We present a study of the time decay of magnetic states in type-II superconductors. The mean esca... more We present a study of the time decay of magnetic states in type-II superconductors. The mean escape time of flux quanta from the pinning centers is calculated by considering the well-known washboard potential and a pinning potential appropriate to the case of pinning center dimensions l much larger than the coherence length ξ. We find that, in both cases, the attempt frequency in the Arrhenius formula depends on the current density J. Finally, by plotting the E(J) curves, we show that the dissipation due to flux creep mechanisms goes to zero much faster in the second case, where l ⪢ ξ is assumed.
ABSTRACT We introduce a set of phenomenological relations connecting characteristic quantities of... more ABSTRACT We introduce a set of phenomenological relations connecting characteristic quantities of large scale cosmological structures to the fundamental quantum scales of nucleons. The relations lead to predictions on the relevant mechanical and thermodynamical properties of galaxies, which are in excellent agreement with the experimentally observed data.
The algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-de... more The algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-deformation of the Weyl-Heisenberg algebra hq(1). The doubling of the degrees of freedom, the set of the tilde-conjugation rules, the Bogoliubov transformation and its generator have a direct and simple interpretation in terms of operators and of properties of hq(1). The notion of “thermal degree of freedom” introduced by Umezawa also finds a more specific formalization since the corresponding “thermal conjugate momentum” can be formally introduced, thus providing us with a set of canonical “thermal” variables.
In the past years a relcvant amount of information has been colleeted about the physical properti... more In the past years a relcvant amount of information has been colleeted about the physical properties of self-coupled Bose fields in two and three space-time dimensions, in the frame of the constructive approach to relativistic quantum field theory. The most interesting ...
ABSTRACT Introducing a description of the collective transverse dynamics of charged (proton) beam... more ABSTRACT Introducing a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations, we show that the transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.
We describe the transverse beam distribution in particle accelerators within the controlled, stoc... more We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of stochastic mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Schrödinger-like (SL) equation. The space charge effects have been introduced in recent papers by coupling this S-L equation with the Maxwell equations. We analyze the space-charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self-consistent solutions are related to the (external and space-charge) potentials both when we suppose that the external field is harmonic (constant focusing), and when we a priori prescribe the shape of the stationary solution. We then proceed to discuss a few other ideas by introducing generalized Student distributions, namely, non-Gaussian, Lévy infinitely divisible (but not stable) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Lévy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws and in the case (b) the discontinuities of the Lévy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.
We study the evolution of purity, entanglement, and total correlations of general two-mode contin... more We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.
We show how to recover all the features of the Euclidean-Markov structure for the vector-meson fi... more We show how to recover all the features of the Euclidean-Markov structure for the vector-meson field, starting from the stochastic quantization procedure.
A simple inequality relating the root mean square deviations of position and osmotic velocity for... more A simple inequality relating the root mean square deviations of position and osmotic velocity for a diffusion process is presented and, in the framework of Nelson's stochastic mechanics, is related to the Heisenberg position-momentum uncertainty relations.
It is shown that the characteristic observed radius, velocity, and temperature of a typical galax... more It is shown that the characteristic observed radius, velocity, and temperature of a typical galaxy can be inferred from Planck action constant through a phenomenological scaling law on all cosmological scales.
In the past years a relcvant amount of information has been colleeted about the physical properti... more In the past years a relcvant amount of information has been colleeted about the physical properties of self-coupled Bose fields in two and three space-time dimensions, in the frame of the constructive approach to relativistic quantum field theory. The most interesting ...
This work faces the problem of the origin of the logarithmic character of the Gompertzian growth.... more This work faces the problem of the origin of the logarithmic character of the Gompertzian growth. We show that the macroscopic, deterministic Gompertz equation describes the evolution from the initial state to the final stationary value of the median of a log-normally distributed, stochastic process. Moreover, by exploiting a stochastic variational principle, we account for self-regulating feature of Gompertzian growths
Spectral representations and recursive equations among Schwinger functions are exploited to obtai... more Spectral representations and recursive equations among Schwinger functions are exploited to obtain nonperturbative relations—spectral mass sum rules—involving mean values of spectral masses and physical parameters of the theory in interacting Fermi fields models. For the Yukawa model in two space-time dimensions, the finite part of the mass sum rule is extracted, and upper bounds (mean-field-like) on the average spectral mass and on the physical mass are obtained.
