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Many machine learning models use the manipulation of dimensions as a driving force to enable models to identify and learn important features in data. In the case of sequential data this manipulation usually happens on the token dimension level. Despite the fact that many tasks require a change in sequence length itself, the step of sequence length reduction usually happens out of necessity and in a single step. As far as we are aware, no model uses the sequence length reduction step as an additional opportunity to tune the models performance. In fact, sequence length manipulation as a whole seems to be an overlooked direction. In this study we introduce a novel attention-based method that allows for the direct manipulation of sequence lengths. To explore the method's capabilities, we employ it in an autoencoder model. The autoencoder reduces the input sequence to a smaller sequence in latent space. It then aims to reproduce the original sequence from this reduced form. In this setting, we explore the methods reduction performance for different input and latent sequence lengths. We are able to show that the autoencoder retains all the significant information when reducing the original sequence to half its original size. When reducing down to as low as a quarter of its original size, the autoencoder is still able to reproduce the original sequence with an accuracy of around 90%., Comment: 8 pages, 5 images, 1 table

In a previous work I constructed R-negative scissors states in the Two-Rotors Model in which the rotors are two-sided classical bodies. Such states have |K| = 1; 0 components and negative space parity. Here I extend this work including reflections in a plane through the rotors symmetry axes obtaining also R-negative states of positive parity. I then associate reflections and R-operations with corresponding operations on internal noncollective variables of the rotors. I evaluate the em transition strengths of these states and compare them with the corresponding strengths of R-positive scissors modes., Comment: 6 pages; 0 figures

It is well known that diverse pieces of models and physical ideas coming from different areas of physics converged in the BCS theory of superconductivity. On the contrary it is little known that the formalism developed in the Tomonaga quantum field theory of the pion-nucleon system was an important ingredient for the development of BCS theory. We discuss the evolution of these ideas in quantum field theory providing an unconventional historical perspective., Comment: 8 pages, in Proceedings Int. Conf. Superstripes 2016, Ischia, Italy, July 23-29, 2016

The eigenfunctions of the Two-Rotors Model are superpositions of states corresponding to precessions of the rotors around two orthogonal axes. In Nuclear Physics such an entanglement has not been directly confirmed. We discuss how it might be observed and compare with the application of the TRM to single domain nanoparticles. In the latter case, in addition to the present indirect evidence there is the possibility of direct observation in experiments at temperatures of the order of 1 K., Comment: 11 pages, 2 figures

The occurrence of scissors modes in crystals that have deformed ions in their cells has been predicted some time ago. The theoretical value of their energy is rather uncertain, however, ranging between 10 and a few tenths of eV, with the corresponding widths of 10^-7, 10^-6 eV. Their observation by resonance fluorescence experiments therefore requires a photon spectrometer covering a wide energy range with a very high resolving power. We propose and discuss a new experiment in which such difficulties are overcome by measuring with a SQUID the variation of the magnetic field associated with the excitation of scissors modes., Comment: 8 pages, 2 figures

In previous investigations of the Two-Rotor Model with axially symmetric rotors the wave functions were assumed to be invariant under inversion of the axes of the rotors, which restricted the spectrum to positive parity states. We relax this condition requiring only that the wave functions be invariant under the square of the inversion operators. As a result we get positive as well as negative parity states that are all split by tunneling effect., Comment: 5 pages

We argue that for some species of magnetic nanoparticles the macrospin can have a nonvanishing moment of inertia and then an orbital angular momentum. We represent such nanoparticles by two interacting rigid rotors one of which has a large spin attached to the body, namely by a Two Rotor Model with spin. By this model we can describe in a unified way the cases of nanoparticles free and stuck in an elastic or rigid matrix. We evaluate the magnetic susceptibilities for the latter case and under some realistic assumptions we get results in closed form. A crossover between thermal and purely quantum hopping occurs at a temperature much larger than that at which purely quantum tunneling becomes important. A comparison with some experimental data is outlined., Comment: 5 pages, 2 figures

The Two-Rotor Model predicts two levels above the Scissors Modes with degenerate intrinsic energy. They have $J^{\pi}= 0^+,2^+$ and are referred to as overtones. Their energy is below threshold for nucleon emission, which should make them observable. The $J^{\pi}=0^+$ overtone, that has the structure of an isovector breathing mode, has vanishing $E0$ amplitude so that cannot be directly excited, but it could be reached in the decay of the $J=2^+$ overtone. We discuss such a process and evaluate the $B(E2)$ strength, which, however, turns out to be very small., Comment: 4 pages, no figure

In the absence of interaction it is well known that the Kogut-Susskind regularizations of fermions in the spin and flavor basis are equivalent to each other. In this paper we clarify the difference between the two formulations in the presence of interaction with gauge fields. We then derive an explicit expression of the transfer matrix in the spin basis by a unitary transformation on that one in the flavor basis which is known. The essential key ingredient is the explicit construction of the fermion Fock space for variables which live on blocks. Therefore the transfer matrix generates time translations of two lattice units., Comment: 16 pages

