16 Novembre, 2006 15:00

Sezione di Probabilità e Statistica Matematica

Hypercontractivity for a Quantum Ornstein-Uhlenbeck Semigroup

dott.ssa Raffaella Carbone, Università di Pavia

Laboratorio Didattico IV piano

abstract

abstract

We prove hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup on the entire algebra B(h) of bounded operators on a separable Hilbert space h.
We exploit the particular structure of the spectrum together with hypercontractivity of the corresponding birth and death process and a proper decomposition of the domain.
We can also deduce that the semigroup verifies a logarithmic Sobolev inequality and gain an elementary rough estimate of the best constant.

9 Novembre, 2006 16:10

Sezione di Probabilità e Statistica Matematica

Dilations of covariant quantum dynamical semigroups

prof. Kalyan B. Sinha, JNCASR, Bangalore

Aula Seminari III piano

abstract

abstract

A theory of stochastic dilation of the Hudson Parthasarathy type of a covariant quantum dynamical semigroup on a C* or von Neumann
algebra is constructed. The additional assumption of symmetry of the semigroup with respect to a semifinte trace allows the use of Hilbert space methods, while covariance with respect to the action of a Lie group on the algebra gives a better control on the domain of the (unbounded) generator.

9 Novembre, 2006 17:20

Sezione di Probabilità e Statistica Matematica

Numerical simulation of stochastic evolution equations associated to quantum Markov semigroups.

prof. Carlos Mora, Universidad de Concecpcion

Aula Seminari III piano

abstract

abstract

This talk addresses the computation of the mean value of quantum observables at a given time. We first deal with the probabilistic representation of the solution to the quantum Markov master equations by means of the stochastic Schroedinger equations. Then, we treat the weak numerical solution of the non-linear stochastic Schroedinger equations in situations where the dimension of the state space is finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic Schroedinger equations.

7 Novembre, 2006 10:50

Seminario Matematico e Fisico di Milano

Giornata Tibiletti - Ricordo di Cesarina Marchionna Tibiletti

Guido Zappa, Universita` di Firenze

Dipartimento di Matematica - Università degli Studi di Milano

This talk addresses the computation of the mean value of quantum observables at a given time. We first deal with the probabilistic representation of the solution to the quantum Markov master equations by means of the stochastic Schroedinger equations. Then, we treat the weak numerical solution of the non-linear stochastic Schroedinger equations in situations where the dimension of the state space is finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic Schroedinger equations.

7 Novembre, 2006 11:25

Seminario Matematico e Fisico di Milano

Giornata Tibiletti - Flexible groups and their Groups Algebras

Otto Kegel, Universita` di Friburgo

Dipartimento di Matematica - Università degli Studi di Milano

This talk addresses the computation of the mean value of quantum observables at a given time. We first deal with the probabilistic representation of the solution to the quantum Markov master equations by means of the stochastic Schroedinger equations. Then, we treat the weak numerical solution of the non-linear stochastic Schroedinger equations in situations where the dimension of the state space is finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic Schroedinger equations.

7 Novembre, 2006 12:15

Seminario Matematico e Fisico di Milano

Giornata Tibiletti - Gruppi nilpotenti semilineari che risultano monomiali

Maria Clara Tamburini, Universita` Cattolica di Brescia

Dipartimento di Matematica - Università degli Studi di Milano

This talk addresses the computation of the mean value of quantum observables at a given time. We first deal with the probabilistic representation of the solution to the quantum Markov master equations by means of the stochastic Schroedinger equations. Then, we treat the weak numerical solution of the non-linear stochastic Schroedinger equations in situations where the dimension of the state space is finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic Schroedinger equations.

7 Novembre, 2006 14:30

Seminario Matematico e Fisico di Milano

Giornata Tibiletti - Punti notevoli del quadrangolo piano completo

Benedetto Scimeni, Universita` di Padova

Dipartimento di Matematica - Università degli Studi di Milano

This talk addresses the computation of the mean value of quantum observables at a given time. We first deal with the probabilistic representation of the solution to the quantum Markov master equations by means of the stochastic Schroedinger equations. Then, we treat the weak numerical solution of the non-linear stochastic Schroedinger equations in situations where the dimension of the state space is finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic Schroedinger equations.

7 Novembre, 2006 15:20

Seminario Matematico e Fisico di Milano

Giornata Tibiletti - Parole sincronizzanti e collasanti: approccio algebrico e informatico

Alessandra Cherubini, Politecnico di Milano

Dipartimento di Matematica - Università degli Studi di Milano

This talk addresses the computation of the mean value of quantum observables at a given time. We first deal with the probabilistic representation of the solution to the quantum Markov master equations by means of the stochastic Schroedinger equations. Then, we treat the weak numerical solution of the non-linear stochastic Schroedinger equations in situations where the dimension of the state space is finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic finite. Finally, we develop error estimation for the convergence of the explicit Euler scheme applied to the linear stochastic Schroedinger equations.

7 Novembre, 2006 13:30

Sezione di Probabilità e Statistica Matematica

Examples of non commutative manifolds

prof. Kalyan B. Sinha, JNCASR, Bangalore

Aula Seminari III piano

abstract

abstract

Some concrete non-commutative spaces and some aspects of geometry on them are studied. In some examples Weyl asymptotics are discussed while in others, Dixmier trace makes its appearance.

6 Novembre, 2006 17:00

Sezione di Probabilità e Statistica Matematica

Modellistica di nanomateriali

Roberto Contro, Dip. di Ingegneria Strutturale - PoliMI

Aula seminari MOX, Dipartimento di Matematica

Some concrete non-commutative spaces and some aspects of geometry on them are studied. In some examples Weyl asymptotics are discussed while in others, Dixmier trace makes its appearance.