No Country for Young Men even less for Women… Updated!

Here some interesting articles about what in Italy is called “La Fuga dei Cervelli” (Brains’ Escape). No, this is not the title of a new SF book, but a long standing phenomenon deeply affecting people with high educational level in Italy.

Article One: Non è un paese per giovani? Come uscire dall’impasse
Article Two: La Fuga dei talenti: «L’Italia? Un paese per vecchi gestito da vecchi»

Personally I don’t consider it a bad thing moving myself to an other country for living and work, and this is what I’m ready to do…
I think that our generation has the great oppoturnity of moving in other countries with a greater easiness than in the past, so we mustn’t miss it. But in Italy seems that the most of people look at youth moving in other countries for living as a sad thing and partially they are right. The sadness come from the fact Italy can’t (want not?) provide the right opportunities to young generations maybe because of lack of trust maybe because of fear of the change…

to be continued…

What business is it of yours where I'm from, f r i e n d o ?

THE CASA ABADINA GUARDIANS…

Great movies reviews here!

• Dipankara’s Blog

A Quote by Lao Tzu

Kindness in words creates confidence.
Kindness in thinking creates profoundness.
Kindness in giving creates love. - Lao Tzu

New Universities

I read the article written by Manuel Castels a Spanish sociologist, speaking about the Spain Universities and making some social considerations on the actual role of the University in the modern era and how it should be in a modern Country.
The article has been taken from the site of the “Internazionale” a popular Italian weekly magazine reporting articles taken from foreign journals and magazines.

Remembering Square Wells…

Quantum effects → must show an appreciable relative variation over a distance of the order of a wavelength.

Square Potentials → discontinuities of the first kind.

Schrödinger equation →

→ linear combination of imaginary exponentials:

 → linear combination of real exponentials:

The parameters of these combinations are fixed by the condition of continuity of the wavefunction and of its first derivative at the points of discontinuity of the potential.

Eingenfunction → solution bounded everywhere (at both and ).

Energy lower than the potential over the entire interval (; ) →No solutions

Molecular Nanomagnets

From D. Gatteschi, R. Sessoli, J. Villain book: Molecular Nanomagnets (2006)

The Spin Hamiltonian approach is widely used in various spectroscopies.

The Spin Hamiltonian approach eliminates all the orbital coordinates needed to describe the system and replaces them with spin coordinates, taking advantage of the symmetry properties of the system. An example of these approximations coming from the symmetry is the quencing of orbital angular momentum of the magnetic bricks.

The system with orbitally non-degenerate ground states are usually well treated with the Spin Hamiltonian approach.

Interaction (Intermediate) Representation

From A. Messiah’s Quantum Mechanics p.321 and 722 ff. , Dover (1999)

Any unitary transformation of the vectors and the observables of the Schrödinger (or Heisenberg) representations defines a new representation.

Any problem of quantum mechanics essentially consists of the determination of the properties of the unitary operator . *

In the intermediate representation, we suppose that the Hamiltonian can be put in the form:

where is the Hamiltonian of a Schrödinger equation whose solution is know.

Let be the evolution operator corresponding to . We obtain vectors and observables in the interaction representation by applying the unitary tranformation to the Schrödinger ones.

The evolution operator for the states in the intermediate representation is:

 

The time dependence of is determined by:

The vectors in the intermediate representation move in time satisfying the Schrödinger equation:

On the other hand, the physical quantities are represented by moving observables that are subject to the Heisenberg equation of motion written with the “unperturbed” Hamiltonian :

…

The evolution operator in the interaction representation is:

→

This Integral equation can be solved by iteration.

To fit with the introduction of the  C. Kittel’s book Quantum Theory of Solids and Abrikosov’s Methods of Quantum Field Theory in Statistical Physics, we note that, if is time independent and putting we have:

Macroscopic Quantum Tunneling & Coherence

E. M.Chudnovsky, L. Gunther – Quantum Tunneling of Magnetization in Small Ferromagnetic Particles. Phys. Rev. Lett. 60, 661 (1988)

Macroscopic Quantum Tunneling (MQT) correspond to the tunneling of a macroscopic variable trough the barrier between two minima of the effective potential of a macroscopic system.

We consider a small ferromagnetic particle enough small to form a single magnetic domain (→ Stoner-Wohlfarth model). Equilibrium easy directions of the magnetic moment correspond to the local minima of the energy:

Since  is an axial vector (aka pseudvector) any minimum of the energy  is at least twice degenerate with respect to two opposite directions of .

If the exchange interaction is so much strong to suppress the dynamics of the individual spins of the particle,  can be regarded as a single quantum variable.

The projection of  onto one of the easy directions in general does not commute with the energy , this means that the eigenvalues of the projection in general are not conserved quantum numbers even at  (this is not surprising because the magnetic anisotropy appears as a result of  relativistic interactions → Landau, Lifshitz – Electrodynamics of Continuous Media).

As consequence of the last statement, can tunnel between the energy minima.

Tunneling removes the degeneracy of the ground state and put the particle into a state of lower energy wherein  and . Angular brackets denote quantum average.

In presence of a magnetic field, the potential energy has, in general, one absolute minimum and several local minima so that the problem of MQT from metastable states arises.

The first reference to quantum tunneling of the magnetic moment was proposed as explanation of the experimental data indicating that transitions between different orientations of the magnetic moment in single domain nickel particles do not disappear completely with a decrease in temperature at absolute zero.

Macroscopic Quantum Coherence (experimental point of view)
For two successive measurements of separated by the time interval one should obtain the effect of macroscopic quantum coherence:

at , and neglecting dissipation. is the tunneling matrix element.

For both macroscopic quantum coherence and MQT the key quantity is the tunneling rate , which should be calculated in terms of the macroscopic parameters describing single-domain particles.

Ovrec’s Laboratory Rules

1. Don’t take any initiative if you are alone.
2. Perform laboratory work only when another person is present.
3. Be quiet!