We assume that the most important quark correlations are pairwise at all baryon densities. We introduce correlated pairs by means of Bogoliubov transformations which are functions of time and spatial gauge fields, in the formalism of the transfer matrix with lattice regularization. The dependence on time and gauge fields allows us to enforce gauge invariance and other symmetries term by term in the transformed quantities. The resulting action should be suitable for the description of multiquark mesons and baryons as states of a quark and a diquark. We derive the quark contribution to the free energy at finite chemical potential in a certain approximation. Its expression cannot be evaluated analytically, but it has a definite sign., Comment: 36 pages

Scissors modes were predicted in the framework of the Two-Rotor Model. This model has an intrinsic harmonic spectrum, so that the level above the Scissors Mode, the first overtone, has excitation energy twice that of the Scissors Mode. Since the latter is of the order of 3 MeV in the rare earth region, the energy of the overtone is below threshold for nucleon emission, and its width should remain small enough for the overtone to be observable. We find that $B(E2)\uparrow_{overtone} = {3 /over 64 \theta_0^{2}}B(E2)\uparrow_{scissors}$, where $\theta_0$ is the zero-point oscillation amplitude, which in the rare earth region is of order $ 10^{-1}$., Comment: 5 pages, Rapid Communications

We have developed a method to derive the (approximate) quark contribution to the fermion free energy of QCD on a lattice, at finite temperature and chemical potential, with Kogut-Susskind fermions in the flavor basis. We show here the expression at zero temperature. This result has been obtained at the lowest order of the nilpotency expansion. At this order the well known "sign problem" does not arise and the quark contribution to the action can be used as a statistical weight in the Monte Carlo simulations., Comment: 7 pages, presented at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Sardinia, Italy, June 14-19, 2010

We apply to lattice QCD a bosonization method previously developed in which dynamical bosons are generated by time-dependent Bogoliubov transformations. The transformed action can be studied by an expansion in the inverse of the nilpotency index, which is the number of fermionic states in the structure function of composite bosons. When this number diverges the model is solved by the saddle point method which has a variational interpretation. We give a stationary covariant solution for a background matter field whose fluctuations describe mesons. In the saddle point approximations live fermionic quasiparticles with quark quantum numbers which are confined, in the sense that they propagate only in pointlike color singlets. Conditions for chiral symmetry breaking are determined, to be studied numerically, and a derivation of mesons-nucleons action is outlined., Comment: 33 pages

A recent experiment has questioned the standard relative value of spin-orbit and crystal-field strengths in rare-earth $4f$ electron systems, according to which the first should be one order of magnitude larger that the second. We find it difficult to reconcile the standard values of crystal field strength with the Single Ion Model of magnetic anisotropy. If in rare-earth systems the spin-orbit force is much larger than the crystal field, however, spin and orbit of $4f$ electrons should be locked to each other. For rare earths with non-vanishing spin, an applied magnetic field should rotate both spin and charge density profile. We suggest experiments to investigate the possible occurrence of such Spin-Orbit Locking, thus making a test of the standard picture, by studying the Scissors Modes in such systems., Comment: 8 pages, 3 figures

We recently suggested that the Scissors Mode (a collective excitation in which one system rotates with respect another one conserving its shape) can occur in crystals with axially symmetric atoms as a precession of these atoms around the anisotropy axis of their cells, giving rise to a form of dichroism. In the present paper we investigate how the Scissors Mode can be realized in crystals with cubic symmetry and evaluate its photo-absorption cross-section. This turns out to be of the same order of magnitude as that for crystals with axially symmetric atoms, but does not exhibit any correlation between the direction of the photon and the axes of the cell., Comment: 4 pages, 2 figures

In a recent study of the magnetic properties of rare-earth systems the two extreme situations have been considered in which the crystalline electrostatic field is large or small with respect to the spin-orbit interaction. In the first case the orbitals of localized electrons are firmly coupled to the lattice so that while an applied magnetic field rotates the spin, the charge profile remains fixed to the lattice. In the second case an applied magnetic field rotates both spin and density profile, even though through a very small angle. We show that in this second case we have, in addition to the use of photons or electrons, the possibility of exciting and observing the Scissors Mode in crystals in a way analogous to that used in Bose-Einstein Condensates., Comment: This paper has been withdrawn by the authors. It is replaced by arXiv:1004.2220

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian., Comment: 25 pages

Recently a new bosonization method has been used to derive, at zero fermion density, an effective action for relativistic field theories whose partition function is dominated by fermionic composites, chiral mesons in the case of QCD. This approach shares two important features with variational methods: the restriction to the subspace of the composites, and the determination of their structure functions by a variational calculation. But unlike standard variational methods it treats excited states at the same time and on the same footing as the ground state. I extend this method including states of nonvanishing fermion (baryon) number and derive an effective action for QCD at finite temperature and baryon density. I test the result on a four-fermion interaction model.

