# G. Landolfi's research while affiliated with Università del Salento and other places

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## Publications (41)

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter ω(t) varies continuously during evolution so to realize quenching protocols of different types. To this scope we focus on the case where ω(t)2 behaves like a Morse potential, up to pos...

We consider a family of thermodynamic models such that the energy density can be expressed as an asymptotic expansion in the scale formal parameter and whose terms are suitable functions of the volume density. We examine the possibility to construct solutions for the Maxwell thermodynamic relations relying on their symmetry properties and deduce th...

We consider a family of thermodynamic models such that the energy density can be expressed as an asymptotic expansion in the scale formal parameter and whose terms are suitable functions of the volume density. We examine the possibility to construct solutions for the Maxwell thermodynamic relations relying on their symmetry properties and deduce th...

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter $\omega(t)$ varies during evolution so to display either a non harmonic hole or barrier. To this scope we focus on the case where $\omega(t)^2$ behaves like a Morse potential, up to po...

A bstract
We consider the conformal A n Toda theory in AdS 2 . Due to the bulk full Virasoro symmetry, this system provides an instance of a non-gravitational AdS 2 /CFT 1 correspondence where the 1d boundary theory enjoys enhanced $$ ``\frac{1}{2}- Virasoro" $$ “ 1 2 − Virasoro ” symmetry. General boundary correlators are expected to be captured b...

We consider the conformal $A_{n}$ Toda theory in AdS$_{2}$. Due to the bulk full Virasoro symmetry, this system provides an instance of a non-gravitational $\text{AdS}_{2}$/$\text{CFT}_{1}$ correspondence where the 1d boundary theory enjoys enhanced "$\frac{1}{2}$-Virasoro" symmetry. General boundary correlators are expected to be captured by the r...

Complex biochemical pathways or regulatory enzyme kinetics can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. This discipline provides a set of tools for quantifying and understanding the dialogue between reactants, whose framing into a solid and consistent mathematical description is of pivotal...

Inspired by the recent developments in the study of the thermodynamics of van der Waals fluids via the theory of nonlinear conservation laws and the description of phase transitions in terms of classical (dissipative) shock waves, we propose a novel approach to the construction of multi-parameter generalisations of the van der Waals model. The theo...

We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion in regard to basic examples of one-dimensional non-autonomous dynamical systems enjoying the property that thei...

We discuss conditions giving rise to stationary position-momentum correlations among quantum states in the Fock and coherent basis associated with the natural invariant for the one-dimensional time-dependent quadratic Hamiltonian operators such as the Kanai-Caldirola Hamiltonian. We also discuss some basic features such as quantum decoherence of th...

In this paper, we consider quantization of powers of the ratio between the Hamiltonian coordinates for position and momentum in one-dimensional systems. The domain of the operators consists of square integrable functions over a finite real interval to ensure boundedness and self-adjointness. The spectral problems for the operators that result from...

Time-dependent dynamical systems with a particular emphasis on models attaining the minimum value of uncertainty formula are considered. The role of the Bogolubov coefficients, in general and in the context of the loss of minimum uncertainty, is analyzed. Different fluctuation values on squeezed states are performed. The decoherence energy is param...

Equations which define classical configurations of strings in R3 are presented in a simple form. General properties as well as particular classes of solutions of these equations are considered.

We consider time-dependent quadratic Hamiltonians in the supersymmetric quantum mechanical framework. We study the quantum
mechanical properties of some basic states in the fermionic sector of the Hilbert space. To understand the differences between
the bosonic and fermionic sectors better, we focus on periodic quadratic Hamiltonians of the Paul-tr...

We address generalized measurements of linear multimode operators and discuss some aspects relevant to constructing angle
operators for arbitrary quadratic Hamiltonian systems via Weyl-ordered expansions in terms of position and momentum operators.

The definition of the phase variable for a classical time-dependent oscillator as the natural variable canonically conjugated to the Ermakov invariant is revised. Some implications of the result at the quantum level are discussed and an exact formal expression in terms of Weyl-ordered operators is given for the associated phase operator.

We address the generalized measurement of the two-boson operator Zγ = a1 + γa†2 which, for |γ|2 ≠ 1, is not normal and cannot be detected by a joint measurement of quadratures on the two bosons. We explicitly construct the minimal Naimark extension, which involves a single additional bosonic system, and present its decomposition in terms of two-bos...

In classical mechanics a transformation in phase space is said to be canonoid if it maps only some Hamiltonian systems into Hamiltonian systems. Once canonoid transformations are considered, these systems can be classically described by means of Lagrangians or Hamiltonians other than the conventional ones. In this context, a basic role is played by...

We apply a theoretical frame developed for the study of time-dependent oscillators to investigate trans-Planckian modifications induced to the standard inflationary cosmological models. Results concerning massless scalar fields subjected either the generalized Corley–Jacobson or the Unruh nonlinear dispersion relations are obtained and discussed.

Some results following from the analysis of generalized time-dependent oscillators in the framework of the Lie group theory are reviewed. Their role in treating aspects concerning the loss of coherence in cosmological models is discussed.

The Canham–Helfrich membrane model is discussed by making use of the generalized Weierstrass representation formulae for arbitrary surfaces immersed into the three-dimensional Euclidean space . Particular solutions of the shape equation are considered and correlators describing thermal fluctuations in the one-loop approximation are computed.

We investigate dynamical systems with time-dependent mass and frequency, with particular attention on models attaining the minimum value of uncertainty formula. A criterium of minimum uncertainty is presented and illustrated by means of explicit and exactly solved examples. The role of the Bogolubov coefficients, in general and in the context of mi...

