Modular quantum computing and quantum-like devices

The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and on the other hand, that such modules may be constructed out of classical systems obeying quantum-like equations where a space coordinate is the evolution parameter (thus playing the role of time in the quantum algorithms).

Supervariable and BRST Approaches to a Reparameterization Invariant Nonrelativistic System

We exploit the theoretical strength of the supervariable and Becchi-Rouet-Stora-Tyutin (BRST) formalisms to derive the proper (i.e., off-shell nilpotent and absolutely anticommuting) (anti-)BRST symmetry transformations for the reparameterization invariant model of a nonrelativistic (NR) free particle whose space x and time t variables are a function of an evolution parameter τ . The infinitesimal reparameterization (i.e., 1D diffeomorphism) symmetry transformation of our theory is defined w.r.t. this evolution parameter τ . We apply the modified Bonora-Tonin (BT) supervariable approach (MBTSA) as well as the (anti)chiral supervariable approach (ACSA) to BRST formalism to discuss various aspects of our present system. For this purpose, our 1D ordinary theory (parameterized by τ ) is generalized onto a 1 , 2 -dimensional supermanifold which is characterized by the superspace coordinates Z M = τ , θ , θ ¯ where a pair of the Grassmannian variables satisfy the fermionic relationships: θ 2 = θ ¯ 2 = 0 , θ θ ¯ + θ ¯ θ = 0 , and τ is the bosonic evolution parameter. In the context of ACSA, we take into account only the 1 , 1 -dimensional (anti)chiral super submanifolds of the general 1 , 2 -dimensional supermanifold. The derivation of the universal Curci-Ferrari- (CF-) type restriction, from various underlying theoretical methods, is a novel observation in our present endeavor. Furthermore, we note that the form of the gauge-fixing and Faddeev-Popov ghost terms for our NR and non-SUSY system is exactly the same as that of the reparameterization invariant SUSY (i.e., spinning) and non-SUSY (i.e., scalar) relativistic particles. This is a novel observation, too.

Modeling the spectrum and composition of ultrahigh-energy cosmic rays with two populations of extragalactic sources

We fit the ultrahigh-energy cosmic-ray (UHECR, $$E\gtrsim 0.1$$ E ≳ 0.1 EeV) spectrum and composition data from the Pierre Auger Observatory at energies $$E\gtrsim 5\cdot 10^{18}$$ E ≳ 5 · 10 18 eV, i.e., beyond the ankle using two populations of astrophysical sources. One population, accelerating dominantly protons ($$^1$$ 1 H), extends up to the highest observed energies with maximum energy close to the GZK cutoff and injection spectral index near the Fermi acceleration model; while another population accelerates light-to-heavy nuclei ($$^4$$ 4 He, $$^{14}$$ 14 N, $$^{28}$$ 28 Si, $$^{56}$$ 56 Fe) with a relatively low rigidity cutoff and hard injection spectrum. A significant improvement in the combined fit is noted as we go from a one-population to two-population model. For the latter, we constrain the maximum allowed proton fraction at the highest-energy bin within 3.5$$\sigma $$ σ statistical significance. In the single-population model, low-luminosity gamma-ray bursts turn out to match the best-fit evolution parameter. In the two-population model, the active galactic nuclei is consistent with the best-fit redshift evolution parameter of the pure proton-emitting sources, while the tidal disruption events could be responsible for emitting heavier nuclei. We also compute expected cosmogenic neutrino flux in such a hybrid source population scenario and discuss possibilities to detect these neutrinos by upcoming detectors to shed light on the sources of UHECRs.

Nilpotent charges of a toy model of Hodge theory and an 𝒩 = 2 SUSY quantum mechanical model: (Anti-)chiral supervariable approach

We derive the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for the system of a toy model of Hodge theory (i.e. a rigid rotor) by exploiting the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral supervariables that are defined on the appropriately chosen [Formula: see text]-dimensional super-submanifolds of the general [Formula: see text]-dimensional supermanifold on which our system of a one [Formula: see text]-dimensional (1D) toy model of Hodge theory is considered within the framework of the augmented version of the (anti-)chiral supervariable approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism. The general [Formula: see text]-dimensional supermanifold is parametrized by the superspace coordinates [Formula: see text], where [Formula: see text] is the bosonic evolution parameter and [Formula: see text] are the Grassmannian variables which obey the standard fermionic relationships: [Formula: see text], [Formula: see text]. We provide the geometrical interpretations for the symmetry invariance and nilpotency property. Furthermore, in our present endeavor, we establish the property of absolute anticommutativity of the conserved fermionic charges which is a completely novel and surprising observation in our present endeavor where we have considered only the (anti-)chiral supervariables. To corroborate the novelty of the above observation, we apply this ACSA to an [Formula: see text] SUSY quantum mechanical (QM) system of a free particle and show that the [Formula: see text] SUSY conserved and nilpotent charges do not absolutely anticommute.

Relativistic point particles in external fields

Motion of a point particle (a particle without any internal structure) in the context of special relativity is investigated. The study is based on the action principle with either time or the proper time regarded as the evolution parameter. Actions corresponding to the motion of particle in general external tensor fields are obtained.

If time is a local observable, then Hawking radiation is unitary

In the usual formulation of quantum theory, time is a global classical evolution parameter, not a local quantum observable. On the other hand, both canonical quantum gravity (which lacks fundamental time-evolution parameter) and the principle of spacetime covariance (which insists that time should be treated on an equal footing with space) suggest that quantum theory should be slightly reformulated, in a manner that promotes time to a local observable. Such a reformulated quantum theory is unitary in a more general sense than the usual quantum theory. In particular, this promotes the non-unitary Hawking radiation to a unitary phenomenon, which avoids the black-hole information paradox.