Fabio Scardigli

Politecnico di Milano, Milano, Lombardy, Italy

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Publications (32)24.87 Total impact

  • Source
    Fabio Scardigli, Roberto Casadio
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    ABSTRACT: We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.
    07/2014;
  • Petr Jizba, Fabio Scardigli
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    ABSTRACT: There is a theoretical evidence that relativistically invariant quantum dynamics at (enough) large space-time scales can result from a cooperative process of two inter-correlated non-relativistic stochastic dynamics, operating at different energy scales. We show that the Euclidean transition amplitude for a relativistic particle is identical to the transition probability of a Brownian particle propagating in a granular space. We discuss the issue of the robustness of the special-relativistic quantum mechanics thus obtained under small changes in the granular-space distribution. Experimental implications for early Universe cosmology are also briefly outlined.
    03/2014; 504(1).
  • Fabio Scardigli
    12/2013;
  • Source
    Roberto Casadio, Octavian Micu, Fabio Scardigli
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    ABSTRACT: We address the issue of (quantum) black hole formation by particle collision in quantum physics. We start by constructing the horizon wave-function for quantum mechanical states representing two highly boosted non-interacting particles that collide in a one-dimensional space. From this wave-function, we then derive a probability that the system becomes a black hole as a function of the initial momenta and spatial separation between the particles. This probability allows us to extend the hoop conjecture to quantum mechanics and estimate corrections to its classical counterpart.
    Physics Letters B. 11/2013; 732.
  • Source
    R. Casadio, F. Scardigli
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    ABSTRACT: A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. In order to combine these two pictures, we introduce a horizon wave-function determined by the particle wave-function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.
    06/2013;
  • Petr Jizba, Fabio Scardigli
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    ABSTRACT: We present a new theoretical evidence that a relativistically invariant quantum dynamics at large enough space-time scales can be derived from two inter-correlated genuinely non-relativistic stochastic processes that operate at different energy scales. This leads to Feynman amplitudes that are, in the Euclidean regime, identical to transition probability of a Brownian particle propagating through a granular space. Our observation implies a preferred frame and can have distinct experimental signatures. Ensuing implications for special and doubly-special relativity, quantum field theory, quantum gravity and cosmology are discussed.
    Journal of Physics Conference Series 06/2013; 442(1):2054-.
  • Source
    Petr Jizba, Fabio Scardigli
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    ABSTRACT: We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be held responsible for the emergence at larger scales of various symmetries. For illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed.
    European Physical Journal C 01/2013; 73(7). · 5.25 Impact Factor
  • Petr Jizba, Hagen Kleinert, Fabio Scardigli
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    ABSTRACT: We study uncertainty relations as formulated in a crystal-like universe, whose lattice spacing is of order of Planck length. For Planck energies, the uncertainty relation for position and momenta has a lower bound equal to zero. Connections of this result with double special relativity, and with't Hooft's deterministic quantization proposal, are briefly pointed out. We then apply our formulae to micro black holes, and we derive a new mass-temperature relation for Schwarzschild (micro) black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, we obtain both a finite Hawking's temperature and a zero rest-mass remnant at the end of the micro black hole evaporation.
    06/2012;
  • Source
    Petr Jizba, Fabio Scardigli
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    ABSTRACT: We show how a Brownian motion on a short scale can originate a relativistic motion on scales larger than the particle's Compton wavelength. Thus, Lorentz symmetry appears to be not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength, is taken. We also present the generalizations needed to accommodate in our scheme the doubly special relativistic dynamics. In this way, a previously unsuspected, common stochastic origin of the two frameworks is revealed for the first time. Issues such as generalized commutation relations are also discussed.
    Journal of Physics Conference Series 05/2012; 361(1):012026.
  • Fabio Scardigli, Christine Gruber, Pisin Chen
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    ABSTRACT: We consider the production of primordial micro black holes (MBH) remnants in the early universe. These objects induce the universe to be in a matter-dominated era before the onset of inflation. Effects of such an epoch on the CMB power spectrum are discussed and computed both analytically and numerically. By comparison with the latest observational data from the WMAP collaboration, we find that our model appears to explain the quadrupole anomaly of the CMB power spectrum.
    International Journal of Modern Physics Conference Series. 03/2012;
  • P Jizba, F Scardigli
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    ABSTRACT: Using the concept known as a superstatistics path integral we show that a Wiener process on a short spatial scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. We also present the modifications necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is revealed.
    Journal of Physics Conference Series 01/2012; 343(1).
  • Petr Jizba, Fabio Scardigli
    [Show abstract] [Hide abstract]
    ABSTRACT: Using the concept known as a superstatistics path integral we show that a Wiener process on a short spatial scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. Here we place a special emphasis on the modifications that are necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is revealed. Salient issues such as generalized commutation relations and a connection with Feynman chessboard model are also discussed.
    International Journal of Modern Physics B 01/2012; 26(12):41003-. · 0.46 Impact Factor