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function $\sigma(\eta)$ of the conformal time $\eta$, called the auxiliary field equation. At the classical level, $\sigma(\eta)$ can be expressed by means of two independent solutions...

The study of features of rigid surfaces systems is commonly performed by making use of the Monge representation. We briefly outline two alternative ways to proceed and show some new results they lead to.

Rigid string world sheets in R4 are described by means of a
representation of the Weierstrass type. Correlators for the full rigid
string action in the one-loop approximation over minimal backgrounds are
calculated.

We show that horizon divergences for scalar fields in infinitely massive black hole backgrounds can be eliminated by resorting to a maximal acceleration principle.

The introduction of an upper limit to the proper acceleration of point-like particles may lead to new as well as interesting results in the particle production scheme of QFT in curved space-times. Some examples are discussed.

Weierstrass type representations for surfaces in 4D spaces are presented. Integrable deformations of surfaces in these spaces generated by the Davey-Stewartson hierarchy are discussed. A simple noncommutative extension of Weierstrass type representations is finally proposed.

Generalized Weierstrass formulae for surfaces in four-dimensional space $\Bbb{R}^{4}$ are used to study (anti)self-dual rigid string configurations. It is shown that such configurations are given by superminimal immersions into $\Bbb{R}^{4}$. Explicit formulae for generic (anti)instantons are presented. Particular classes of surfaces are also analy...

Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfaces are generated by the Davey -Stewartson hierarchy. Geometrically these deformations are characteriz...

The generalized Weierstrass representation for surfaces in $\Bbb{R}^{3}$ is used to study quantum effects for strings governed by Polyakov-Nambu-Goto action. Correlators of primary fields are calculated exactly in one-loop approximation for the pure extrinsic Polyakov action. Geometrical meaning of infrared singularity is discussed. The Nambu-Goto...

Equations which define classical configurations of strings in R3 are presented in a simple form. General properties as well as particular classes of solutions of these equations are considered.

The main objectives of this research activity are: i) the study of new algebraic and analytic as-pects of models integrable or solvable in some sense, both continuous and discrete, with special attention to multidimensional systems, and their physical applications, f.i. in field theory, plasma physics, nonlinear optics, multidimensional ferro-magne...

## Citations

... See recent works[51,52,[58][59][60][61][62] on integrable (or solvable) theories on AdS 2 .7 We thank João Penedones for pointing out the relevance of this picture for our formulae. ...

... The problem of constructing suitable partial differential equations for state functions of thermodynamic systems and the study of critical properties in terms of critical asymptotics of the solutions to these equations is an active field of research which brought further insights on a variety of classical systems, see e.g. [34][35][36][37][38][39], and appears to be promising for the study of complex systems [40,41]. Studies exploiting the Lie symmetry analysis can be therefore carried out for other systems of physical interest. ...

... Indeed, differential equations involving the partition functions (or related quantities) of thermodynamic models have been extensively investigated in the literature, see for example [27][28][29][30][31][32][33][34][35][36][37]. In particular, they allow us to express the equation of state (or the self-consistency equations) governing the equilibrium dynamics of the system in terms of solutions of non-linear differential equations, and to describe phase transition phenomena as the development of shock waves, thus linking critical behaviours to gradient catastrophe theory [38][39][40][41]. In a recent work [36], a direct connection between the thermodynamics of ferromagnetic models with interactions of order p and the equations of the Burgers hierarchy was established by linking the solution of the latter as the equilibrium solution of the order parameter of the former (i.e. the global magnetization m). ...

... Equations 1.8a, 1.8b, 1.8c are the differential version of the generalized Weierstrass-Enneper representation (the integration version) in (2) of [8] for example. The Konopelchenko-Weierstrass-Enneper representation is a powerful tool for the analysis of Polyakov string theory problems [8]. ...

... [1][2][3]). Its generalizations to generic surfaces conformally immersed into the three and four dimensional spaces have been proposed recently in [4][5][6][7][8]. These generalized Weierstrass representations (GWRs) were based on the two-dimensional Dirac equation and they allow to costruct any analytic surface in R 4 and R 3 . ...

... To remove the vacuum ambiguity, in this paper we shall proceed in the most economical way, by demanding that at initial time t = 0 the operator a(0) coincides with a 0 in (18): µ(0) = 1 and ν(0) = 0. This requirement fixes initial conditions to the Ermakov differential equation (1) as follows [32]: ...

... string theory. Based on the GW formulas, it has been shown [4] that one can represent the Euler- Lagrange equation for the Nambu-Goto-Polyakov action in a simple form. Common solutions of this equation and the GW system which provide surfaces in R 3 also describe classical configurations of strings. ...

... [55] Formal questions can be obviously raised in respect to the definition and the action of position and momentum operators and of their inverse, which in turn address to the properties of canonically conjugated operators. Implications can be discussed similarly to the case of operators Tm,n; see, for instance, investigations [28,50] for possible consequences of confinement. ...

... Among them, the Canham-Helfrich model is typically used to describe cell membrane pattern formation in a water-based environment, driven by the curvature energy per unit area of the closed lipid bilayer, osmotic pressure, and surface tension [59]. This model captures cell membrane patterns without the molecular dynamics of the lipid bilayer. ...

... A first set of papers concerns primarily the characterization of canonoid transformations and their relations with canonical transformations: [7,22,4,28,5,3]. A second set deals primarily with applications of canonoid transformations to the analysis of Hamiltonian systems: [26,14]. ...