670 citations · 3.3k across the 47 of their papers we have counts for
48 papers
Perturbative criteria for the ergodicity of interacting dissipative quantum lattice systems
Lorenzo Bertini, Alberto De Sole, Gustavo Posta +1
We introduce a class of quantum Markov semigroups describing the evolution of interacting quantum lattice systems, specified either as generic qudits or as fermions. The correspond…
Poisson vertex algebras and Hamiltonian PDE
Alberto De Sole, Victor G. Kac, Daniele Valeri
We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical…
Adler-Oevel-Ragnisco type operators and Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
The theory of triples of Poisson brackets and related integrable systems, based on a classical R-matrix R in End_F(g), where g is a finite dimensional associative algebra over a fi…
Trace distance ergodicity for quantum Markov semigroups
Lorenzo Bertini, Alberto De Sole, Gustavo Posta
We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral de…
On Lax operators
Alberto De Sole, Victor G. Kac, Daniele Valeri
We define a Lax operator as a monic pseudodifferential operator of order , such that the Lax equations $\dfrac{\partial L(\partial)}{\partial t_k}=[(L^{\frac…
Classical and variational Poisson cohomology
Bojko Bakalov, Alberto De Sole, Reimundo Heluani +2
We prove that, for a Poisson vertex algebra V, the canonical injective homomorphism of the variational cohomology of V to its classical cohomology is an isomorphism, provided that…
An operadic approach to vertex algebra and Poisson vertex algebra cohomology
Bojko Bakalov, Alberto De Sole, Reimundo Heluani +1
We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomo…
A Lax type operator for quantum finite W-algebras
Alberto De Sole, Victor Kac, Daniele Valeri
For a reductive Lie algebra g, its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients in the quantum finite…
Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We prove that any classical affine W-algebra W(g,f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of…
Finite W-algebras for gl_N
Alberto De Sole, Victor G. Kac, Daniele Valeri
We study the quantum finite W-algebras W(gl_N,f), associated to the Lie algebra gl_N, and its arbitrary nilpotent element f. We construct for such an algebra an r_1 x r_1 matrix L(…
Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies
Alberto De Sole, Victor G. Kac, Daniele Valeri
We apply the new method for constructing integrable Hamiltonian hierarchies of Lax type equations developed in our previous paper, to show that all W-algebras W(gl_N,f) carry such…
A new scheme of integrability for (bi)Hamiltonian PDE
Alberto De Sole, Victor G. Kac, Daniele Valeri
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the cla…
Quantitative analysis of Clausius inequality
L. Bertini, A. De Sole, D. Gabrielli +2
In the context of driven diffusive systems, for thermodynamic transformations over a large but finite time window, we derive an expansion of the energy balance. In particular, we c…
Double Poisson vertex algebras and non-commutative Hamiltonian equations
Alberto De Sole, Victor G. Kac, Daniele Valeri
We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of d…
On integrability of some bi-Hamiltonian two field systems of PDE
Alberto De Sole, Victor G. Kac, Refik Turhan
We continue the study of integrability of bi-Hamiltonian systems with a compatible pair of local Poisson structures (H_0,H_1), where H_0 is a strongly skew-adjoint operator. This i…
Structure of classical (finite and affine) W-algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to…
Macroscopic fluctuation theory
Lorenzo Bertini, Alberto De Sole, Davide Gabrielli +2
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a varie…
Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, t…
Integrability of Dirac reduced bi-Hamiltonian equations
Alberto De Sole, Victor G. Kac, Daniele Valeri
First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the rem…
Singular degree of a rational matrix pseudodifferential operator
Sylvain Carpentier, Alberto De Sole, Victor G. kac
In our previous work we studied minimal fractional decompositions of a rational matrix pseudodifferential operator: H=A/B, where A and B are matrix differential operators, and B is…
On classical finite and affine W-algebras
Alberto De Sole
This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory o…
Some remarks on non-commutative principal ideal rings
Sylvain Carpentier, Alberto De Sole, Victor G. Kac
We prove some algebraic results on the ring of matrix differential operators over a differential field in the generality of non-commutative principal ideal rings. These results are…
A new approach to the Lenard-Magri scheme of integrability
Alberto De Sole, Victor G. Kac, Refik Turhan
We develop a new approach to the Lenard-Magri scheme of integrability of bi-Hamiltonian PDE's, when one of the Poisson structures is a strongly skew-adjoint differential operator.
Non-local Hamiltonian structures and applications to the theory of integrable systems I
Alberto De Sole, Victor G. Kac
We develop a rigorous theory of non-local Hamiltonian structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee ap…