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(2000 - 2018)
(2000 - 2018)
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Article 1 Read 1 Citation The solution of the sixth Hilbert problem: the ultimate Galilean revolution Published: 19 March 2018
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, doi: 10.1098/rsta.2017.0224
I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: ‘physics from no physics’. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann’s axioms for quantum theory), or contain physical primitives as ‘clock’, ‘rigid rod’, ‘force’, ‘inertial mass’ (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.
Article 2 Reads 2 Citations Quantum Walks, Weyl Equation and the Lorentz Group Published: 24 April 2017
Foundations of Physics, doi: 10.1007/s10701-017-0086-3
Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata and walks starting from very general principles. The intrinsic discreteness of this framework is reconciled with the continuous Lorentz symmetry by reformulating the notion of inertial reference frame in terms of the constants of motion of the quantum walk dynamics. In particular, among the symmetries of the quantum walk which recovers the Weyl equation—the so called Weyl walk—one finds a non linear realisation of the Poincaré group, which recovers the usual linear representation in the small wave-vector limit. In this paper we characterise the full symmetry group of the Weyl walk which is shown to be a non linear realization of a group which is the semidirect product of the Poincaré group and the group of dilations.
Article 3 Reads 12 Citations Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems Published: 07 June 2016
Physical Review Letters, doi: 10.1103/physrevlett.116.237201
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies. DOI:http://dx.doi.org/10.1103/PhysRevLett.116.237201 © 2016 American Physical Society
Article 1 Read 10 Citations Quantum cellular automaton theory of light Published: 01 May 2016
Annals of Physics, doi: 10.1016/j.aop.2016.02.009
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of quantum systems, without using space–time and mechanics (D’Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Article 1 Read 11 Citations Second law of thermodynamics under control restrictions Published: 22 April 2016
Physical Review E, doi: 10.1103/physreve.93.042126
The second law of thermodynamics, formulated as an ultimate bound on the maximum extractable work, has been rigorously derived in multiple scenarios. However, the unavoidable limitations that emerge due to the lack of control on small systems are often disregarded when deriving such bounds, which is specifically important in the context of quantum thermodynamics. Here we study the maximum extractable work with limited control over the working system and its interaction with the heat bath. We derive a general second law when the set of accessible Hamiltonians of the working system is arbitrarily restricted. We then apply our bound to particular scenarios that are important in realistic implementations: limitations on the maximum energy gap and local control over many-body systems. We hence demonstrate in what precise way the lack of control affects the second law. In particular, contrary to the unrestricted case, we show that the optimal work extraction is not achieved by simple thermal contacts. Our results not only generalize the second law to scenarios of practical relevance, but also take first steps in the direction of local thermodynamics. DOI:http://dx.doi.org/10.1103/PhysRevE.93.042126 ©2016 American Physical Society
Article 1 Read 4 Citations Quantum walks, deformed relativity and Hopf algebra symmetries Published: 18 April 2016
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, doi: 10.1098/rsta.2015.0232
We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014 Phys. Rev. A 90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras–the usual Poincaré and the κ-Poincaré algebras.