  • Source
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    ABSTRACT: In the framework of 't Hooft's "deterministic quantization" proposal, we show how to obtain from a composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be also interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region, the system can be described in terms of two irreducible elementary subsystems, corresponding to two independent quantum harmonic oscillators.
    Journal of Physics Conference Series 01/2012; 343(1).
  • Petr Jizba, Hagen Kleinert, Fabio Scardigli
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    ABSTRACT: We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of order of Planck length -- a "world crystal". For energies near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momentum does not pose any lower bound. We apply these results to micro black holes physics, where we derive a new mass-temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass-temperature formula predicts both a finite Hawking's temperature and a zero rest-mass remnant at the end of the black hole evaporation. We also briefly mention some connections of the world crystal paradigm with 't Hooft's quantization and double special relativity.
    11/2011;
  • Petr Jizba, Hagen Kleinert, Fabio Scardigli
    [Show abstract] [Hide abstract]
    ABSTRACT: We study uncertainty relations as formulated in a crystal-like universe, whose lattice spacing is of order of Planck length. For Planck energies, the uncertainty relation for position and momenta has a lower bound equal to zero. Connections of this result with double special relativity, and with 't Hooft's deterministic quantization proposal, are briefly pointed out. We then apply our formulae to micro black holes, and we derive a new mass-temperature relation for Schwarzschild (micro) black holes. In contrast to standard results based on Heisen-berg and stringy uncertainty relations, we obtain both a finite Hawking's temperature and a zero rest-mass remnant at the end of the micro black hole evaporation.
    Journal of Physics Conference Series 07/2011; 306(1):012026.
  • Source
    Petr Jizba, Fabio Scardigli
    [Show abstract] [Hide abstract]
    ABSTRACT: Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. This can be described in terms of polycrystalline vacuum. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. By analyzing the robustness of such a special relativity under small variations in the polycrystalline grain-size distribution we naturally arrive at the notion of doubly-special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as the role of gauge fixing in emergent relativity, generalized commutation relations, Hausdorff dimensions of representative path-integral trajectories and a connection with Feynman chessboard model are also discussed.
    Physical review D: Particles and fields 05/2011;
  • Petr Jizba, Hagen Kleinert, Fabio Scardigli
    [Show abstract] [Hide abstract]
    ABSTRACT: We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of order of Planck length --- a "world crystal". For energies near the border of the Brillouin zone, i.e. for Planckian energies, the uncertainty relation for position and momentum does not pose any lower bound. We apply these results to micro black holes physics, where we derive a new mass-temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass-temperature formula predicts both a finite Hawking's temperature and a zero rest-mass remnant at the end of the black hole evaporation.
    International Journal of Modern Physics D 01/2011; 20:2003-2007. · 1.03 Impact Factor
  • Source
    Fabio Scardigli, Christine Gruber, Pisin Chen
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider the production of primordial micro black holes (MBH) remnants in the early universe. These objects induce the universe to be in a matter-dominated era before the onset of inflation. Effects of such an epoch on the CMB power spectrum are discussed and computed both analytically and numerically. By comparison with the latest observational data from the WMAP collaboration, we find that our model is able to explain the quadrupole anomaly of the CMB power spectrum.
    Physical review D: Particles and fields 09/2010; 83(6).
  • Source
    Petr Jizba, Hagen Kleinert, Fabio Scardigli
    [Show abstract] [Hide abstract]
    ABSTRACT: We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of the order of Planck length -- "world crystal". In the particular case when energies lie near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momenta does not pose any lower bound on involved uncertainties. We apply our results to micro black holes physics, where we derive a new mass-temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass-temperature formula predicts both a finite Hawking's temperature and a zero rest-mass remnant at the end of the micro black hole evaporation. We also briefly mention some connections of the world crystal paradigm with 't Hooft's quantization and double special relativity. Comment: 13 pages, 2 figures, latex4
    Physical review D: Particles and fields 12/2009;
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper aims at the development of 't Hooft's quantization proposal to describe composite quantum mechanical systems. In particular, we show how 't Hooft's method can be utilized to obtain from two classical Bateman oscillators a composite quantum system corresponding to a quantum isotonic oscillator. For a suitable range of parameters, the composite system can be also interpreted as a particle in an effective magnetic field interacting through a spin-orbital interaction term. In the limit of a large separation from the interaction region we can identify the irreducible subsystems with two independent quantum oscillators.
    International Journal of Modern Physics A 07/2009; 24:3652-3659. · 1.13 Impact Factor

Publication Stats

318 Citations
24.87 Total Impact Points

Institutions

  • 2013
    • Politecnico di Milano
      Milano, Lombardy, Italy
  • 2005–2013
    • Kyoto University
      • Yukawa Institute for Theoretical Physics
      Kioto, Kyōto, Japan
  • 2012
    • Academia Sinica
      • Institute of Physics
      Taipei, Taipei, Taiwan
  • 2009–2011
    • National Taiwan University
      • • Department of Physics
      • • "Leung" Center for Cosmology and Particle Astrophysics
      Taipei, Taipei, Taiwan
  • 1999–2003
    • Universität Bern
      • Institute for Theoretical Physics
      Berna, Bern, Switzerland
    • University of Milan
      • Department of Physics
      Milano, Lombardy, Italy