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F. Ventriglia

Publications and source records attributed to F. Ventriglia.

32 records · Page 2Linked to original sources
arXiv2005

On the meaning and interpretation of Tomography in abstract Hilbert spaces

The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity decompositions in the Hilbert space of hermitian linear operators, with trace formula as scalar product of operators. Decompositions of identity are considered with respect to over-complete families of projectors labeled by extra parameters and containing a measure, depending on these parameters. It plays the role of a Gram-Schmidt orthonormalization kernel. When the measure is equal to one, the decomposition of identity coincides with a positive operator valued measure (POVM) decomposition. Examples of spin tomography, photon number tomography and symplectic tomography are reconsidered in this new framework.

quant-ph↗
arXiv2005

Alternative Algebraic Structures from Bi-Hamiltonian Quantum Systems

We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture in terms of deformations of the associative product on the space of observables.

quant-ph↗
arXiv2005

Tomograms in the Quantum-Classical transition

The quantum-classical limits for quantum tomograms are studied and compared with the corresponding classical tomograms, using two different definitions for the limit. One is the Planck limit where $\hbar \to 0$ in all $\hbar $-dependent physical observables, and the other is the Ehrenfest limit where $\hbar \to 0$ while keeping constant the mean value of the energy.The Ehrenfest limit of eigenstate tomograms for a particle in a box and a harmonic oscillatoris shown to agree with the corresponding classical tomograms of phase-space distributions, after a time averaging. The Planck limit of superposition state tomograms of the harmonic oscillator demostrating the decreasing contribution of interferences terms as $\hbar \to 0$.

quant-ph↗
arXiv2005

Alternative structures and bi-Hamiltonian systems on a Hilbert space

We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems.

math-ph↗
arXiv2003

Quantum Systems and Alternative Unitary Descriptions

Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We show how different invariant Hermitian scalar products give rise to different descriptions of a quantum system in the Ehrenfest and Heisenberg picture.

quant-ph↗
arXiv2003

Modelling of strain effects in manganite films

Thickness dependence and strain effects in films of $La_{1-x}A_xMnO_3$ perovskites are analyzed in the colossal magnetoresistance regime. The calculations are based on a generalization of a variational approach previously proposed for the study of manganite bulk. It is found that a reduction in the thickness of the film causes a decrease of critical temperature and magnetization, and an increase of resistivity at low temperatures. The strain is introduced through the modifications of in-plane and out-of-plane electron hopping amplitudes due to substrate-induced distortions of the film unit cell. The strain effects on the transition temperature and transport properties are in good agreement with experimental data only if the dependence of the hopping matrix elements on the $Mn-O-Mn$ bond angle is properly taken into account. Finally variations of the electron-phonon coupling linked to the presence of strain turn out important in influencing the balance of coexisting phases in the film

cond-mat.str-el↗
arXiv2003

Infrared conductivity of a one-dimensional charge-ordered state: quantum lattice effects

The optical properties of the charge-ordering ($CO$) phase of the one-dimensional (1D) half-filled spinless Holstein model are derived at zero temperature within a well-known variational approach improved including second-order lattice fluctuations. Within the $CO$ phase, the static lattice distortions give rise to the optical interband gap, that broadens as the strength of the electron-phonon ($el-ph$) interaction increases. The lattice fluctuation effects induce a long subgap tail in the infrared conductivity and a wide band above the gap energy. The first term is due to the multi-phonon emission by the charge carriers, the second to the interband transitions accompanied by the multi-phonon scattering. The results show a good agreement with experimental spectra.

cond-mat.str-el↗
arXiv2003

Infrared absorption of the charge-ordering phase: Lattice effects

The phase diagram of the half-filled spinless Holstein model for electrons interacting with quantum phonons is derived in three dimensions extending at finite temperature $T$ a variational approach introduced for the one-dimensional T=0 case. Employing the variational scheme, the spectral and optical properties of the system are evaluated in the different regimes that characterize the normal and ordered state. The effects of the charge-ordering ($CO$) induce a transfer of spectral weight from low to high energies in the conductivity spectra, as the temperature decreases or the strength of the electron-phonon ($el-ph$) interaction increases. The inclusion of effects of lattice fluctuations is able to smooth the inverse square-root singularity expected for the case of the mean-field approach and determines a subgap tail absorption. Moreover, in the weak to intermediate coupling regime, a two-component structure is obtained within the $CO$ phase at low frequency: the remnant Drude-like term and the incipient absorption band centered around the gap energy.

cond-mat.str-el↗
arXiv2002

Electron Double Refraction in Hybrid Systems with Rashba Spin-Orbit Coupling

We study the scattering of an electron in a definite state of spin at an interface of an hybrid system with a Rashba spin-orbit coupling on one side. Out of the normal incidence the double refraction phenomenon appears, with one or two limit angles for the total reflection. We show that this double refraction gives rise to a spin-dependent conductance of a Quantum Point Contact separating a ferromagnet and a two dimensional electron gas. The birefringence allows the spin filtering with a single interface.

cond-mat.mes-hall↗
arXiv2002

Alternative Structures and Bihamiltonian Systems

In the study of bi-Hamiltonian systems (both classical and quantum) one starts with a given dynamics and looks for all alternative Hamiltonian descriptions it admits.In this paper we start with two compatible Hermitian structures (the quantum analog of two compatible classical Poisson brackets) and look for all the dynamical systems which turn out to be bi-Hamiltonian with respect to them.

quant-ph↗
arXiv2002

On the effects of the magnetic field and the isotopic substitution upon the infrared absorption of manganites

Employing a variational approach that takes into account electron-phonon and magnetic interactions in $La_{1-x}A_xMnO_3$ perovskites with $0<x<0.5$, the effects of the magnetic field and the oxygen isotope substitution on the phase diagram, the electron-phonon correlation function and the infrared absorption at $x=0.3$ are studied. The lattice displacements show a strong correlation with the conductivity and the magnetic properties of the system. Then the conductivity spectra are characterized by a marked sensitivity to the external parameters near the phase boundary.

cond-mat.str-el↗
arXiv2001

Polaron and bipolaron formation in the Hubbard-Holstein model: role of next-nearest neighbor electron hopping

The influence of next-nearest neighbor electron hopping, $t^{\prime}$, on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of $t^{\prime}$ induces a strong anisotropy in the lattice distortions favoring the formation of nearest neighbor intersite bipolaron. The role of $t^{\prime}$, electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.

cond-mat.str-el↗