We apply a new bosonization technique to relativistic field theories of fermions whose partition function is dominated by bosonic composites, and derive the effective action for these bosons. The derivation respects all symmetries, including gauge invariance, with the exception of Euclidean invariance which must be checked a posteriori. We use a lattice regularization which should make applications to gauge theories easier. We test the method on a fermion field theory with quartic interaction in the limit when the number of flavours N_f is large, and show that it reproduces the exact results in the bosonic sector, namely condensation of a compositeboson with the right mass which breaks the discrete chiral invariance of the model. Moreover we determine the structure function of the condensed composite, whose spatial part turns out to be identical to that of the Cooper pairs of the BCS model of superconductivity., Comment: 34 pages, final version

I recently proposed a method of bosonization based on the use of coherent states of fermion composites, whose validity was restricted to smooth structure functions. In the present paper I remove this limitation and derive results which hold for arbitrary interactions and structure functions. The method respects all symmetries and in particular fermion number conservation. It reproduces exactly the results of the pairing model of atomic nuclei and of the BCS model of superconductivity in the number conserving form of the quasi-chemical equilibrium theory., Comment: 5 pages, no figure

We present a new method of bosonization of fermion systems applicable when the partition function is dominated by composite bosons. Restricting the partition function to such states we get an euclidean bosonic action from which we derive the Hamiltonian. Such a procedure respects all the fermion symmetries, in particular fermion number conservation, and provides a boson mapping of all fermion operators., Comment: 12 pages

We suggest that in an anisotropic crystal there should be a new mechanism of dichroism related to a scissors mode, a kind of excitation observed in several other many-body systems. Such an effect should be found in crystals, amorphous systems and also metallo-proteins. Its signature is a strong magnetic dipole transition amplitude, which is a function of the angle between the momentum of the photon and the anisotropy axis of the cell., Comment: 5 pages, 2 figures

Recently it has been found that in a noncompact formulation of the SU(2) gauge theory on a lattice the physical volume is larger than in the Wilson theory with the same number of sites. In its original formulation such noncompact regularization is directly applicable to U(N) theories for any N and to SU(N) theories for N=2 only. In this work we extend it to SU(N) for any N and investigate some of its properties., Comment: Lattice2001(improvement)

Recently it has been found that in a noncompact lattice regularization of the SU(2) gauge theory the physical volume is larger than in the Wilson theory with the same number of sites. In its original formulation the noncompact regularization is directly applicable to U(n) theories for any n and to SU(n) theories for n=2. In this paper we extend it to SU(n) for any n and investigate some of its properties., Comment: 14 pages

We evaluate the pion_0 into two gammas decay amplitude by an effective action derived from QCD in the quark composites approach, getting the standard value. We also verify that our effective action correctly reproduces the chiral anomaly., Comment: 17 LaTeX2e pages

The standard QCD action is improved by the addition of irrelevant operators built with chiral composites. An effective Lagrangian is derived in terms of auxiliary fields, which has the form of the phenomenological chiral Lagrangians. Our improved QCD action appears promising for numerical simulations as the pion physics is explicitely accounted for by the auxiliary fields., Comment: As presented at the Lattice 2000 Conference held in Bangalore

We investigate QCD at finite temperature in the quark composites approach, which is based on the use of quark composites with hadronic quantum numbers as fundamental variables. We find that chiral symmetry restoration and quark deconfinement are one and the same first order phase transition, whose critical temperature, in a one loop approximation, is $T= 2\sqrt{\Omega} \rho^{-2}m_{\pi}$, where $m_{\pi}$ is the pion mass, $\Omega=24$ the number of up and down quark components, and $\rho$ a parameter of order 1 whose precise value can be determined by the study of the pion-pion interaction., Comment: LaTex, 5 pages

We derive the pion-nucleon interaction in the framework of a new perturbative approach to QCD, based on the use of quark composites as fundamental variables. The composites with the quantum numbers of the nucleons are assumed as new integration variables in the Berezin integral which defines the partition function, while the composites with the quantum numbers of the chiral mesons are replaced by auxiliary bosonic fields. The action is modified by the addition of irrelevant operators which provide the kinetic terms for these composites, and the quark action is treated as a perturbation. The resulting expansion has the quark confinement built in. To first order we get the pion-nucleon interaction of the Yukawa model., Comment: published version

We present a perturbative approach to QCD based on quark composites, that is barions and mesons, as fundamental variables., Comment: 4 pages LaTeX, to appear in the proceedings of ``Path Integrals from peV to TeV'', Florence-Italy, August 25-29, 1998

A quadratic action in even Grassmann variables with the quantum numbers of the pions has been studied. It includes the $\sigma$-field in order to be invariant under SU(2)_L times SU(2)_R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined., Comment: Talk presented at Lattice '97 (Theoretical Developments), Edinburgh (UK), July 1997. LaTeX2e, 3 pages, uses espcrc2

In the framework of an approach to bosonization based on the use of fermionic composites as fundamental variables, a quadratic action in even Grassmann variables with the quantum numbers of the pions has been constructed. It includes the sigma-field in order to be invariant under SU(2)_L times SU(2)]_R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. A squared mass for the pions is generated according to PCAC. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined., Comment: 18 pages, accepted for publication on Nuclear Physics B