We present a study of the time decay of magnetic states in type-II superconductors. The mean esca... more We present a study of the time decay of magnetic states in type-II superconductors. The mean escape time of flux quanta from the pinning centers is calculated by considering the well-known washboard potential and a pinning potential appropriate to the case of pinning center dimensions l much larger than the coherence length ξ. We find that, in both cases, the attempt frequency in the Arrhenius formula depends on the current density J. Finally, by plotting the E(J) curves, we show that the dissipation due to flux creep mechanisms goes to zero much faster in the second case, where l ⪢ ξ is assumed.
ABSTRACT We introduce a set of phenomenological relations connecting characteristic quantities of... more ABSTRACT We introduce a set of phenomenological relations connecting characteristic quantities of large scale cosmological structures to the fundamental quantum scales of nucleons. The relations lead to predictions on the relevant mechanical and thermodynamical properties of galaxies, which are in excellent agreement with the experimentally observed data.
The algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-de... more The algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-deformation of the Weyl-Heisenberg algebra hq(1). The doubling of the degrees of freedom, the set of the tilde-conjugation rules, the Bogoliubov transformation and its generator have a direct and simple interpretation in terms of operators and of properties of hq(1). The notion of “thermal degree of freedom” introduced by Umezawa also finds a more specific formalization since the corresponding “thermal conjugate momentum” can be formally introduced, thus providing us with a set of canonical “thermal” variables.
In the past years a relcvant amount of information has been colleeted about the physical properti... more In the past years a relcvant amount of information has been colleeted about the physical properties of self-coupled Bose fields in two and three space-time dimensions, in the frame of the constructive approach to relativistic quantum field theory. The most interesting ...
ABSTRACT Introducing a description of the collective transverse dynamics of charged (proton) beam... more ABSTRACT Introducing a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations, we show that the transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.
We describe the transverse beam distribution in particle accelerators within the controlled, stoc... more We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of stochastic mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Schrödinger-like (SL) equation. The space charge effects have been introduced in recent papers by coupling this S-L equation with the Maxwell equations. We analyze the space-charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self-consistent solutions are related to the (external and space-charge) potentials both when we suppose that the external field is harmonic (constant focusing), and when we a priori prescribe the shape of the stationary solution. We then proceed to discuss a few other ideas by introducing generalized Student distributions, namely, non-Gaussian, Lévy infinitely divisible (but not stable) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Lévy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws and in the case (b) the discontinuities of the Lévy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.
We study the evolution of purity, entanglement, and total correlations of general two-mode contin... more We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.
We show how to recover all the features of the Euclidean-Markov structure for the vector-meson fi... more We show how to recover all the features of the Euclidean-Markov structure for the vector-meson field, starting from the stochastic quantization procedure.
A simple inequality relating the root mean square deviations of position and osmotic velocity for... more A simple inequality relating the root mean square deviations of position and osmotic velocity for a diffusion process is presented and, in the framework of Nelson's stochastic mechanics, is related to the Heisenberg position-momentum uncertainty relations.
It is shown that the characteristic observed radius, velocity, and temperature of a typical galax... more It is shown that the characteristic observed radius, velocity, and temperature of a typical galaxy can be inferred from Planck action constant through a phenomenological scaling law on all cosmological scales.
In the past years a relcvant amount of information has been colleeted about the physical properti... more In the past years a relcvant amount of information has been colleeted about the physical properties of self-coupled Bose fields in two and three space-time dimensions, in the frame of the constructive approach to relativistic quantum field theory. The most interesting ...
This work faces the problem of the origin of the logarithmic character of the Gompertzian growth.... more This work faces the problem of the origin of the logarithmic character of the Gompertzian growth. We show that the macroscopic, deterministic Gompertz equation describes the evolution from the initial state to the final stationary value of the median of a log-normally distributed, stochastic process. Moreover, by exploiting a stochastic variational principle, we account for self-regulating feature of Gompertzian growths
Spectral representations and recursive equations among Schwinger functions are exploited to obtai... more Spectral representations and recursive equations among Schwinger functions are exploited to obtain nonperturbative relations—spectral mass sum rules—involving mean values of spectral masses and physical parameters of the theory in interacting Fermi fields models. For the Yukawa model in two space-time dimensions, the finite part of the mass sum rule is extracted, and upper bounds (mean-field-like) on the average spectral mass and on the physical mass are obtained.
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Papers by Silvio Siena