abstract. We present two possible strategies to obtain a lower bounded Hamiltonian for three bosons interacting through zero-range interactions. First, we investigate a family of zero-range Hamiltonians defined in a Hilbert space of tensorial wave functions. Then, we examine the regularizing effect of an ultraviolet cutoff on the boundary conditions satisfied by functions in the form domain of zero-range Hamiltonians of a three boson system.

One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid.
Riccardo Adami, Simone Dovetta
PDF download, published online 3 december 2018.

Abstract. We investigate the existence of ground states for the focusing Nonlinear Schrödinger Equation on the infinite three-dimensional cubic grid. We extend the result found for the analogous two-dimensional grid by proving an appropriate Sobolev inequality giving rise to a family of critical Gagliardo-Nirenberg inequalities that hold for every nonlinearity power from 10/3 to 6, namely, from the L²-critical power for the same problem in R³ to the critical power for the same problem in R. Given the Gagliardo-Nirenberg inequality, the problem of the existence of ground state can be treated as already done for the two-dimensional grid.

A note on the infrared problem in model field theories.
Massimo Bertini, Diego Noja, Andrea Posilicano
PDF download, published online 29 november 2018.

Abstract. In this note we critically re-examine the usual procedure of quantization of classical wave equations with static sources. We point out that the origin of infrared difficulties in the so called van Hove model is related to the complex Hilbert space structure one puts on the classical phase space and the corresponding unitarization of the classical symplectic evolution. Whereas in the usual framework the condition of infrared regularity forces the total charge of the external source to vanish, in our setting the infrared regularity condition is equivalent to having a source with a finite (electrostatic) energy. A similar analysis could be applied to models of field-particle interaction such as the Nelson model.

Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis.
Alessandro Michelangeli, Giuseppe Pitton
PDF download, published online 28 november 2018.

Abstract. We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.

Locally invertible σ--harmonic mappings.
Giovanni Alessandrini, Vincenzo Nesi
PDF download, published online 22 november 2018.

Abstract. We extend a classical theorem by H. Lewy to planar σ-harmonic mappings, that is mappings U whose components u¹ and u² solve a divergence structure elliptic equation div (σ∇ uⁱ)=0, for i=1,2. A similar result is established for pairs of solutions of certain second order non--divergence equations.

Hamiltonians for Two-Anyon Systems.
Michele Correggi, Luca Oddis
PDF download, published online 22 november 2018.

Abstract. We study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for non-interacting anyons and prove their closedness and boundedness from below. We then show that the corresponding self-adjoint operators give rise to a one-parameter family of extensions of the naive two-anyon Schrödinger operator. We finally extend the results in presence of a two-body radial interaction.

On inverses of Krein's Q-functions.
Claudio Cacciapuoti, Davide Fermi, Andrea Posilicano
PDF download, published online 22 november 2018.

Abstract. Not availabe in HTML format, see the PDF file.

Rendiconti di Matematica e delle sue Applicazioni

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