arXiv subjects

R. Maciocco

Publications and source records attributed to R. Maciocco.

5 recordsLinked to original sources

arXiv1999

Effective Hamiltonian with holomorphic variables

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian - depending on quantum coupling and temperature - and classical-like expressions for the averages of observables. In this work the PQSCHA is derived in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the path integral for the Weyl symbol of the density matrix, makes it possible to approach directly general Hamiltonians given in terms of bosonic creation and annihilation operators.

cond-mat.stat-mech↗

arXiv1998

Effective Hamiltonian with holomorphic variables

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian. In this work the PQSCHA is reformulated in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the olomorphic path integral for the Weyl symbol of the density matrix, makes it possible to directly approach general Hamiltonians given in terms of bosonic creation and annihilation operators.

cond-mat.stat-mech↗

arXiv1998

Effective Potential and Quantum Dynamical Correlators

The approach to the calculation of quantum dynamical correlation functions is presented in the framework of the Mori theory. An unified treatment of classic and quantum dynamics is given in terms of Weyl representation of operators and holomorphic variables. The range of validity of an approximate molucular dynamics is discussed

cond-mat.stat-mech↗

arXiv1996

Cohomological Properties of Differential Calculi on Hopf Algebras

In this report we give an intrinsic treatment of the results we developed in a previous work connecting the differential calculi on Hopf algebras to the Drinfeld double. In the first place we recover that bicovariant bimodules are in one to one correspondence with the Drinfeld double representations; we then introduce a Hochschild cohomology of the algebra of functions and discuss the main result stating that each differential calculus is associated to a 1-cocycle satisfying an additional invariance condition with respect to a natural action. Defining a Hochschild cohomology of the double, the above invariance becomes a condition with respect to the enveloping algebra component of the double that must be added to the 1-cocycle relation.

q-alg↗

arXiv1995

Quantum Double and Differential Calculi

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is connected to the existence of a particular (n+1)--dimensional representation of the double. An example of bicovariant differential calculus on the non quasitriangular quantum group E_q(2) is developed. The construction is studied in terms of Hochschild cohomology and a correspondence between differential calculi and 1-cocycles is proved. Some differences of calculi on quantum and finite groups with respect to Lie groups are stressed.

q-alg↗